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<html><head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta charset="utf-8">
<title>zad1</title>
<script type="text/javascript" src="zad1_files/MathJax.js" charset="utf-8"></script>
<script type="text/javascript">
// MathJax disabled, set as null to distingish from *missing* MathJax,
// where it will be undefined, and should prompt a dialog later.
window.mathjax_url = "mathjax/MathJax.js";
</script>
<link rel="stylesheet" href="zad1_files/jquery-wijmo.css" type="text/css">
<link rel="stylesheet" href="zad1_files/codemirror.css">
<link rel="stylesheet" href="zad1_files/markdown.css">
<link rel="stylesheet" href="zad1_files/rst.css">
<link rel="stylesheet" href="zad1_files/ipython.css">
<link rel="stylesheet" href="zad1_files/default.css">
<link rel="stylesheet" href="zad1_files/prettify.css">
<link rel="stylesheet" href="zad1_files/boilerplate.css" type="text/css">
<link rel="stylesheet" href="zad1_files/layout.css" type="text/css">
<link rel="stylesheet" href="zad1_files/base.css" type="text/css">
<link rel="stylesheet" href="zad1_files/notebook.css" type="text/css">
<link rel="stylesheet" href="zad1_files/renderedhtml.css" type="text/css">
<meta name="read_only" content="False">
<style type="text/css">#MathJax_Zoom {position: absolute; background-color: #F0F0F0; overflow: auto; display: block; z-index: 301; padding: .5em; border: 1px solid black; margin: 0; font-family: serif; font-size: 85%; font-weight: normal; font-style: normal; text-align: left; text-indent: 0; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; box-shadow: 5px 5px 15px #AAAAAA; -webkit-box-shadow: 5px 5px 15px #AAAAAA; -moz-box-shadow: 5px 5px 15px #AAAAAA; -khtml-box-shadow: 5px 5px 15px #AAAAAA; filter: progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')}
#MathJax_ZoomOverlay {position: absolute; left: 0; top: 0; z-index: 300; display: inline-block; width: 100%; height: 100%; border: 0; padding: 0; margin: 0; background-color: white; opacity: 0; filter: alpha(opacity=0)}
</style><style type="text/css">#MathJax_About {position: fixed; left: 50%; width: auto; text-align: center; border: 3px outset; padding: 1em 2em; background-color: #DDDDDD; cursor: default; font-family: message-box; font-size: 120%; font-style: normal; text-indent: 0; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; z-index: 201; border-radius: 15px; -webkit-border-radius: 15px; -moz-border-radius: 15px; -khtml-border-radius: 15px; box-shadow: 0px 10px 20px #808080; -webkit-box-shadow: 0px 10px 20px #808080; -moz-box-shadow: 0px 10px 20px #808080; -khtml-box-shadow: 0px 10px 20px #808080; filter: progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')}
.MathJax_Menu {position: absolute; background-color: white; color: black; width: auto; padding: 5px 0px; border: 1px solid #CCCCCC; margin: 0; cursor: default; font: menu; text-align: left; text-indent: 0; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; z-index: 201; border-radius: 5px; -webkit-border-radius: 5px; -moz-border-radius: 5px; -khtml-border-radius: 5px; box-shadow: 0px 10px 20px #808080; -webkit-box-shadow: 0px 10px 20px #808080; -moz-box-shadow: 0px 10px 20px #808080; -khtml-box-shadow: 0px 10px 20px #808080; filter: progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')}
.MathJax_MenuItem {padding: 1px 2em; background: transparent}
.MathJax_MenuTitle {background-color: #CCCCCC; margin: -5px 0 0 0; text-align: center; font-style: italic; font-size: 80%; color: #444444; padding: 2px 0; overflow: hidden}
.MathJax_MenuArrow {position: absolute; right: .5em; color: #666666}
.MathJax_MenuActive .MathJax_MenuArrow {color: white}
.MathJax_MenuCheck {position: absolute; left: .7em}
.MathJax_MenuRadioCheck {position: absolute; left: .7em}
.MathJax_MenuLabel {padding: 1px 2em 3px 1.33em; font-style: italic}
.MathJax_MenuRule {border-top: 1px solid #DDDDDD; margin: 4px 3px}
.MathJax_MenuDisabled {color: GrayText}
.MathJax_MenuActive {background-color: #606872; color: white}
</style><style type="text/css">#MathJax_Message {position: fixed; left: 1px; bottom: 2px; background-color: #E6E6E6; border: 1px solid #959595; margin: 0px; padding: 2px 8px; z-index: 102; color: black; font-size: 80%; width: auto; white-space: nowrap}
#MathJax_MSIE_Frame {position: absolute; top: 0; left: 0; width: 0px; z-index: 101; border: 0px; margin: 0px; padding: 0px}
.MathJax_Error {color: #CC0000; font-style: italic}
</style><style type="text/css">@media print { body { overflow: visible !important; } }.ui-widget-content { border: 0px; }</style><style type="text/css">#MathJax_Zoom {position: absolute; background-color: #F0F0F0; overflow: auto; display: block; z-index: 301; padding: .5em; border: 1px solid black; margin: 0; font-family: serif; font-size: 85%; font-weight: normal; font-style: normal; text-align: left; text-indent: 0; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; box-shadow: 5px 5px 15px #AAAAAA; -webkit-box-shadow: 5px 5px 15px #AAAAAA; -moz-box-shadow: 5px 5px 15px #AAAAAA; -khtml-box-shadow: 5px 5px 15px #AAAAAA; filter: progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')}
#MathJax_ZoomOverlay {position: absolute; left: 0; top: 0; z-index: 300; display: inline-block; width: 100%; height: 100%; border: 0; padding: 0; margin: 0; background-color: white; opacity: 0; filter: alpha(opacity=0)}
</style><style type="text/css">#MathJax_About {position: fixed; left: 50%; width: auto; text-align: center; border: 3px outset; padding: 1em 2em; background-color: #DDDDDD; cursor: default; font-family: message-box; font-size: 120%; font-style: normal; text-indent: 0; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; z-index: 201; border-radius: 15px; -webkit-border-radius: 15px; -moz-border-radius: 15px; -khtml-border-radius: 15px; box-shadow: 0px 10px 20px #808080; -webkit-box-shadow: 0px 10px 20px #808080; -moz-box-shadow: 0px 10px 20px #808080; -khtml-box-shadow: 0px 10px 20px #808080; filter: progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')}
.MathJax_Menu {position: absolute; background-color: white; color: black; width: auto; padding: 5px 0px; border: 1px solid #CCCCCC; margin: 0; cursor: default; font: menu; text-align: left; text-indent: 0; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; z-index: 201; border-radius: 5px; -webkit-border-radius: 5px; -moz-border-radius: 5px; -khtml-border-radius: 5px; box-shadow: 0px 10px 20px #808080; -webkit-box-shadow: 0px 10px 20px #808080; -moz-box-shadow: 0px 10px 20px #808080; -khtml-box-shadow: 0px 10px 20px #808080; filter: progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')}
.MathJax_MenuItem {padding: 1px 2em; background: transparent}
.MathJax_MenuTitle {background-color: #CCCCCC; margin: -5px 0 0 0; text-align: center; font-style: italic; font-size: 80%; color: #444444; padding: 2px 0; overflow: hidden}
.MathJax_MenuArrow {position: absolute; right: .5em; color: #666666}
.MathJax_MenuActive .MathJax_MenuArrow {color: white}
.MathJax_MenuCheck {position: absolute; left: .7em}
.MathJax_MenuRadioCheck {position: absolute; left: .7em}
.MathJax_MenuLabel {padding: 1px 2em 3px 1.33em; font-style: italic}
.MathJax_MenuRule {border-top: 1px solid #DDDDDD; margin: 4px 3px}
.MathJax_MenuDisabled {color: GrayText}
.MathJax_MenuActive {background-color: #606872; color: white}
</style><style type="text/css">#MathJax_Message {position: fixed; left: 1px; bottom: 2px; background-color: #E6E6E6; border: 1px solid #959595; margin: 0px; padding: 2px 8px; z-index: 102; color: black; font-size: 80%; width: auto; white-space: nowrap}
#MathJax_MSIE_Frame {position: absolute; top: 0; left: 0; width: 0px; z-index: 101; border: 0px; margin: 0px; padding: 0px}
.MathJax_Error {color: #CC0000; font-style: italic}
</style></head><body style="overflow: auto;"><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 3px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre>x</pre></div><div style="position: relative"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative" draggable="true"><pre class="CodeMirror-cursor"> </pre><div></div></div></div></div></div></div></div></div><div tabindex="-1" class="text_cell_render rendered_html"><h1><headingcell level="1"></headingcell></h1>
<h1>Zadaća 1 - diskretne strukture s teorijom brojeva</h1></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 1px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre>x</pre></div><div style="position: relative"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative" draggable="true"><pre class="CodeMirror-cursor"> </pre><div></div></div></div></div></div></div></div></div><div tabindex="-1" class="text_cell_render rendered_html"><p>Učitavanje pomoćne biblioteke za "ljepši ispis brojeva" [ naredba ispis() ]</p></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [1]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 261px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 30px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span><span class="cm-keyword">from</span><span class="cm-null"> </span><span class="cm-variable">pomocne_metode</span><span class="cm-null"> </span><span class="cm-keyword">import</span><span class="cm-null"> </span><span class="cm-operator">*</span><span class="cm-null">;</span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 261px; visibility: hidden;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-keyword">from</span><span class="cm-null"> </span><span class="cm-variable">pomocne_metode</span><span class="cm-null"> </span><span class="cm-keyword">import</span><span class="cm-null"> </span><span class="cm-operator">*</span><span class="cm-null">;</span></pre></div></div></div></div></div></div></div></div></div><div style="display: none;" class="output vbox"></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 30px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>Učitavanje svih zadataka 1-9 iz jedne datoteke</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-null">Učitavanje svih zadataka 