Question

Write C++ programs that create TEN(10) different N*N magic squares. A square matrix is the arrangement of the numbers 1, 2, ., N2, in which the sum of rows, columns, and diagonals are the same. The users (i.e., TAs) will specify the size of the square matrix: N. The value N must be an odd number between 3 and 15. Example Run For example, you program is expected to run as the following way. NOTE: We only list 5 magic squares on this example INPUT> Enter the size of a magic square: 3 OUTPUT» Magic Square #1 is: OUTPUT> Checking the sums of every row OUTPUT> Checking the sums of every column: 15 15 15 OUTPUT>> Checking the sums of every diagnoal: 15 15 15 15 15

Answer 1

Screenshot of the code:

//Include this header file while using //visual studio. #include "stdafx.h" //Include the required header file #include <iostream> #include <string.h> //Use the standard naming convention. using namespace std; //Define the function createMagicSquare () void createMagicSquare (int num) //Create an array to store magic square //matrix elements. int** magicSgMa trix = new int* [num]; for (inti- 0; i < num; ++i) magicSqMatrix[i] - new int [num] ; //Initialize all the elements of the //magic square matrix to 0. i inum; i++) for (int j = 0; j < nu magicSgMa trix [1] [j 0; - //Initialize the i and j index values of //the matrix //The row position is num/2 and column //position is num-1 for the first element. int i = num / 2; //start the for loop from 1 to n 2. for (int index-1; index < num*num;) //If the row index and column index is -1 //and num respectively. //Decrement the column index by 2. j=num-2;

//Make the row index to 0. //Otherwise. else //If the column index is equal to num, //then make it column index to 0. if (j num) //If the row index is less than 0, //then make the row index to num - 1 if (i < 0) num- 1; //If the element of the matrix at the //index (i, j) is not equal to 0. if (magicSqMatrix[i][j]) //Decrement the column index by 2. //Increment the row index by 1. 1+t; //Continue the loop. continue; //otherwise. else //Make the matrix element at the index //(i, j) to num++ magicSaMa trix [1] [j] = index++; //Increment the row index by 1 j+ti //Decrement the column index by 1. //start the for loop till size of matrix num.

for (i-0i< num; //start the for loop till size of matrix < num; j++) //Display the mtrix elements //num. for (j 0; cout << magicSqMatrix[i][j] <<""; cout <"n"; //Iitialize the required variables to store row //sum, column sum, and diagonal sum. int sumOfRows, sumOfCols, sumOfDiagonals; sumOfRows = 0; sumofCols0; sumOfDiagonals0 //Display the sum of each rows cout << "OUTPUT>> Checking the sums of every row: "; //start the for loop till the size of matrix. for (int index = 0; index < num; index++) //Initialize the variable sumofRows to 0 sumOfRows - 0; //start the for loop till the size of matrix. for (int col index = 0; col index < num; col index++) /Calculate the sum of rows. sumofRows += magicSgMatrix [index] [col indexl: //Display the sum of rows. cout <sumof Rows <<""; cout << endl; /Sumof each column cout<< "OUTPUT>> Checking the sums of every " cout << "column:" //start the for loop tǐїї the size of matrix.

for (int col index 0; col index < num; col index++) //Initialize thevariable sumOfCols to 0. //start the for loop till the size of matrix. for (int index-0; index < num; index++) /Calculate the sum of columns. sumOfCols + magicSqMatrix [index] [col index]; //Display the sum of columns. cout<sumOfCols <<"" cout << endl; //Display the sum of diagonals. cout << "OUTPUT>> Checking the sums of every "; cout << "diagonal: "; //start the for loop till the size of matrix. for (int row index = 0; row index < num; +trow index) for (int col index - 0; сої index < num; ++col index) //If the both row and column index are //equal. if (row index == col index) //Calculate the diagonal sum, sumOfDiagonals +- magicSqMatrix[row_index] [col_index]; //Display the sum of diagonals. cout << sumOfDiagonals<<""; sumOfDiagonals0; //start the for loop till the size of matrix. for (int row index = 0; row index < num; ++row index)

for (int col index = 0; col index < num; ++col index) //If the both row and column index are if ( (row in dex + colindex)-(num- 1)) - //Calculate the diagonal sum. sumofDiagonals += magicSqMatrix[row index] [col index]; //Display the sum of diagonals cout << sumOfDiagonals << ""; cout << endl; for (inti- 0; i < num; ++i) deletel magicSgMatrixlil; delete[] magicSqMatrix; //Start the execution of the main() method. int main() //Declare the required variables int index; int size; index 1; //start the while loop till 10 while (index <= 10) //Prompt the user to enter the size of the //matrix. cout << "Enter the size of a magic square: " cin >> size; if (size >= 3 && size <= 15) if (size % 2 != 0) cout << "Magic Squre #" << index <<"is: "<< endl; createMagicSquare (size); cout << endl;

