main (1).cpp

//
//  pa1.cpp
//  ProgrammingAssignment#1 Magic Squares
//  Created by Dania Etienne  on 09/29/17.
//  Copyright © 2017 Dania Etienne . All rights reserved.
//

#include <iostream>
using namespace std;

// In this code an input(N) of a user between is used to produce 5 different N*N magic squares.

// A magic square is a N*N matrix of the integers 1 to N^2 where the sums of all the rows, columns, and diagonals are equal.Each number in the matrix occurs exactly once.


int main(int argc, const char * argv[]) {
    
    //STEP ONE: The user is asked to specify the size of the magic square. This value is assigned to N.
    // The boolean variable show is also created to end the program if an invalid number  is entered.
    bool show=false;
    int N=0;
    int Input=0;
    std::cout << "INPUT>> Enter the size of a magic square:";
    cin>>Input;
    std::cout <<"\n";
    
    // The if statement takes care of really large or small numbers that are not odd.
    if (Input>2 && Input<16){
            //checks if between 2 and 16.
        if (Input%2==0){
            // checks if odd.
        }
        else{
            N=Input;
            show=true;
        }
    }
    if (show==true){

    //STEP TWO: The magic square is created and the values are assigned to zero.
    int Magic[N][N];
    for (int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            Magic[i][j]=0;
        }
    }
    
    //STEP THREE: The first/original magic square is produced.
   
    int Lim= (N*N);
    int Initial = 1;
    int row = 0;
    int col = (N / 2);
    int row1;
    int col1;
    while (Initial <= Lim) {
        Magic[row][col] = Initial;
        Initial ++;
        row1 = row;
        col1 = col;
        row -= 1;
        col += 1;
        if (row == -1) {
            row = N - 1;
        }
        if (col == N) {
            col = 0;
        }
        if (Magic[row][col] != 0) {
            row = row1 + 1;
            col = col1;
            if (row == -1) {
                row = N - 1;
            }
        }
    }
   
// A for loop is used to prints out the Matrix.
for (int i = 0; i < N; i++) {
    for (int j = 0; j < N; j++) {
        std::cout <<(Magic[i][j]);
       std::cout <<" ";
    }
    std::cout <<"\n";
}
std::cout <<"\n";
    
    //Calculate the sums of every row:
    std::cout << "OUTPUT>> Checking the sums of every row:";
    int sumRow=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
               sumRow+= Magic[i][j];
                cout << sumRow;
                cout << " ";
                sumRow=0;
            }
            else{
                sumRow+= Magic[i][j];
            }
        }
    }
    //Calculate the sums of every column:
    std::cout << "OUTPUT>> Checking the sums of every column:";
    int sumCol=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
                sumCol+=Magic[j][i];
                std::cout << sumCol;
                std::cout << " ";
                sumCol=0;
            }
            else{
               sumCol+=Magic[j][i];
            }
        }
    }
    
    // Calculate sums of the diagonals:
    std::cout << "OUTPUT>> Checking the sums of every diagonal:";
    int diag1=0;
    int diag2=0;
    
    for (int i=0; i<N; i++) {
        int j=i;
        if (j==(N-1)) {
            (diag1)+=Magic[i][j];
            std::cout << diag1;
            std::cout << " ";
        }
        else {
            (diag1)+=Magic[i][j];
        }
    }
    
    for(int i=0; i<N;i++){
        int n=(N-i-1);
        if(i==(N-1)){
            (diag2)+=Magic[i][n];
            std::cout << diag2;
            std::cout << " ";
        }
        else{
            (diag2)+=Magic[i][n];
        }
    }
    std::cout <<"\n";
    std::cout <<"\n";
    
    //STEP FOUR: The second magic square is printed out.
 int MirrorFlip[N][N];
    
    int m=0;
    int n=0;
    for (int a=0; a<N ;a++) {
        for (int b=0; b<N ;b++){
            m=N-1-a;
            n=N-1-b;
            MirrorFlip[a][b]=Magic[m][n];
        }
    }
    // Prints out Matrix.
    for (int i=0; i<N; i++) {
        for (int j=0; j<N; j++){
            std::cout <<(MirrorFlip[i][j]);
            std::cout <<" ";
        }
        std::cout <<"\n";
    }
    std::cout <<"\n";
    