1-9 iz jedne datoteke</span></pre></div></div></div></div></div></div></div></div><div style="display: block;" tabindex="-1" class="text_cell_render rendered_html"><p>Učitavanje svih zadataka 1-9 iz jedne datoteke</p></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [2]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 153px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 30px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span><span class="cm-keyword">from</span><span class="cm-null"> </span><span class="cm-variable">sve</span><span class="cm-null"> </span><span class="cm-keyword">import</span><span class="cm-null"> </span><span class="cm-operator">*</span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 153px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-keyword">from</span><span class="cm-null"> </span><span class="cm-variable">sve</span><span class="cm-null"> </span><span class="cm-keyword">import</span><span class="cm-null"> </span><span class="cm-operator">*</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 30px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>Učitavanje svih brojeva iz datoteka u riječnike broj {} i prim {}</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-null">Učitavanje svih brojeva iz datoteka u riječnike broj {} i prim {}</span></pre></div></div></div></div></div></div></div></div><div style="display: block;" tabindex="-1" class="text_cell_render rendered_html"><p>Učitavanje svih brojeva iz datoteka u riječnike broj {} i prim {}</p></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [3]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 276px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span> dat=open("testni_brojevi/broj"+str(i)+".txt")</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-variable">broj</span><span class="cm-null">={}</span></pre><pre><span class="cm-keyword">for</span><span class="cm-null"> </span><span class="cm-variable">i</span><span class="cm-null"> </span><span class="cm-operator">in</span><span class="cm-null"> </span><span class="cm-variable">range</span><span class="cm-null">(</span><span class="cm-number">1</span><span class="cm-null">,</span><span class="cm-number">9</span><span class="cm-null">):</span></pre><pre><span class="cm-null"> </span><span class="cm-variable">dat</span><span class="cm-null">=</span><span class="cm-variable">open</span><span class="cm-null">(</span><span class="cm-string">"testni_brojevi/broj"</span><span class="cm-operator">+</span><span class="cm-builtin">str</span><span class="cm-null">(</span><span class="cm-variable">i</span><span class="cm-null">)</span><span class="cm-operator">+</span><span class="cm-string">".txt"</span><span class="cm-null">)</span></pre><pre><span class="cm-null"> </span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-variable">i</span><span class="cm-null">]=</span><span class="cm-builtin">int</span><span class="cm-null">(</span><span class="cm-variable">dat.read</span><span class="cm-null">())</span></pre><pre><span class="cm-null"> </span><span class="cm-variable">dat.close</span><span class="cm-null">()</span></pre><pre><span class="cm-null"> </span><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"\nBroj"</span><span class="cm-null">,</span><span class="cm-variable">i</span><span class="cm-null">,</span><span class="cm-string">":"</span></pre><pre><span class="cm-null"> </span><span class="cm-variable">ispis</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-variable">i</span><span class="cm-null">],</span><span class="cm-number">120</span><span class="cm-null">)</span></pre><pre><span class="cm-variable">prirodni</span><span class="cm-null">={}</span></pre><pre><span class="cm-keyword">for</span><span class="cm-null"> </span><span class="cm-variable">i</span><span class="cm-null"> </span><span class="cm-operator">in</span><span class="cm-null"> </span><span class="cm-variable">range</span><span class="cm-null">(</span><span class="cm-number">1</span><span class="cm-null">,</span><span class="cm-number">3</span><span class="cm-null">):</span></pre><pre><span class="cm-null"> </span><span class="cm-variable">dat</span><span class="cm-null">=</span><span class="cm-variable">open</span><span class="cm-null">(</span><span class="cm-string">"testni_brojevi/P"</span><span class="cm-operator">+</span><span class="cm-builtin">str</span><span class="cm-null">(</span><span class="cm-variable">i</span><span class="cm-null">)</span><span class="cm-operator">+</span><span class="cm-string">".txt"</span><span class="cm-null">)</span></pre><pre><span class="cm-null"> </span><span class="cm-variable">prirodni</span><span class="cm-null">[</span><span class="cm-variable">i</span><span class="cm-null">]=</span><span class="cm-builtin">int</span><span class="cm-null">(</span><span class="cm-variable">dat.read</span><span class="cm-null">())</span></pre><pre><span class="cm-null"> </span><span class="cm-variable">dat.close</span><span class="cm-null">()</span></pre><pre><span class="cm-null"> </span><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"\nPrirodni broj"</span><span class="cm-null">,</span><span class="cm-variable">i</span><span class="cm-null">,</span><span class="cm-string">":"</span></pre><pre><span class="cm-null"> </span><span class="cm-variable">ispis</span><span class="cm-null">(</span><span class="cm-variable">prirodni</span><span class="cm-null">[</span><span class="cm-variable">i</span><span class="cm-null">],</span><span class="cm-number">120</span><span class="cm-null">)</span></pre><pre> </pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>Broj 1 :
16491972357
Broj 2 :
74252994229
Broj 3 :
11588211132896623
Broj 4 :
5037198379880902775509
Broj 5 :
157185313392988000551911896400170592487677012994370713978929029923429401550082475447984786746452639138991004211140190061\
322888036069093891668715744150496017420418219740831771727623037319682153393
Broj 6 :
160669557356118187788117507750653516765161469361581396791900868927560360519376495164385264059109836314601358402026154049\
362533325988448523184884813611090484079472410875681562815635868149134080614215931198737538338243874798708554231253709155\
371023031078097727330353537783
Broj 7 :
160842859157712627185412199007652574983291749367673360248010477348538138925249133427334011551919271567778861491287264570\
674198879198588557423506434313619407292846159837534016725864335234196553503714121098404491301453289544324660212970999516\
0310513462513839573710638482030571210068201
Broj 8 :
385132038563169217435067576285371753039092537553088979481280814480799756146394774792734017277945707638984276896761255932\
097138647480268020580014893831938305680089735383561906178035773819614077936090365506756128316837714897271140559632786565\
984399680926277018761264270802091712228247949818899330344281134125551390534466580840193435655500679577782744501459586227\
223981377572707646312515999
Prirodni broj 1 :
344563975893181784831939618614186817325329569509663067243991475416744211925328024442890815492086972659515839375983714733\
863014269516324014400617156282231481210385535561553370650830273418610809943200210604056519158826545418459033775935334392\
71928526067763429496448150117276833594446863632109641941627491249235882339404373225948839135854099741607213
Prirodni broj 2 :
618918778336154774216861198928982219334565904314238592972041939671681907905085039186658761336019169778142688283726784707\
039184085984040957524678863097537499605371139819267962214566771628824475500946906431567899409728135894658093621364380223\
418604440761320023960993804693517966326614564054095145924428385811771678642249646900478323860602108947778427467359336611\
51517891723802296574115997203364654236627418562565428565504384750523961420396693212696808419
</pre></div></div></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 7px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre>x</pre></div><div style="position: relative"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative" draggable="true"><pre class="CodeMirror-cursor"> </pre><div></div></div></div></div></div></div></div></div><div tabindex="-1" class="text_cell_render rendered_html"><h1><headingcell level="2"></headingcell></h1>
<h1>Zadatak 10 - testiranje zadataka 2-9 na testnim brojevima</h1>
<h1><headingcell level="3"></headingcell></h1>
<h1>Zadatak 2 - ispitivanje prostosti</h1></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [4]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=provjeraProstosti(broj[1])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px; visibility: hidden;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">provjeraProstosti</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">1</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: 3
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [5]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=provjeraProstosti(broj[2])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">provjeraProstosti</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">2</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: 2347
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [6]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=provjeraProstosti(broj[3])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">provjeraProstosti</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">3</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.06 s, sys: 0.00 s, total: 0.06 s
Wall time: 0.06 s
Rezultat: 434683
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [7]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=provjeraProstosti(broj[4])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">provjeraProstosti</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">4</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.12 s, sys: 0.00 s, total: 0.12 s
Wall time: 0.13 s
Rezultat: 434683