//Increment the index of the loop indext+ elsee cout << "Please enter an odd value"; cout << "of"; cout << "size of matrix. " << endl; else cout "Please enter the value of size" cout <<"of matrix between 3 and 15.'" くく endl; //Use this command while using visual studio system ("pause"); return 0;

Sample Output:

Enter the size of a magic square: 3 Magic Squre #1 is: 2 7 6 9 5 1 4 3 8 OUTPUT> Checking the sums of every row: 15 15 15 OUTPUT> Checking the sums of every column: 15 15 15 OUTPUT> Checking the sums of every diagonal: 15 15 Enter the size of a magic square: 5 Magic Squre #2 is: 9 3 22 16 15 2 21 20 14 8 25 19 13 7 1 18 12 6 5 24 11 10 4 23 17 OUTPUT> Checking the sums of every row: 65 65 65 65 65 OUTPUT> Checking the sums of every column: 65 65 65 65 65 OUTPUT> Checking the sums of every diagonal: 65 65 Enter the size of a magic square: 7 Magic Squre #3 is: 20 12 4 45 37 29 28 11 3 44 36 35 27 19 2 43 42 34 26 18 10 49 41 33 25 17 9 1 40 32 24 16 8 7 48 31 23 15 14 6 47 39 22 21 13 5 46 38 30 OUTPUT> Checking the sums of every row: 175 175 175 175 175 175 175 OUTPUT> Checking the sums of every column: 175 175 175 175 175 175 175 OUTPUT> Checking the sums of every diagonal: 175 175

Enter the size of a magic square: 9 Magic Squre #4 is: 35 25 15 5 76 66 56 46 45 24 14 4 75 65 55 54 44 34 13 3 74 64 63 53 43 33 23 2 73 72 62 52 42 32 22 12 81 71 61 51 41 31 21 11 1 59 49 39 29 19 18 8 79 69 48 38 28 27 17 7 78 68 58 37 36 26 16 6 77 67 57 47 OUTPUT> Checking the sums of every row: 369 369 369 369 369 369 369 369 369 OUTPUT> Checking the sums of every column: 369 369 369 369 369 369 369 369 369 OUTPUT> Checking the sums of every diagonal: 369 369 Enter the size of a magic square: 11 Magic Squre #5 is: 54 42 30 18 6 115 103 91 79 67 66 41 29 17 5 114 102 90 78 77 65 53 28 16 4 113 101 89 88 76 64 52 40 15 3 112 100 99 87 75 63 51 39 27 121 109 97 85 73 61 49 37 25 13 1 108 96 84 72 60 48 36 24 12 11 12Θ 95 83 71 59 47 35 23 22 10 1I9 107 82 70 58 46 34 33 21 9 118 106 94 69 57 45 44 32 20 8 117 105 93 81 56 55 43 31 19 7 116 104 92 80 68 OUTPUT> Checking the sums of every row: 671 671 671 671 671 671 671 671 671 671 671 OUTPUT> Checking the sums of every column: 671 671 671 671 671 671 671 671 671 671 671 OUTPUT> Checking the sums of every diagonal: 671 671 Enter the size of a magic square: 13 Magic Squre #6 is: 77 63 49 35 21 7 162 148 134 120 106 92 91 62 48 34 20 6 161 147 133 119 105 104 90 76 47 33 19 5 160 146 132 118 117 103 89 75 61

