C++    Magic Square A magic square of order n is an arrangement of n2 numbers, usually distinct integers,…

C++

Magic Square

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Order Essay

A magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.

Write a C++ program that can create and display magic squares of any size, which will be entered at the runtime. The size could be varying from 3 to 15.

Allow your program to run continuously as often as the user wishes to test with the other sizes. Before ending the program, your name as the programmer must be displayed.

Note: with the same size n entered at repeated runs, there should be different squares displayed; That meant if the same square was always displayed for the same input size, it is wrong.

For references: http://en.wikipedia.org/wiki/Magic_square

Sample

            ~-~-~-~-~-~-~-~-~-~-~-~-~

                             Magic Square Generator

                           ~-~-~-~-~-~-~-~-~-~-~-~-~

           Enter desired size of magic square (3 – 15) or 0 to end: gj

                             ERROR! Invalid Value!

   Enter desired size of magic square (3 – 15) or 0 to end: 5

                 With size 5, the Magic Number is 65

                          ————————-

                          | 2| 22| 10| 19| 12|

                          ————————-

                          | 25| 1| 17| 16| 6|

                          ————————-

                          | 5| 20| 21| 8| 11|

                          ————————-

                          | 24| 7| 3| 18| 13|

                          ————————-

                          | 9| 15| 14| 4| 23|

                          ————————-

                        Press key to continue…

Enter desired size of magic square (3 – 15) or 0 to end: 15

                 With size 15, the Magic Number is 1695

           ———————————————————————

           | 11| 42|119| 14| 47| 16|152| 41|221|213| 83|210|224|206| 96|

           ———————————————————————

           |192| 79| 73|216| 80| 36|135|201| 81| 43| 94|208|134| 3|120|

           ———————————————————————

           |109|185| 22|222| 53|167| 12| 46| 61|165|181| 62| 75|155|180|

           ———————————————————————

           |186| 44|102| 48|223|127|108|153|144| 38| 98|168| 64| 19|173|

           ———————————————————————

           |169|145|191|197| 8|189|124|122| 92| 52| 99| 57| 35|195| 20|

           ———————————————————————

           |115| 45|103|184| 29|214| 74| 65| 87|176|163| 68|170| 30|172|

           ———————————————————————

         | 24|143|150|198|211|154| 50|100| 49| 67| 37|182| 33|166|131|

           ———————————————————————

           |101|142|117|218| 85|118| 54|146|179| 27| 69| 23|136|203| 77|

           ———————————————————————

           | 91|161|113|125|156| 58|202| 60| 32|162|121|188| 59|160| 7|

           ———————————————————————

           |159| 66| 71|148|139| 2|157| 84| 90|217|111| 78|187|110| 76|

           ———————————————————————

           |171|220| 39| 5| 88|177| 1|112|215| 25|147|128|133| 51|183|

           ———————————————————————

           |196| 40| 26| 10|116|200|225|164| 89|194|104|105| 31|132| 63|

           ———————————————————————

           | 13|174|158| 72|190| 93| 86| 56|199| 70|107| 55|193|123|106|

           ———————————————————————

                        Press key to continue…

Expert Answer

answers

here we have written program to calculate magic square. in which following inputs are required

1. Press ‘C’ to continue or ‘Q’ to quit the repeatation.

2. Enter the number for which you want magic square

————————————————————————–

CODE:

// author: rajdeep-paliwal

#include<stdio.h>

#include<string.h>

#include<iostream.h>

#include<stdlib.h>

// we wrote a function to generate odd sized magic squares

void generateSquare(int n)

{

int magicSquare[15][15];

// firstly set all slots as 0

memset(magicSquare, 0, sizeof(magicSquare));

// Initialize position for 1

int i = n/2;

int j = n-1;

// here we put all values one by one in magic square

for (int num=1; num <= n*n; )

{

if (i==-1 && j==n) //3rd condition

{

j = n-2;

i = 0;

}

else

{

// here we took 1st condition helper if next number

// goes to out of square’s right side

if (j == n)

j = 0;

// 1st condition helper if next number

// is goes to out of square’s upper side

if (i < 0)

i=n-1;

}

if (magicSquare[i][j]) //2nd condition

{

j -= 2;

i++;

continue;

}

else

magicSquare[i][j] = num++; //set number

j++; i–; //1st condition

}

// Print magic square

printf(“n The Magic Square for n=%d:n Sum of ”

“each row or column %d:nn”, n, n*(n*n+1)/2);

for (i=0; i<n; i++)

{

for (j=0; j<n; j++)

printf(“%3d “, magicSquare[i][j]);

printf(“n”);

}

}

// main function to operate other function

int main()

{

int n = 7; // Works only when n is odd. set 7 as default.

char c;

while(1)

{

cout << “nn Press C to Continue or Q to Quit: “;

cin >> c;

if(c == ‘Q’)

{

break;

}

cout << “nn Please enter the number: “;

cin >> n;

if(n%2 == 0)

{

cout << ” Please enter odd values only. Try again!”;

}

else

{

cout << “n You have entered ” << n;

generateSquare (n);

}

}

return 0;

}

—————————————————————————————–

OUTPUT:

DOSBox 0.74, Cpu speed: max 100% cycles, Frameskip 0, Program: :NTURBOC3 BIN>TC C NTURB0C3 Projects MAGICS 1.CPP Press C to Continue or Q to Quit: C Please enter the number 9 You have entered 9 The Magic Square for n-9 Sum of each row or columnm 369: 35 25 15 5 76 66 56 46 45 24 14 4 75 65 55 54 44 34 13 3 74 64 63 53 4333 23 2 73 72 62 52 42 32 22 12 81 71 61 51 41 31 21 11 1 70 60 50 40 30 20 10 9 80 59 49 39 29 19 18 8 79 69 48 38 28 27 1?7 7868 58 37 36 26 16 6 77 67 57 47 Press C to Continue or Q to Quit:

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