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [8]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 17.5px; left: 180px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">re</span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 17.5px; left: 180px; visibility: hidden;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">provjeraProstosti</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">5</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text"><pre><span class="ansired">---------------------------------------------------------------------------</span>
<span class="ansired">KeyboardInterrupt</span> Traceback (most recent call last)
<span class="ansigreen">/home/ori/Desktop/notebook/<ipython-input-8-520b853a4592></span> in <span class="ansicyan"><module></span><span class="ansiblue">()</span>
<span class="ansigreen">----> 1</span><span class="ansired"> </span>get_ipython<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">.</span>magic<span class="ansiblue">(</span><span class="ansiblue">u'time rez=provjeraProstosti(broj[5])'</span><span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen"> 2</span> <span class="ansigreen">print</span> <span class="ansiblue">"Rezultat:"</span><span class="ansiblue">,</span>rez<span class="ansiblue"></span>
<span class="ansigreen">/usr/lib/python2.7/dist-packages/IPython/core/interactiveshell.pyc</span> in <span class="ansicyan">magic</span><span class="ansiblue">(self, arg_s, next_input)</span>
<span class="ansigreen"> 1983</span> self<span class="ansiblue">.</span>_magic_locals <span class="ansiblue">=</span> sys<span class="ansiblue">.</span>_getframe<span class="ansiblue">(</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">.</span>f_locals<span class="ansiblue"></span>
<span class="ansigreen"> 1984</span> <span class="ansigreen">with</span> self<span class="ansiblue">.</span>builtin_trap<span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">-> 1985</span><span class="ansired"> </span>result <span class="ansiblue">=</span> fn<span class="ansiblue">(</span>magic_args<span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen"> 1986</span> <span class="ansired"># Ensure we're not keeping object references around:</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 1987</span> self<span class="ansiblue">.</span>_magic_locals <span class="ansiblue">=</span> <span class="ansiblue">{</span><span class="ansiblue">}</span><span class="ansiblue"></span>
<span class="ansigreen">/usr/lib/python2.7/dist-packages/IPython/core/magic.pyc</span> in <span class="ansicyan">magic_time</span><span class="ansiblue">(self, parameter_s)</span>
<span class="ansigreen"> 2023</span> <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen"> 2024</span> st <span class="ansiblue">=</span> clk<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen">-> 2025</span><span class="ansired"> </span><span class="ansigreen">exec</span> code <span class="ansigreen">in</span> glob<span class="ansiblue">,</span> locs<span class="ansiblue"></span>
<span class="ansigreen"> 2026</span> end <span class="ansiblue">=</span> clk<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen"> 2027</span> out <span class="ansiblue">=</span> None<span class="ansiblue"></span>
<span class="ansigreen">/home/ori/Desktop/notebook/<timed exec></span> in <span class="ansicyan"><module></span><span class="ansiblue">()</span>
<span class="ansigreen">/home/ori/Desktop/notebook/sve.pyc</span> in <span class="ansicyan">provjeraProstosti</span><span class="ansiblue">(n)</span>
<span class="ansigreen"> 57</span> <span class="ansigreen">if</span> n <span class="ansiblue">%</span> i <span class="ansiblue">==</span> <span class="ansicyan">0</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen"> 58</span> <span class="ansigreen">return</span> i<span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen">---> 59</span><span class="ansired"> </span>i<span class="ansiblue">+=</span><span class="ansicyan">1</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 60</span> <span class="ansigreen">return</span> <span class="ansicyan">1</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 61</span> <span class="ansired">##</span>
<span class="ansiblue"></span>
<span class="ansired">KeyboardInterrupt</span>:
</pre></div></div></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 5px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre>x</pre></div><div style="position: relative"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative" draggable="true"><pre class="CodeMirror-cursor"> </pre><div></div></div></div></div></div></div></div></div><div tabindex="-1" class="text_cell_render rendered_html"><p>Zbog
toga što na broju 5 funkcija već oduzima previše vremena nema smisla
testirati da li će u razumnom vremenu dati dobre rezultate na većim
brojevima broj 6, 7 i 8</p>
<p><headingcell level="3"></headingcell></p>
<p>Zadatak 3 - ispitivanje prostosti Miller-Rabinovim testom</p></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [9]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 153px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">millerR</span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 153px; visibility: hidden;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">millerRab</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">1</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: False
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [10]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=millerRab(broj[2])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">millerRab</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">2</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: False
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [11]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=millerRab(broj[3])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">millerRab</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">3</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: False
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [12]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=millerRab(broj[4])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">millerRab</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">4</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: False
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [13]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=millerRab(broj[5])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">millerRab</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">5</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: False
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [14]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=millerRab(broj[6])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">millerRab</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">6</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.01 s
Rezultat: False
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [15]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=millerRab(broj[7])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">millerRab</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">7</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.01 s
Rezultat: False
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [16]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=millerRab(broj[8])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">millerRab</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">8</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s
Wall time: 0.02 s
Rezultat: False
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [17]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">mill</span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">millerRab</span><span class="cm-null">(</span><span class="cm-variable">prirodni</span><span class="cm-null">[</span><span class="cm-number">1</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.01 s
Rezultat: False
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [18]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 65px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=millerRab(prirodni[2])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">millerRab</span><span class="cm-null">(</span><span class="cm-variable">prirodni</span><span class="cm-null">[</span><span class="cm-number">2</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre><pre> </pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.40 s, sys: 0.00 s, total: 0.40 s
Wall time: 0.42 s
Rezultat: True
</pre></div></div></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 65px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span># Zadatak 4 - Fermatova metoda faktorizacije</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-null"># </span><span class="cm-tag"><headingcell</span><span class="cm-null"> </span><span class="cm-attribute">level</span><span class="cm-null">=</span><span class="cm-string">3</span><span class="cm-tag">></span></pre><pre> </pre><pre><span class="cm-null"># Zadatak 4 - Fermatova metoda faktorizacije</span></pre></div></div></div></div></div></div></div></div><div style="display: block;" tabindex="-1" class="text_cell_render rendered_html"><h1><headingcell level="3"></headingcell></h1>
<h1>Zadatak 4 - Fermatova metoda faktorizacije</h1></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [19]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=fermat(broj[1])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">fermat</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">1</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: (128909, 127935)
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [20]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=fermat(broj[2])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">fermat</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">2</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: (273223, 271767)