32 18 4 159 145 131 13θ 116 102 88 74 60 46 17 3 158 144 143 129 115 1ΘΊ 87 73 59 45 31 2 157 156 142 128 114 10θ 86 72 58 44 3θ 16 169 155 141 127 113 99 85 71 57 43 29 15 1 154 14е 126 112 98 84 70 56 42 28 14 13 168 139 125 111 97 83 69 55 41 27 26 12 167 153 124 11Θ 96 82 68 54 40 39 25 11 166 152 138 109 95 81 67 53 52 38 24 10 165 151 137 123 94 80 66 65 51 37 23 9 164 150 136 122 108 79 78 64 5Θ 36 22 8 163 149 135 121 1θ7 93 OUTPUT>> Checking the sums of every ro : 1105 1105 1105 1105 11Θ5 1105 1105 1105 1105 11e5 1105 1105 1105 OUTPUT> Checking the sums of every column: 1105 1105 1105 1105 1105 1105 1105 1105 1105 1105 1105 1105 1105 OUTPUT> Checking the sums of every diagonal: 1105 1105 size of a magic square: Enter the Magic Squre #7 is: 104 88 72 56 40 24 8 217 201 185 169 153 137 121 120 87 71 55 39 23 7 216 200 184 168 152 136 135 119 103 70 54 38 22 6 215 199 183 167 151 150 134 118 102 86 53 37 21 5 214 198 182 166 165 149 133 117 1ΘΊ 85 69 36 20 4 213 197 181 180 164 148 132 116 100 84 68 52 19 3 212 196 195 179 163 147 131 115 99 83 67 51 35 2 211 21Θ 194 178 162 146 130 114 98 82 66 50 34 18 225 209 193 177 161 145 129 113 97 81 65 49 33 17 1 208 192 176 160 144 128 112 96 80 64 48 32 16 15 224 191 175 159 143 127 111 95 79 63 47 31 30 14 223 207 174 158 142 126 11Θ 94 78 62 46 45 29 13 222 2Θ6 19e 157 141 125 1Θ9 93 77 61 60 44 28 12 221 2Θ5 189 173 14θ 124 108 92 76 75 59 43 27 11 22e 204 188 172 156 123 187 91 90 74 58 42 26 1Θ 219 203 187 171 155 139 1Θ6 1Θ5 89 73 57 41 25 9 218 2Θ2 186 17Θ 154 138 122 OUTPUT> Checking the sums of every row: 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 OUTPUT Checking the sums of every column: 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 OUTPUT> Checking the sums of every diagonal: 1695 1695

Enter the size of a magic square: 7 Magic Squre #8 is: 20 12 4 45 37 29 28 11 3 44 36 35 27 19 2 43 42 34 26 18 10 49 41 33 25 17 9 1 40 32 24 16 8 7 48 31 23 15 14 6 47 39 22 21 13 5 46 38 30 OUTPUT> Checking the sums of every row: 175 175 175 175 175 175 175 OUTPUT> Checking the sums of every column: 175 175 175 175 175 175 175 OUTPUT> Checking the sums of every diagonal: 175 175 Enter the size of a magic square: 5 Magic Squre #9 is: 9 3 22 16 15 2 21 20 14 8 25 19 13 7 1 18 12 6 5 24 11 10 4 23 17 OUTPUT> Checking the sums of every row: 65 65 65 65 65 OUTPUT> Checking the sums of every column: 65 65 65 65 65 OUTPUT> Checking the sums of every diagonal: 65 65 Enter the size of a magic square: 3 Magic squre #10 is: 2 7 6 9 5 1 4 3 8 OUTPUT> Checking the sums of every row: 15 15 15 OUTPUT> Checking the sums of every column: 15 15 15 OUTPUT> Checking the sums of every diagonal: 15 15 Press any key to continue .. .

Code to copy:

//Include this header file while using
//visual studio.
#include "stdafx.h"
//Include the required header file.
#include <iostream>
#include <string.h>
//Use the standard naming convention.
using namespace std;
//Define the function createMagicSquare().
void createMagicSquare(int num)
{
     //Create an array to store magic square
     //matrix elements.
     int** magicSqMatrix = new int*[num];
     for (int i = 0; i < num; ++i)
          magicSqMatrix[i] = new int[num];
   