    //Calculate the sums of every row:
    std::cout << "OUTPUT>> Checking the sums of every row:";
    sumRow=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
                sumRow+= MirrorFlip[i][j];
                cout << sumRow;
                cout << " ";
                sumRow=0;
            }
            else{
                sumRow+= MirrorFlip[i][j];
            }
        }
    }
    //Calculate the sums of every column:
    std::cout << "OUTPUT>> Checking the sums of every column:";
    sumCol=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
               sumCol+=MirrorFlip[j][i];
                std::cout << sumCol;
                std::cout << " ";
                sumCol=0;
            }
            else{
                sumCol+=MirrorFlip[j][i];
            }
        }
    }
    
    // Calculate sums of the diagonals:
    std::cout << "OUTPUT>> Checking the sums of every diagonal:";
    diag1=0;
    diag2=0;
    for (int i=0; i<N; i++) {
        int j=i;
        if (j==(N-1)) {
            (diag1)+=MirrorFlip[i][j];
            std::cout << (diag1);
            std::cout << " ";
        }
        else {
             (diag1)+=MirrorFlip[i][j];
        }
    }
    
    for(int i=0; i<N;i++){
        int n=(N-i-1);
        if(i==(N-1)){
             (diag2)+=MirrorFlip[i][n];
            std::cout << (diag2);
            std::cout << " ";
        }
        else{
            (diag2)+=MirrorFlip[i][n];
        }
    }
    std::cout <<"\n";
    std::cout <<"\n";

    
    //STEP FIVE: The third magic square is produced.
    int Rotate[N][N];
    
    for (int i=0; i<N; i++) {
        for (int j=0; j<N; j++){
            Rotate[i][j]=Magic[N-j-1][i];
    }
    }
    // Prints out Matrix.
    for (int i=0; i<N; i++) {
        for (int j=0; j<N; j++){
            std::cout <<(Rotate[i][j]);
            std::cout <<" ";
        }
        std::cout <<"\n";
    }
std::cout <<"\n";
    
    //Calculate the sums of every row:
    std::cout << "OUTPUT>> Checking the sums of every row:";
    sumRow=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
               sumRow+= Rotate[i][j];
                cout << sumRow;
                cout << " ";
                sumRow=0;
            }
            else{
                sumRow+= Rotate[i][j];
            }
        }
    }
    //Calculate the sums of every column:
    std::cout << "OUTPUT>> Checking the sums of every column:";
    sumCol=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
                 sumCol+=Rotate[j][i];
                std::cout << sumCol;
                std::cout << " ";
                sumCol=0;
            }
            else{
                sumCol+=Rotate[j][i];
            }
        }
    }
    
    // Calculate sums of the diagonals:
    std::cout << "OUTPUT>> Checking the sums of every diagonal:";
    diag1=0;
    diag2=0;
    for (int i=0; i<N; i++) {
        int j=i;
        if (j==(N-1)) {
            (diag1)+=Rotate[i][j];
            std::cout << (diag1);
            std::cout << " ";
        }
        else {
             (diag1)+=Rotate[i][j];
        }
    }
    
    for(int i=0; i<N;i++){
        int n=(N-i-1);
        if(i==(N-1)){
            (diag2)+=Rotate[i][n];
            std::cout << (diag2);
            std::cout << " ";
        }
        else{
             (diag2)+=Rotate[i][n];
        }
    }
    std::cout <<"\n";
    std::cout <<"\n";
    


//STEP SIX: The fourth magic square is produced.

int Spin[N][N];

for (int i=0; i<N; i++) {
    for (int j=0; j<N; j++){
        Spin[i][j]=Magic[j][N-i-1];
    }
}
// Prints out Matrix.
for (int i=0; i<N; i++) {
    for (int j=0; j<N; j++){
        std::cout <<(Spin[i][j]);
        std::cout <<" ";
        }
        std::cout <<"\n";
        }

    std::cout <<"\n";
    
    
    //Calculate the sums of every row:
    std::cout << "OUTPUT>> Checking the sums of every row:";
    sumRow=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
                sumRow+= Spin[i][j];
                cout << sumRow;
                cout << " ";
                sumRow=0;
            }
            else{
               sumRow+= Spin[i][j];
            }
        }
    }
    //Calculate the sums of every column:
    std::cout << "OUTPUT>> Checking the sums of every column:";
    sumCol=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
                sumCol+=Spin[j][i];
                std::cout << sumCol;
                std::cout << " ";
                sumCol=0;
            }
            else{
                sumCol+=Spin[j][i];
            }
        }
    }
    