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [21]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=fermat(broj[3])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">fermat</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">3</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: (107655291, 107641817)
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [22]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=fermat(broj[4])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">fermat</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">4</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: (70973286258, 70973159698)
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [23]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=fermat(broj[5])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">fermat</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">5</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: (12537356714754031459208241722151213659225431522303927468258166926231879758423094745898070165787881L, 12537356714754031459208241722151213659225431522299498882652997761246923424591009735381752874938895L)
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [24]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=fermat(broj[7])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">fermat</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">7</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: (1268238381211168940647889786810581373809535976675770575036711367480491524725624665711336708930513961356031487354959394545817717789759179230179L, 1268238381211168940647889786810581373809535976675770575036711367480491423998731287183318467071024525191343254837947014068337384825970743715525L)
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [25]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=fermat(broj[8])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px; visibility: hidden;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">fermat</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">8</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: (19624781236058893133922527560249348205081760323874903599091349190905117929597961357743784559126869245064261866136378436096220773234180843452201664414250871025746117147389268382742853928446896327L, 19624781236058893133922527560249348205081760323874903599091349190905117929597961357743784559126861143875113280662335862812769308572194347934053271351063249091919446761323764866495316762130442493L)
</pre></div></div></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 82px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>Zadatak 5 - Pollardova p metoda</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre class=""> </pre><pre><span class="cm-tag"><headingcell</span><span class="cm-null"> </span><span class="cm-attribute">level</span><span class="cm-null">=</span><span class="cm-string">3</span><span class="cm-tag">></span></pre><pre> </pre><pre><span class="cm-null">Zadatak 5 - Pollardova p metoda</span></pre></div></div></div></div></div></div></div></div><div style="display: block;" tabindex="-1" class="text_cell_render rendered_html"><p><headingcell level="3"></headingcell></p>
<p>Zadatak 5 - Pollardova p metoda</p></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [26]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 17.5px; left: 189px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 17.5px; left: 189px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">1</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: 153
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [27]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=pollard(broj[2])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">2</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: 2351
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [28]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=pollard(broj[3])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">3</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: 434683
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [29]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=pollard(broj[4])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">4</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: 434683
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [30]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=pollard(broj[5])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">5</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.16 s, sys: 0.00 s, total: 0.16 s
Wall time: 0.17 s
Rezultat: 123458201
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [31]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=pollard(broj[6])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">6</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.74 s, sys: 0.00 s, total: 0.75 s
Wall time: 0.76 s
Rezultat: 9345234109
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [32]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=pollard(broj[7])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">7</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 5.18 s, sys: 0.00 s, total: 5.18 s
Wall time: 5.23 s
Rezultat: 19223456827
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [33]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=pollard(broj[8])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">8</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 7.96 s, sys: 0.00 s, total: 7.97 s
Wall time: 8.01 s
Rezultat: 19223456827
</pre></div></div></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 82px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span># Zadatak 6 - Modificirana Pollardova p metoda</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre> </pre><pre><span class="cm-null"># </span><span class="cm-tag"><headingcell</span><span class="cm-null"> </span><span class="cm-attribute">level</span><span class="cm-null">=</span><span class="cm-string">3</span><span class="cm-tag">></span></pre><pre> </pre><pre><span class="cm-null"># Zadatak 6 - Modificirana Pollardova p metoda</span></pre></div></div></div></div></div></div></div></div><div style="display: block;" tabindex="-1" class="text_cell_render rendered_html"><h1><headingcell level="3"></headingcell></h1>
<h1>Zadatak 6 - Modificirana Pollardova p metoda</h1></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [34]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=improvedPollard(broj[1])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">improvedPollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">1</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: 7026831
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [35]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=improvedPollard(broj[2])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">improvedPollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">2</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: 5517797
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [36]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=improvedPollard(broj[3])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">improvedPollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">3</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: 434683
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [37]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=improvedPollard(broj[4])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">improvedPollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">4</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: 434683
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [38]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=improvedPollard(broj[5])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">improvedPollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">5</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.12 s, sys: 0.00 s, total: 0.12 s
Wall time: 0.13 s
Rezultat: 123458201
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [39]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=improvedPollard(broj[6])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">improvedPollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">6</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 1.40 s, sys: 0.00 s, total: 1.41 s
Wall time: 1.49 s
Rezultat: 9345232087
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [40]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=improvedPollard(broj[7])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">improvedPollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">7</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 3.21 s, sys: 0.00 s, total: 3.21 s
Wall time: 3.31 s
Rezultat: 9223456793
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [41]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=improvedPollard(broj[8])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">improvedPollard</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">8</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 3.83 s, sys: 0.00 s, total: 3.83 s
Wall time: 3.99 s
Rezultat: 19223456827
</pre></div></div></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 82px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span># Zadatak 7 - Modificirana Pollard ro -1 metoda</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre> </pre><pre><span class="cm-null"># </span><span class="cm-tag"><headingcell</span><span class="cm-null"> </span><span class="cm-attribute">level</span><span class="cm-null">=</span><span class="cm-string">3</span><span class="cm-tag">></span></pre><pre> </pre><pre><span class="cm-null"># Zadatak 7 - Modificirana Pollard ro -1 metoda</span></pre></div></div></div></div></div></div></div></div><div style="display: block;" tabindex="-1" class="text_cell_render rendered_html"><h1><headingcell level="3"></headingcell></h1>
