Skip to content

Commit

Permalink
Update intro-to-dp.md
Browse files Browse the repository at this point in the history 
Added links to standard problems.
  • Loading branch information
@Zyad-Ayad
Zyad-Ayad committed Apr 24, 2024
1 parent 6c693ed commit 762f076
Showing 1 changed file with 16 additions and 42 deletions.
58 changes: 16 additions & 42 deletions src/dynamic_programming/intro-to-dp.md
View file
Original file line number Diff line number Diff line change
Expand Up @@ -130,48 +130,22 @@ That's it. That's the basics of dynamic programming: Don't repeat work you've do
One of the tricks to getting better at dynamic programming is to study some of the classic examples.

## Classic Dynamic Programming Problems
<dl>
<dt>0-1 Knapsack</dt>
<dd>given a set of items, each with a weight and a value, and a knapsack with a maximum capacity.</dd>

<dt>Subset Sum</dt>
<dd>you are given a set of integers and a target sum. The task is to determine whether there exists a subset of the given set whose elements sum up to the target sum.</dd>

<dt>Longest Increasing Subsequence</dt>
<dd>It's a problem that asks for the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order.</dd>

<dt>Counting all possible paths from top left to bottom right corner of a matrix</dt>
<dd>solved using dynamic programming or recursion with memoization.</dd>

<dt>Longest Common Subsequence</dt>
<dd>Given two sequences (usually strings), the task is to find the length of the longest subsequence that is common to both sequences.</dd>

<dt>Longest Path in a Directed Acyclic Graph (DAG)</dt>
<dd>Unlike finding the longest path in a general graph, which is an NP-hard problem, finding the longest path in a DAG can be solved efficiently using dynamic programming.</dd>

<dt>Longest Palindromic Subsequence</dt>
<dd>Finding the Longest Palindromic Subsequence (LPS) of a given string.</dd>

<dt>Rod Cutting</dt>
<dd>It involves finding the maximum revenue that can be obtained by cutting a rod of length n into smaller pieces and selling them. </dd>

<dt>Edit Distance</dt>
<dd>It involves finding the minimum number of operations required to transform one string into another, where the allowed operations are insertion, deletion, or substitution of a single character. </dd>

<dt>Bitmask Dynamic Programming</dt>
<dd>Bitmask Dynamic Programming is a technique used to solve combinatorial optimization problems, where the state can be represented compactly using bitmasks. </dd>

<dt>Digit Dynamic Programming</dt>
<dd>Digit Dynamic Programming is a technique used to solve problems related to digits of a number. </dd>

<dt>Dynamic Programming on Trees</dt>
<dd>a technique used to solve various problems related to trees, such as finding the longest path, computing subtree properties, or counting certain structures within the tree. </dd>

<dt>Range Dynamic Programming</dt>
<dd>Range Dynamic Programming is a technique used to solve problems where you need to find optimal solutions for subranges within a given range or array. </dd>


</dl>
| Name | Description | Example Poblems |
| ---------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | ----------------------------------------------------------------------------------------------------------------------------------------------- |
| 0-1 Knapsack | 0-1 Knapsack | given a set of items, each with a weight and a value, and a knapsack with a maximum capacity. | [D - Knapsack 1 (](https://atcoder.jp/contests/dp/tasks/dp_d)[atcoder.jp](http://atcoder.jp)[)](https://atcoder.jp/contests/dp/tasks/dp_d) |
| 0-1 Knapsack |
| Subset Sum | you are given a set of integers and a target sum. The task is to determine whether there exists a subset of the given set whose elements sum up to the target sum. | |
| Longest Increasing Subsequence | It's a problem that asks for the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order. | [Longest Increasing Subsequence - LeetCode](https://leetcode.com/problems/longest-increasing-subsequence/description/) |
| Counting all possible paths in a matrix. | Solved using dynamic programming or recursion with memoization. | [Unique Paths - LeetCode](https://leetcode.com/problems/unique-paths/description/) |
| Longest Common Subsequence | Given two sequences (usually strings), the task is to find the length of the longest subsequence that is common to both sequences. | [F - LCS (](https://atcoder.jp/contests/dp/tasks/dp_f)[atcoder.jp](http://atcoder.jp)[)](https://atcoder.jp/contests/dp/tasks/dp_f) |
| Longest Path in a Directed Acyclic Graph (DAG) | Unlike finding the longest path in a general graph, which is an NP-hard problem, finding the longest path in a DAG can be solved efficiently using dynamic programming. | [G - Longest Path (](https://atcoder.jp/contests/dp/tasks/dp_g)[atcoder.jp](http://atcoder.jp)[)](https://atcoder.jp/contests/dp/tasks/dp_g) |
| Longest Palindromic Subsequence | Finding the Longest Palindromic Subsequence (LPS) of a given string. | [Longest Palindromic Subsequence - LeetCode](https://leetcode.com/problems/longest-palindromic-subsequence/description/) |
| Rod Cutting | It involves finding the maximum revenue that can be obtained by cutting a rod of length n into smaller pieces and selling them. | |
| Edit Distance | It involves finding the minimum number of operations required to transform one string into another, where the allowed operations are insertion, deletion, or substitution of a single character. | [CSES - Edit Distance](https://cses.fi/problemset/task/1639) |
| Bitmask Dynamic Programming | Bitmask Dynamic Programming is a technique used to solve combinatorial optimization problems, where the state can be represented compactly using bitmasks. | [Problem - F - Codeforces](https://codeforces.com/contest/1043/problem/F) |
| Digit Dynamic Programming | Digit Dynamic Programming is a technique used to solve problems related to digits of a number. | [SPOJ.com](http://SPOJ.com) [- Problem PR003004](https://www.spoj.com/problems/PR003004/) |
| Dynamic Programming on Trees | A technique used to solve various problems related to trees, such as finding the longest path, computing subtree properties, or counting certain structures within the tree. | [P - Independent Set (](https://atcoder.jp/contests/dp/tasks/dp_p)[atcoder.jp](http://atcoder.jp)[)](https://atcoder.jp/contests/dp/tasks/dp_p) |
| Range Dynamic Programming | Range Dynamic Programming is a technique used to solve problems where you need to find optimal solutions for subranges within a given range or array. | |

Of course, the most important trick is to practice.

Expand Down

0 comments on commit 762f076

Please sign in to comment.