    // Calculate sums of the diagonals:
    std::cout << "OUTPUT>> Checking the sums of every diagonal:";
    diag1=0;
    diag2=0;
    for (int i=0; i<N; i++) {
        int j=i;
        if (j==(N-1)) {
            (diag1)+=Spin[i][j];
            std::cout << (diag1);
            std::cout << " ";
        }
        else {
            (diag1)+=Spin[i][j];
        }
    }
    
    for(int i=0; i<N;i++){
        int n=(N-i-1);
        if(i==(N-1)){
          (diag2)+=Spin[i][n];
            std::cout << (diag2);
            std::cout << " ";
        }
        else{
           (diag2)+=Spin[i][n];
        }
    }
    std::cout <<"\n";
    std::cout <<"\n";
    
    
//STEP SEVEN: The fifth magic square is produced.
    
    int Mirror[N][N];
    
    for (int i=0; i<N; i++) {
        for (int j=0; j<N; j++){
            Mirror[i][j]=Magic[N-i-1][j];
            Mirror[N-i-1][j]=Magic[i][j];
        }
    }
    
    // Prints out Matrix.
    for (int i=0; i<N; i++) {
        for (int j=0; j<N; j++){
            std::cout <<(Mirror[i][j]);
            std::cout <<" ";
        }
        std::cout <<"\n";
    }
    
    std::cout <<"\n";
   
    
   
    //Calculate the sums of every row:
    std::cout << "OUTPUT>> Checking the sums of every row:";
    sumRow=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
                sumRow+= Mirror[i][j];
                cout << sumRow;
                cout << " ";
                sumRow=0;
            }
            else{
                sumRow+= Mirror[i][j];
            }
        }
    }
    //Calculate the sums of every column:
    std::cout << "OUTPUT>> Checking the sums of every column:";
    sumCol=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
                sumCol+=Mirror[j][i];
                std::cout << sumCol;
                std::cout << " ";
                sumCol=0;
            }
            else{
                  sumCol+=Mirror[j][i];
            }
        }
    }
    
    // Calculate sums of the diagonals:
    std::cout << "OUTPUT>> Checking the sums of every diagonal:";
    diag1=0;
    diag2=0;
    for (int i=0; i<N; i++) {
        int j=i;
        if (j==(N-1)) {
            (diag1)+=Mirror[i][j];
            std::cout << (diag1);
            std::cout << " ";
        }
        else {
            (diag1)+=Mirror[i][j];
        }
    }
    
    for(int i=0; i<N;i++){
        int n=(N-i-1);
        if(i==(N-1)){
             (diag2)+=Mirror[i][n];
            std::cout << (diag2);
            std::cout << " ";
        }
        else{
             (diag2)+=Mirror[i][n];
        }
    }
    std::cout <<"\n";
    std::cout <<"\n";
    
    
    
// STEP EIGHT: The sixth magic square is produced.
    int Six[N][N];
    
    for (int i=0; i<N; i++) {
        for (int j=0; j<N; j++){
            Six[i][j]=MirrorFlip[N-i-1][j];
            Six[N-i-1][j]=MirrorFlip[i][j];
        }
    }
    // Prints out Matrix.
    for (int i=0; i<N; i++) {
        for (int j=0; j<N; j++){
            std::cout <<(Six[i][j]);
            std::cout <<" ";
        }
        std::cout <<"\n";
    }
    std::cout <<"\n";
    //Calculate the sums of every row:
    std::cout << "OUTPUT>> Checking the sums of every row:";
    sumRow=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
                sumRow+= Six[i][j];
                cout << sumRow;
                cout << " ";
                sumRow=0;
            }
            else{
                sumRow+= Six[i][j];
            }
        }
    }
    //Calculate the sums of every column:
    std::cout << "OUTPUT>> Checking the sums of every column:";
    sumCol=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
                  sumCol+=Six[j][i];
                std::cout << sumCol;
                std::cout << " ";
                sumCol=0;
            }
            else{
                sumCol+=Six[j][i];
            }
        }
    }
    