<h1>Zadatak 7 - Modificirana Pollard ro -1 metoda</h1></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [42]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 63px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">r</span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 63px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollardRo1</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">1</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: (3, 5497324119)
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [43]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=pollardRo1(broj[2])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollardRo1</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">2</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: (2351, 31583579)
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [44]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=pollardRo1(broj[3])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollardRo1</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">3</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 2.44 s, sys: 0.01 s, total: 2.45 s
Wall time: 2.59 s
Rezultat: (434683, 26658993181)
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [45]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=pollardRo1(broj[4])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollardRo1</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">4</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 2.72 s, sys: 0.00 s, total: 2.72 s
Wall time: 2.87 s
Rezultat: (434683, 11588211132896623)
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [46]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 261px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollardRo1</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">5</span><span class="cm-null">])</span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 261px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">pollardRo1</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">5</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text"><pre><span class="ansired">---------------------------------------------------------------------------</span>
<span class="ansired">KeyboardInterrupt</span> Traceback (most recent call last)
<span class="ansigreen">/home/ori/Desktop/notebook/<ipython-input-46-5d68c9e77789></span> in <span class="ansicyan"><module></span><span class="ansiblue">()</span>
<span class="ansigreen">----> 1</span><span class="ansired"> </span>get_ipython<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">.</span>magic<span class="ansiblue">(</span><span class="ansiblue">u'time rez=pollardRo1(broj[5])'</span><span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen"> 2</span> <span class="ansigreen">print</span> <span class="ansiblue">"Rezultat:"</span><span class="ansiblue">,</span>rez<span class="ansiblue"></span>
<span class="ansigreen">/usr/lib/python2.7/dist-packages/IPython/core/interactiveshell.pyc</span> in <span class="ansicyan">magic</span><span class="ansiblue">(self, arg_s, next_input)</span>
<span class="ansigreen"> 1983</span> self<span class="ansiblue">.</span>_magic_locals <span class="ansiblue">=</span> sys<span class="ansiblue">.</span>_getframe<span class="ansiblue">(</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">.</span>f_locals<span class="ansiblue"></span>
<span class="ansigreen"> 1984</span> <span class="ansigreen">with</span> self<span class="ansiblue">.</span>builtin_trap<span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">-> 1985</span><span class="ansired"> </span>result <span class="ansiblue">=</span> fn<span class="ansiblue">(</span>magic_args<span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen"> 1986</span> <span class="ansired"># Ensure we're not keeping object references around:</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 1987</span> self<span class="ansiblue">.</span>_magic_locals <span class="ansiblue">=</span> <span class="ansiblue">{</span><span class="ansiblue">}</span><span class="ansiblue"></span>
<span class="ansigreen">/usr/lib/python2.7/dist-packages/IPython/core/magic.pyc</span> in <span class="ansicyan">magic_time</span><span class="ansiblue">(self, parameter_s)</span>
<span class="ansigreen"> 2023</span> <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen"> 2024</span> st <span class="ansiblue">=</span> clk<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen">-> 2025</span><span class="ansired"> </span><span class="ansigreen">exec</span> code <span class="ansigreen">in</span> glob<span class="ansiblue">,</span> locs<span class="ansiblue"></span>
<span class="ansigreen"> 2026</span> end <span class="ansiblue">=</span> clk<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen"> 2027</span> out <span class="ansiblue">=</span> None<span class="ansiblue"></span>
<span class="ansigreen">/home/ori/Desktop/notebook/<timed exec></span> in <span class="ansicyan"><module></span><span class="ansiblue">()</span>
<span class="ansigreen">/home/ori/Desktop/notebook/sve.pyc</span> in <span class="ansicyan">pollardRo1</span><span class="ansiblue">(n, k, zastavica)</span>
<span class="ansigreen"> 252</span> <span class="ansigreen">while</span> i<span class="ansiblue"><</span>k<span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen"> 253</span> i<span class="ansiblue">+=</span><span class="ansicyan">1</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen">--> 254</span><span class="ansired"> </span>x<span class="ansiblue">=</span>pow<span class="ansiblue">(</span>a<span class="ansiblue">,</span>i<span class="ansiblue">,</span>n<span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen"> 255</span> <span class="ansiblue"></span>
<span class="ansigreen"> 256</span> r<span class="ansiblue">=</span>gcd<span class="ansiblue">(</span>x<span class="ansiblue">-</span><span class="ansicyan">1</span><span class="ansiblue">,</span>n<span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansired">KeyboardInterrupt</span>:
</pre></div></div></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 5px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre>x</pre></div><div style="position: relative"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative" draggable="true"><pre class="CodeMirror-cursor"> </pre><div></div></div></div></div></div></div></div></div><div tabindex="-1" class="text_cell_render rendered_html"><p>Kao
što je očekivano, ova metoda je korisna za pronalazak manjih prostih
faktora, pošto brojevi 5-8 imaju veće proste faktore, funkciju nije
efikasno iskorištavati na njima.</p>
<p><headingcell level="3"></headingcell></p>
<p>Zadatak 8 - Faktorizacija malih brojeva iz skupa N</p></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [47]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 17.5px; left: 126px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezulta</span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 17.5px; left: 126px; visibility: hidden;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktorizacija</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">1</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: {2347: 1, 17: 1, 3: 10, 7: 1}
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [48]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=faktorizacija(broj[2])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px; visibility: hidden;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktorizacija</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">2</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: {13457: 1, 2347: 1, 2351: 1}
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [49]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 17.5px; left: 189px; display: none; visibility: hidden;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator CodeMirror-selected">%</span><span class="cm-variable CodeMirror-selected">time</span><span class="cm-null CodeMirror-selected"> </span><span class="cm-variable CodeMirror-selected">rez</span><span class="cm-null CodeMirror-selected">=</span><span class="cm-variable CodeMirror-selected">faktorizacija</span><span class="cm-null CodeMirror-selected">(</span><span class="cm-variable CodeMirror-selected">broj</span><span class="cm-null CodeMirror-selected">[</span><span class="cm-number CodeMirror-selected">3</span><span class="cm-null CodeMirror-selected">])</span><span class="CodeMirror-selected"> </span></pre><pre><span class="cm-keyword CodeMirror-selected">print</span><span class="cm-null CodeMirror-selected"> </span><span class="cm-string CodeMirror-selected">"Rezultat:"</span><span class="cm-null CodeMirror-selected">,</span><span class="cm-variable CodeMirror-selected">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text"><pre><span class="ansired">---------------------------------------------------------------------------</span>
<span class="ansired">KeyboardInterrupt</span> Traceback (most recent call last)
<span class="ansigreen">/home/ori/Desktop/notebook/<ipython-input-49-2fee6b03b1ab></span> in <span class="ansicyan"><module></span><span class="ansiblue">()</span>
<span class="ansigreen">----> 1</span><span class="ansired"> </span>get_ipython<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">.</span>magic<span class="ansiblue">(</span><span class="ansiblue">u'time rez=faktorizacija(broj[3])'</span><span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen"> 2</span> <span class="ansigreen">print</span> <span class="ansiblue">"Rezultat:"</span><span class="ansiblue">,</span>rez<span class="ansiblue"></span>
<span class="ansigreen">/usr/lib/python2.7/dist-packages/IPython/core/interactiveshell.pyc</span> in <span class="ansicyan">magic</span><span class="ansiblue">(self, arg_s, next_input)</span>
<span class="ansigreen"> 1983</span> self<span class="ansiblue">.</span>_magic_locals <span class="ansiblue">=</span> sys<span class="ansiblue">.</span>_getframe<span class="ansiblue">(</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">.</span>f_locals<span class="ansiblue"></span>