     //Initialize all the elements of the
     //magic square matrix to 0.
     for (int i = 0; i < num; i++)
     {
          for (int j = 0; j < num; j++)
          {
               magicSqMatrix[i][j] = 0;
          }
     }
     //Initialize the i and j index values of
     //the matrix.
     //The row position is num/2 and column
     //position is num-1 for the first element.
     int i = num / 2;
     int j = num - 1;
     //Start the for loop from 1 to n^2.
     for (int index = 1; index <= num*num;)
     {
          //If the row index and column index is -1
          //and num respectively.
          if (i == -1 && j == num)
          {
               //Decrement the column index by 2.
               j = num - 2;
               //Make the row index to 0.
               i = 0;
          }
          //Otherwise.
          else
          {
               //If the column index is equal to num,
               //then make it column index to 0.
               if (j == num)
                     j = 0;
               //If the row index is less than 0,
               //then make the row index to num - 1.
               if (i < 0)
                     i = num - 1;
          }
          //If the element of the matrix at the
          //index (i, j) is not equal to 0.
          if (magicSqMatrix[i][j])
          {
               //Decrement the column index by 2.
               j = j - 2;
               //Increment the row index by 1.
               i++;
               //Continue the loop.
               continue;
          }
          //Otherwise.
          else
               //Make the matrix element at the index
               //(i, j) to num++.
               magicSqMatrix[i][j] = index++;
          //Increment the row index by 1.
          j++;
          //Decrement the column index by 1.
          i--;
     }
     //Start the for loop till size of matrix num.
     for (i = 0; i < num; i++)
     {
          //Start the for loop till size of matrix
          //num.
          for (j = 0; j < num; j++)
          {
               //Display the mtrix elements.
               cout << magicSqMatrix[i][j] << " ";
          }
          cout << "\n";
     }
     //Iitialize the required variables to store row
     //sum, column sum, and diagonal sum.
     int sumOfRows, sumOfCols, sumOfDiagonals;
     sumOfRows = 0;
     sumOfCols = 0;
     sumOfDiagonals = 0;
     //Display the sum of each rows.
     cout << "OUTPUT>> Checking the sums of every row: ";
     //Start the for loop till the size of matrix.
     for (int index = 0; index < num; index++)
     {
          //Initialize the variable sumOfRows to 0.
          sumOfRows = 0;
          //Start the for loop till the size of matrix.
          for (int col_index = 0; col_index < num;
          col_index++)
          {
               //Calculate the sum of rows.
               sumOfRows += magicSqMatrix[index]
               [col_index];
          }
          //Display the sum of rows.
          cout << sumOfRows << " ";
     }
     cout << endl;
     //Sum of each column
     cout << "OUTPUT>> Checking the sums of every ";
     cout << "column: ";
     //Start the for loop till the size of matrix.
     for (int col_index = 0; col_index < num;
     col_index++)
     {
          //Initialize the variable sumOfCols to 0.
          sumOfCols = 0;
          //Start the for loop till the size of matrix.
          for (int index = 0; index < num; index++)
          {
               //Calculate the sum of columns.
               sumOfCols += magicSqMatrix[index]
               [col_index];
          }
          //Display the sum of columns.
          cout << sumOfCols << " ";
     }
     cout << endl;
     //Display the sum of diagonals.
     cout << "OUTPUT>> Checking the sums of every ";
     cout << "diagonal: ";
     //Start the for loop till the size of matrix.
     for (int row_index = 0; row_index < num;
     ++row_index)
     {
          for (int col_index = 0; col_index < num;
          ++col_index)
          {
               //If the both row and column index are
               //equal.
               if (row_index == col_index)
                     //Calculate the diagonal sum.
                     sumOfDiagonals +=
                    magicSqMatrix[row_index][col_index];
          }
     }
     //Display the sum of diagonals.
     cout << sumOfDiagonals << " ";
     sumOfDiagonals = 0;
     //Start the for loop till the size of matrix.
     for (int row_index = 0; row_index < num;
     ++row_index)
     {
          for (int col_index = 0; col_index < num;
          ++col_index)
          {
               //If the both row and column index are
               //equal.
               if ((row_index + col_index) == (num - 1))
                     //Calculate the diagonal sum.
                     sumOfDiagonals +=
                    magicSqMatrix[row_index][col_index];
          }
     }
     //Display the sum of diagonals.
     cout << sumOfDiagonals << " ";
     cout << endl;
     for (int i = 0; i < num; ++i) {
          delete[] magicSqMatrix[i];
     }
     delete[] magicSqMatrix;
}
//Start the execution of the main() method.
int main()
{
     //Declare the required variables.
     int index;
     int size;
     index = 1;
     //Start the while loop till 10.
     while (index <= 10)
     {
          //Prompt the user to enter the size of the
          //matrix.
          cout << "INPUT>> Enter the size of a magic square: ";
          cin >> size;
          if (size >= 3 && size <= 15)
          {
               if (size % 2 != 0)
               {
                     cout << "OUTPUT>> Magic Squre #" << index
                          << " is:" << endl;
                     createMagicSquare(size);
                     cout << endl;
                     //Increment the index of the loop.
                     index++;
               }
               else
               {
                     cout << "Please enter an odd value ";
                     cout << "of ";
                     cout << "size of matrix." << endl;
               }
          }
          else
          {
               cout << "Please enter the value of size ";
               cout << "of matrix between 3 and 15."
                     << endl;
          }
     }
     //Use this command while using visual studio.
     system("pause");
     return 0;
}