    // Calculate sums of the diagonals:
    std::cout << "OUTPUT>> Checking the sums of every diagonal:";
    diag1=0;
    diag2=0;
    for (int i=0; i<N; i++) {
        int j=i;
        if (j==(N-1)) {
          (diag1)+= Six[i][j];
            std::cout << (diag1);
            std::cout << " ";
        }
        else {
           (diag1)+= Six[i][j];
        }
    }
    
    for(int i=0; i<N;i++){
        int n=(N-i-1);
        if(i==(N-1)){
            (diag2)+= Six[i][n];
            std::cout << (diag2);
            std::cout << " ";
        }
        else{
             (diag2)+= Six[i][n];
        }
    }
    std::cout <<"\n";
    std::cout <<"\n";
    
    // STEP NINE: The seventh magic square is produced.
    int Seven[N][N];
    
    for (int i=0; i<N; i++) {
        for (int j=0; j<N; j++){
            Seven[i][j]=Spin[N-i-1][j];
            Seven[N-i-1][j]=Spin[i][j];
        }
    }
    for (int i=0; i<N; i++) {
        for (int j=0; j<N; j++){
            std::cout <<(Seven[i][j]);
            std::cout <<" ";
        }
        std::cout <<"\n";
    }
    std::cout <<"\n";
    
    //Calculate the sums of every row:
    std::cout << "OUTPUT>> Checking the sums of every row:";
    sumRow=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
                sumRow+= Seven[i][j];
                cout << sumRow;
                cout << " ";
                sumRow=0;
            }
            else{
                sumRow+= Seven[i][j];
            }
        }
    }
    //Calculate the sums of every column:
    std::cout << "OUTPUT>> Checking the sums of every column:";
     sumCol=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
                 sumCol+=Seven[j][i];
                std::cout << sumCol;
                std::cout << " ";
                sumCol=0;
            }
            else{
                 sumCol+=Seven[j][i];
            }
        }
    }
    
    // Calculate sums of the diagonals:
    std::cout << "OUTPUT>> Checking the sums of every diagonal:";
    diag1=0;
    diag2=0;
    for (int i=0; i<N; i++) {
        int j=i;
        if (j==(N-1)) {
             (diag1)+= Seven[i][j];
            std::cout << (diag1);
            std::cout << " ";
        }
        else {
            (diag1)+= Seven[i][j];
        }
    }
    
    for(int i=0; i<N;i++){
        int n=(N-i-1);
        if(i==(N-1)){
            (diag2)+= Seven[i][n];
            std::cout << (diag2);
            std::cout << " ";
        }
        else{
          (diag2)+= Seven[i][n];
        }
    }
    std::cout <<"\n";
    std::cout <<"\n";
    
    // STEP TEN: The eigth magic square is produced.
    int Eight[N][N];
    
    for (int i=0; i<N; i++) {
        for (int j=0; j<N; j++){
            Eight[i][j]=Rotate[N-i-1][j];
            Eight[N-i-1][j]=Rotate[i][j];
        }
    }
    for (int i=0; i<N; i++) {
        for (int j=0; j<N; j++){
            std::cout <<(Eight[i][j]);
            std::cout <<" ";
        }
        std::cout <<"\n";
    }
    std::cout <<"\n";
    //Calculate the sums of every row:
    std::cout << "OUTPUT>> Checking the sums of every row:";
    sumRow=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
                sumRow+= Eight[i][j];
                cout << sumRow;
                cout << " ";
                sumRow=0;
            }
            else{
                sumRow+= Eight[i][j];
            }
        }
    }
    //Calculate the sums of every column:
    std::cout << "OUTPUT>> Checking the sums of every column:";
    sumCol=0;
    for( int i=0; i<N; i++){
        for (int j=0; j<N; j++){
            if (j==(N-1)){
                 sumCol+=Eight[j][i];
                std::cout << sumCol;
                std::cout << " ";
                sumCol=0;
            }
            else{
                sumCol+= Eight[j][i];
            }
        }
    }
    
    // Calculate sums of the diagonals:
    std::cout << "OUTPUT>> Checking the sums of every diagonal:";
    diag1=0;
    diag2=0;
    for (int i=0; i<N; i++) {
        int j=i;
        if (i==(N-1)) {
          (diag1)+= Eight[i][j];
            std::cout << (diag1);
            std::cout << " ";
        }
        else {
            (diag1)+=Eight[i][j];
        }
    }

    for(int i=0; i<N;i++){
        int n=(N-i-1);
        if(i==(N-1)){
            (diag2)+=Eight[i][n];
            std::cout << (diag2);
            std::cout << " ";
        }
        else{
            (diag2)+=Eight[i][n];
        }
    }
    std::cout <<"\n";
    std::cout <<"\n";
}
}