<span class="ansigreen"> 1984</span> <span class="ansigreen">with</span> self<span class="ansiblue">.</span>builtin_trap<span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">-> 1985</span><span class="ansired"> </span>result <span class="ansiblue">=</span> fn<span class="ansiblue">(</span>magic_args<span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen"> 1986</span> <span class="ansired"># Ensure we're not keeping object references around:</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 1987</span> self<span class="ansiblue">.</span>_magic_locals <span class="ansiblue">=</span> <span class="ansiblue">{</span><span class="ansiblue">}</span><span class="ansiblue"></span>
<span class="ansigreen">/usr/lib/python2.7/dist-packages/IPython/core/magic.pyc</span> in <span class="ansicyan">magic_time</span><span class="ansiblue">(self, parameter_s)</span>
<span class="ansigreen"> 2023</span> <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen"> 2024</span> st <span class="ansiblue">=</span> clk<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen">-> 2025</span><span class="ansired"> </span><span class="ansigreen">exec</span> code <span class="ansigreen">in</span> glob<span class="ansiblue">,</span> locs<span class="ansiblue"></span>
<span class="ansigreen"> 2026</span> end <span class="ansiblue">=</span> clk<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen"> 2027</span> out <span class="ansiblue">=</span> None<span class="ansiblue"></span>
<span class="ansigreen">/home/ori/Desktop/notebook/<timed exec></span> in <span class="ansicyan"><module></span><span class="ansiblue">()</span>
<span class="ansigreen">/home/ori/Desktop/notebook/sve.pyc</span> in <span class="ansicyan">faktorizacija</span><span class="ansiblue">(n)</span>
<span class="ansigreen"> 276</span> brojac <span class="ansiblue">=</span> <span class="ansicyan">1</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 277</span> <span class="ansigreen">while</span> i <span class="ansiblue"><=</span> n<span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">--> 278</span><span class="ansired"> </span><span class="ansigreen">if</span> n <span class="ansiblue">%</span> i <span class="ansiblue">==</span> <span class="ansicyan">0</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen"> 279</span> n <span class="ansiblue">/=</span> i<span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 280</span> <span class="ansigreen">if</span> faktori<span class="ansiblue">.</span>has_key<span class="ansiblue">(</span>i<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansired">KeyboardInterrupt</span>:
</pre></div></div></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 5px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre>x</pre></div><div style="position: relative"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative" draggable="true"><pre class="CodeMirror-cursor"> </pre><div></div></div></div></div></div></div></div></div><div tabindex="-1" class="text_cell_render rendered_html"><p>Nažalost,
algoritam ne daje dobre rezultate s većim brojevima zato što je
predviđen za brz pronalazak faktora kod manjih brojeva, pa brojevi 3-8
ne daju dobre vremenske rezultate.</p>
<p><headingcell level="3"></headingcell></p>
<p>Zadatak 9 - Faktorizacija brojeva iz skupa N</p></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [51]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 153px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktori</span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 153px; visibility: hidden;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktorizacijaAlgoritam</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">1</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s
Wall time: 0.09 s
Rezultat: {2347: 1, mpz(17): 1, 3: 10, 7: 1}
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [52]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=faktorizacijaAlgoritam(broj[2])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktorizacijaAlgoritam</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">2</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: {13457: 1, mpz(2347): 1, 2351: 1}
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [53]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=faktorizacijaAlgoritam(broj[3])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktorizacijaAlgoritam</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">3</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
Rezultat: {mpz(434683): 1, mpz(26658993181): 1}
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [54]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=faktorizacijaAlgoritam(broj[4])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktorizacijaAlgoritam</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">4</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.01 s
Rezultat: {mpz(434683): 2, mpz(26658993181): 1}
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [55]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=faktorizacijaAlgoritam(broj[5])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktorizacijaAlgoritam</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">5</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.13 s, sys: 0.00 s, total: 0.13 s
Wall time: 0.14 s
Rezultat: {mpz(123456937): 15, mpz(123458201): 9}
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [56]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=faktorizacijaAlgoritam(broj[6])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktorizacijaAlgoritam</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">6</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 2.78 s, sys: 0.00 s, total: 2.79 s
Wall time: 2.83 s
Rezultat: {mpz(9345234109): 12, mpz(9345232087): 15}
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [57]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=faktorizacijaAlgoritam(broj[7])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktorizacijaAlgoritam</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">7</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 4.91 s, sys: 0.00 s, total: 4.91 s
Wall time: 4.99 s
Rezultat: {mpz(9223456793): 18, mpz(19223456827): 10}
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [58]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 65px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span>%time rez=faktorizacijaAlgoritam(broj[8])</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktorizacijaAlgoritam</span><span class="cm-null">(</span><span class="cm-variable">broj</span><span class="cm-null">[</span><span class="cm-number">8</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre><pre> </pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 9.92 s, sys: 0.01 s, total: 9.93 s
Wall time: 10.02 s
Rezultat: {mpz(19223456827): 10, mpz(889223456813): 10, mpz(89223456799): 15}
</pre></div></div></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 65px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span># Zadatak 11 - testiranje dva prirodna broja na prostost i faktorizacija</span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 0px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-null"># </span><span class="cm-tag"><headingcell</span><span class="cm-null"> </span><span class="cm-attribute">level</span><span class="cm-null">=</span><span class="cm-string">2</span><span class="cm-tag">></span></pre><pre> </pre><pre><span class="cm-null"># Zadatak 11 - testiranje dva prirodna broja na prostost i faktorizacija</span></pre></div></div></div></div></div></div></div></div><div style="display: block;" tabindex="-1" class="text_cell_render rendered_html"><h1><headingcell level="2"></headingcell></h1>
<h1>Zadatak 11 - testiranje dva prirodna broja na prostost i faktorizacija</h1></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 1px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre>x</pre></div><div style="position: relative"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative" draggable="true"><pre class="CodeMirror-cursor"> </pre><div></div></div></div></div></div></div></div></div><div tabindex="-1" class="text_cell_render rendered_html"><p>U slučaju da je prirodni broj prost, ispisati ga, a ako nije pokušati pronaći njegovu faktorizaciju na proste brojeve.</p></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox ui-widget-content ui-corner-all"><div class="input hbox"><div class="prompt input_prompt">In [60]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 369px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktorizacijaAlgoritam</span><span class="cm-null">(</span><span class="cm-variable">prirodn</span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 0px; left: 369px; visibility: hidden;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktorizacijaAlgoritam</span><span class="cm-null">(</span><span class="cm-variable">prirodni</span><span class="cm-null">[</span><span class="cm-number">1</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text"><pre><span class="ansired">---------------------------------------------------------------------------</span>
<span class="ansired">KeyboardInterrupt</span> Traceback (most recent call last)
<span class="ansigreen">/home/ori/Desktop/notebook/<ipython-input-60-502d010751c2></span> in <span class="ansicyan"><module></span><span class="ansiblue">()</span>
<span class="ansigreen">----> 1</span><span class="ansired"> </span>get_ipython<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">.</span>magic<span class="ansiblue">(</span><span class="ansiblue">u'time rez=faktorizacijaAlgoritam(prirodni[1])'</span><span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen"> 2</span> <span class="ansigreen">print</span> <span class="ansiblue">"Rezultat:"</span><span class="ansiblue">,</span>rez<span class="ansiblue"></span>
<span class="ansigreen">/usr/lib/python2.7/dist-packages/IPython/core/interactiveshell.pyc</span> in <span class="ansicyan">magic</span><span class="ansiblue">(self, arg_s, next_input)</span>
<span class="ansigreen"> 1983</span> self<span class="ansiblue">.</span>_magic_locals <span class="ansiblue">=</span> sys<span class="ansiblue">.</span>_getframe<span class="ansiblue">(</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">.</span>f_locals<span class="ansiblue"></span>
<span class="ansigreen"> 1984</span> <span class="ansigreen">with</span> self<span class="ansiblue">.</span>builtin_trap<span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">-> 1985</span><span class="ansired"> </span>result <span class="ansiblue">=</span> fn<span class="ansiblue">(</span>magic_args<span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen"> 1986</span> <span class="ansired"># Ensure we're not keeping object references around:</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 1987</span> self<span class="ansiblue">.</span>_magic_locals <span class="ansiblue">=</span> <span class="ansiblue">{</span><span class="ansiblue">}</span><span class="ansiblue"></span>
<span class="ansigreen">/usr/lib/python2.7/dist-packages/IPython/core/magic.pyc</span> in <span class="ansicyan">magic_time</span><span class="ansiblue">(self, parameter_s)</span>
<span class="ansigreen"> 2023</span> <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen"> 2024</span> st <span class="ansiblue">=</span> clk<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen">-> 2025</span><span class="ansired"> </span><span class="ansigreen">exec</span> code <span class="ansigreen">in</span> glob<span class="ansiblue">,</span> locs<span class="ansiblue"></span>
<span class="ansigreen"> 2026</span> end <span class="ansiblue">=</span> clk<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
<span class="ansigreen"> 2027</span> out <span class="ansiblue">=</span> None<span class="ansiblue"></span>
<span class="ansigreen">/home/ori/Desktop/notebook/<timed exec></span> in <span class="ansicyan"><module></span><span class="ansiblue">()</span>
<span class="ansigreen">/home/ori/Desktop/notebook/sve.pyc</span> in <span class="ansicyan">faktorizacijaAlgoritam</span><span class="ansiblue">(n)</span>
<span class="ansigreen"> 305</span> <span class="ansigreen">if</span><span class="ansiblue">(</span>millerRab<span class="ansiblue">(</span>n<span class="ansiblue">)</span><span class="ansiblue">==</span>False<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen"> 306</span> <span class="ansired">#izracunaj jedan faktor</span>
<span class="ansiblue"></span>
<span class="ansigreen">--> 307</span><span class="ansired"> </span>broj<span class="ansiblue">=</span>improvedPollard<span class="ansiblue">(</span>n<span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 308</span> <span class="ansired">#trazi faktor dok ne bude prost broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 309</span> <span class="ansigreen">while</span><span class="ansiblue">(</span>millerRab<span class="ansiblue">(</span>broj<span class="ansiblue">)</span><span class="ansiblue">==</span>False<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">/home/ori/Desktop/notebook/sve.pyc</span> in <span class="ansicyan">improvedPollard</span><span class="ansiblue">(broj, c, counter, zastavica)</span>
<span class="ansigreen"> 195</span> <span class="ansired">#ako je korak>1 a jos nije nasao broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 196</span> <span class="ansigreen">if</span><span class="ansiblue">(</span><span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span> <span class="ansigreen">and</span> c<span class="ansiblue">==</span><span class="ansiblue">-</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> korak<span class="ansiblue">></span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">--> 197</span><span class="ansired"> </span>d<span class="ansiblue">=</span>improvedPollard<span class="ansiblue">(</span>broj<span class="ansiblue">,</span>c<span class="ansiblue">,</span>korak<span class="ansiblue">/</span><span class="ansicyan">2</span><span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 198</span> <span class="ansired">#ako je korak 1 a nije nasao broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 199</span> <span class="ansigreen">elif</span><span class="ansiblue">(</span><span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span> <span class="ansigreen">and</span> c<span class="ansiblue">==</span><span class="ansiblue">-</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> korak<span class="ansiblue">==</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">/home/ori/Desktop/notebook/sve.pyc</span> in <span class="ansicyan">improvedPollard</span><span class="ansiblue">(broj, c, counter, zastavica)</span>
<span class="ansigreen"> 195</span> <span class="ansired">#ako je korak>1 a jos nije nasao broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 196</span> <span class="ansigreen">if</span><span class="ansiblue">(</span><span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span> <span class="ansigreen">and</span> c<span class="ansiblue">==</span><span class="ansiblue">-</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> korak<span class="ansiblue">></span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">--> 197</span><span class="ansired"> </span>d<span class="ansiblue">=</span>improvedPollard<span class="ansiblue">(</span>broj<span class="ansiblue">,</span>c<span class="ansiblue">,</span>korak<span class="ansiblue">/</span><span class="ansicyan">2</span><span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 198</span> <span class="ansired">#ako je korak 1 a nije nasao broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 199</span> <span class="ansigreen">elif</span><span class="ansiblue">(</span><span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span> <span class="ansigreen">and</span> c<span class="ansiblue">==</span><span class="ansiblue">-</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> korak<span class="ansiblue">==</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">/home/ori/Desktop/notebook/sve.pyc</span> in <span class="ansicyan">improvedPollard</span><span class="ansiblue">(broj, c, counter, zastavica)</span>
<span class="ansigreen"> 195</span> <span class="ansired">#ako je korak>1 a jos nije nasao broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 196</span> <span class="ansigreen">if</span><span class="ansiblue">(</span><span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span> <span class="ansigreen">and</span> c<span class="ansiblue">==</span><span class="ansiblue">-</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> korak<span class="ansiblue">></span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">--> 197</span><span class="ansired"> </span>d<span class="ansiblue">=</span>improvedPollard<span class="ansiblue">(</span>broj<span class="ansiblue">,</span>c<span class="ansiblue">,</span>korak<span class="ansiblue">/</span><span class="ansicyan">2</span><span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 198</span> <span class="ansired">#ako je korak 1 a nije nasao broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 199</span> <span class="ansigreen">elif</span><span class="ansiblue">(</span><span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span> <span class="ansigreen">and</span> c<span class="ansiblue">==</span><span class="ansiblue">-</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> korak<span class="ansiblue">==</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">/home/ori/Desktop/notebook/sve.pyc</span> in <span class="ansicyan">improvedPollard</span><span class="ansiblue">(broj, c, counter, zastavica)</span>
<span class="ansigreen"> 195</span> <span class="ansired">#ako je korak>1 a jos nije nasao broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 196</span> <span class="ansigreen">if</span><span class="ansiblue">(</span><span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span> <span class="ansigreen">and</span> c<span class="ansiblue">==</span><span class="ansiblue">-</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> korak<span class="ansiblue">></span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">--> 197</span><span class="ansired"> </span>d<span class="ansiblue">=</span>improvedPollard<span class="ansiblue">(</span>broj<span class="ansiblue">,</span>c<span class="ansiblue">,</span>korak<span class="ansiblue">/</span><span class="ansicyan">2</span><span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 198</span> <span class="ansired">#ako je korak 1 a nije nasao broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 199</span> <span class="ansigreen">elif</span><span class="ansiblue">(</span><span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span> <span class="ansigreen">and</span> c<span class="ansiblue">==</span><span class="ansiblue">-</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> korak<span class="ansiblue">==</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">/home/ori/Desktop/notebook/sve.pyc</span> in <span class="ansicyan">improvedPollard</span><span class="ansiblue">(broj, c, counter, zastavica)</span>
<span class="ansigreen"> 195</span> <span class="ansired">#ako je korak>1 a jos nije nasao broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 196</span> <span class="ansigreen">if</span><span class="ansiblue">(</span><span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span> <span class="ansigreen">and</span> c<span class="ansiblue">==</span><span class="ansiblue">-</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> korak<span class="ansiblue">></span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">--> 197</span><span class="ansired"> </span>d<span class="ansiblue">=</span>improvedPollard<span class="ansiblue">(</span>broj<span class="ansiblue">,</span>c<span class="ansiblue">,</span>korak<span class="ansiblue">/</span><span class="ansicyan">2</span><span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 198</span> <span class="ansired">#ako je korak 1 a nije nasao broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 199</span> <span class="ansigreen">elif</span><span class="ansiblue">(</span><span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span> <span class="ansigreen">and</span> c<span class="ansiblue">==</span><span class="ansiblue">-</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> korak<span class="ansiblue">==</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">/home/ori/Desktop/notebook/sve.pyc</span> in <span class="ansicyan">improvedPollard</span><span class="ansiblue">(broj, c, counter, zastavica)</span>
<span class="ansigreen"> 195</span> <span class="ansired">#ako je korak>1 a jos nije nasao broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 196</span> <span class="ansigreen">if</span><span class="ansiblue">(</span><span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span> <span class="ansigreen">and</span> c<span class="ansiblue">==</span><span class="ansiblue">-</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> korak<span class="ansiblue">></span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">--> 197</span><span class="ansired"> </span>d<span class="ansiblue">=</span>improvedPollard<span class="ansiblue">(</span>broj<span class="ansiblue">,</span>c<span class="ansiblue">,</span>korak<span class="ansiblue">/</span><span class="ansicyan">2</span><span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 198</span> <span class="ansired">#ako je korak 1 a nije nasao broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 199</span> <span class="ansigreen">elif</span><span class="ansiblue">(</span><span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span> <span class="ansigreen">and</span> c<span class="ansiblue">==</span><span class="ansiblue">-</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> korak<span class="ansiblue">==</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">/home/ori/Desktop/notebook/sve.pyc</span> in <span class="ansicyan">improvedPollard</span><span class="ansiblue">(broj, c, counter, zastavica)</span>
<span class="ansigreen"> 199</span> <span class="ansigreen">elif</span><span class="ansiblue">(</span><span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span> <span class="ansigreen">and</span> c<span class="ansiblue">==</span><span class="ansiblue">-</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> korak<span class="ansiblue">==</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen"> 200</span> c <span class="ansiblue">=</span> random<span class="ansiblue">.</span>randint<span class="ansiblue">(</span><span class="ansicyan">1</span><span class="ansiblue">,</span> broj<span class="ansiblue">-</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen">--> 201</span><span class="ansired"> </span>d<span class="ansiblue">=</span>improvedPollard<span class="ansiblue">(</span>broj<span class="ansiblue">,</span>c<span class="ansiblue">,</span>korak<span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 202</span> <span class="ansired">#nasao je broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 203</span> <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">/home/ori/Desktop/notebook/sve.pyc</span> in <span class="ansicyan">improvedPollard</span><span class="ansiblue">(broj, c, counter, zastavica)</span>
<span class="ansigreen"> 226</span> <span class="ansigreen">elif</span> <span class="ansiblue">(</span>korak<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">and</span> <span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>None<span class="ansiblue">)</span> <span class="ansigreen">and</span> <span class="ansigreen">not</span> zastavica<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen"> 227</span> c <span class="ansiblue">=</span> random<span class="ansiblue">.</span>randint<span class="ansiblue">(</span><span class="ansicyan">1</span><span class="ansiblue">,</span> broj<span class="ansiblue">-</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen">--> 228</span><span class="ansired"> </span>d<span class="ansiblue">=</span> improvedPollard<span class="ansiblue">(</span>broj<span class="ansiblue">,</span>c<span class="ansiblue">,</span><span class="ansicyan">1</span><span class="ansiblue">,</span>True<span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 229</span> <span class="ansired">#nasao je broj | upisan je prost broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 230</span> <span class="ansigreen">elif</span><span class="ansiblue">(</span>zastavica <span class="ansigreen">and</span> d<span class="ansiblue">==</span>broj<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansigreen">/home/ori/Desktop/notebook/sve.pyc</span> in <span class="ansicyan">improvedPollard</span><span class="ansiblue">(broj, c, counter, zastavica)</span>
<span class="ansigreen"> 218</span> z<span class="ansiblue">=</span>abs<span class="ansiblue">(</span>z<span class="ansiblue">*</span><span class="ansiblue">(</span>x<span class="ansiblue">-</span>y<span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue">%</span>broj<span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 219</span> <span class="ansired">#nzm produkta i n</span>
<span class="ansiblue"></span>
<span class="ansigreen">--> 220</span><span class="ansired"> </span>d<span class="ansiblue">=</span>gmpy<span class="ansiblue">.</span>gcd<span class="ansiblue">(</span>mpz<span class="ansiblue">(</span>z<span class="ansiblue">)</span><span class="ansiblue">,</span>mpz<span class="ansiblue">(</span>broj<span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
<span class="ansigreen"> 221</span> <span class="ansired">##ako je korak>1 a jos nije nasao broj</span>
<span class="ansiblue"></span>
<span class="ansigreen"> 222</span> <span class="ansigreen">if</span> <span class="ansiblue">(</span>korak<span class="ansiblue">></span><span class="ansicyan">1</span> <span class="ansigreen">and</span> <span class="ansiblue">(</span>d<span class="ansiblue">==</span><span class="ansicyan">1</span> <span class="ansigreen">or</span> d<span class="ansiblue">==</span>broj <span class="ansigreen">or</span> d<span class="ansiblue">==</span>None<span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
<span class="ansired">KeyboardInterrupt</span>:
</pre></div></div></div></div><div tabindex="2" class="cell border-box-sizing code_cell vbox"><div class="input hbox"><div class="prompt input_prompt">In [59]:</div><div class="input_area box-flex1"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 17.5px; left: 180px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-ipython"><div style="position: relative; height: 47px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">re</span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative;" draggable="true"><pre style="top: 17.5px; left: 180px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-operator">%</span><span class="cm-variable">time</span><span class="cm-null"> </span><span class="cm-variable">rez</span><span class="cm-null">=</span><span class="cm-variable">faktorizacijaAlgoritam</span><span class="cm-null">(</span><span class="cm-variable">prirodni</span><span class="cm-null">[</span><span class="cm-number">2</span><span class="cm-null">])</span></pre><pre><span class="cm-keyword">print</span><span class="cm-null"> </span><span class="cm-string">"Rezultat:"</span><span class="cm-null">,</span><span class="cm-variable">rez</span></pre></div></div></div></div></div></div></div></div></div><div style="display: -moz-box;" class="output vbox"><div class="hbox output_area"><div class="prompt"></div><div class="box_flex1 output_subarea output_text output_stream output_stdout"><pre>CPU times: user 0.40 s, sys: 0.00 s, total: 0.40 s
Wall time: 0.44 s
Rezultat: {61891877833615477421686119892898221933456590431423859297204193967168190790508503918665876133601916977814268828372678470703918408598404095752467886309753749960537113981926796221456677162882447550094690643156789940972813589465809362136438022341860444076132002396099380469351796632661456405409514592442838581177167864224964690047832386060210894777842746735933661151517891723802296574115997203364654236627418562565428565504384750523961420396693212696808419L: 1}
</pre></div></div></div></div><div tabindex="2" class="cell text_cell border-box-sizing"><div style="display: none;" class="text_cell_input"><div class="CodeMirror"><div style="overflow: hidden; position: relative; width: 1px; height: 0px; top: 0px; left: 1009px;"><textarea style="position: absolute; width: 2px;" wrap="off" autocorrect="off" autocapitalize="off"></textarea></div><div class="CodeMirror-scroll cm-s-default"><div style="position: relative; height: 47px; width: 1941px;"><div style="position: absolute; height: 0; width: 0; overflow: hidden;"><pre><span><span class="cm-null">Nažalost testni prirodni broj P1 nije dao uspješne rezultate, mogući razlozi su nedovoljno iskustvo pri radu s pythonom pa je implementacija algoritama neefikasna za teška računanja, ili pak </span></span></pre></div><div style="position: relative; top: 0px;"><div style="display: none;" class="CodeMirror-gutter"><div class="CodeMirror-gutter-text"></div></div><div class="CodeMirror-lines"><div style="position: relative; width: 1935px;" draggable="true"><pre style="top: 0px; left: 1719px;" class="CodeMirror-cursor"> </pre><div style=""><pre><span class="cm-null">Nažalost testni prirodni broj P1 nije dao uspješne rezultate, mogući razlozi su nedovoljno iskustvo pri radu s pythonom pa je implementacija algoritama neefikasna za teška računanja, ili pak slaba procesorska snaga.</span></pre><pre> </pre></div></div></div></div></div></div></div></div><div style="display: block;" tabindex="-1" class="text_cell_render rendered_html"><p>Nažalost
testni prirodni broj P1 nije dao uspješne rezultate, mogući razlozi su
nedovoljno iskustvo pri radu s pythonom pa je implementacija algoritama
neefikasna za teška računanja, ili pak slaba procesorska snaga.</p></div></div><div style="height: 30%;" class="end_space"></div></body></html>