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M@gic squ@res

moshoo (1)
Hi,
I'm working on c++ magic squares project to generate a random magic squares.
i already did the project but he said that this code only generate the same numbers every time i enter the size of the matrix. for example if you chose size 3 it will give

| 8 | 1 | 6 |

| 3 | 5 | 7 |

| 4 | 9 | 2 |

so when you chose to repeat the program, it has to give me the numbers in different order but still have to be magic squares.

he said that i need to use random function but i'm not sure how to use them on this code?

may someone help me please?

this is my code

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#include <vector>
#include<iostream>

using namespace std;

void OddMagicSquare(vector<vector<int> > &matrix, int n);
void DoublyEvenMagicSquare(vector<vector<int> > &matrix, int n);
void SinglyEvenMagicSquare(vector<vector<int> > &matrix, int n);
void MagicSquare(vector<vector<int> > &matrix, int n);
void PrintMagicSquare(vector<vector<int> > &matrix, int n);

int main(int argc, char* argv[])
{
    int n;
	char again=0;
	do{
       
        
        
		cout<<"\t\t\tEnter order of square: ";
        scanf("%d", &n);
        while (n<3 || n>15)
        {
            cout<<"\nError: n must be greater than 2 and less than 16:";
            cin.clear();
            fflush(stdin);
            cin>>n;
            
            
        }
        cout<<"\t\t    ===============================\n\n"<< endl;
        vector<vector<int> > matrix(n, vector<int> (n, 0));
        
        
        
        MagicSquare(matrix, n);
        
        //Print results
        PrintMagicSquare(matrix, n);
        cout << " Do you want to continue? (y/n)";
        cin>>again;
	}while( again=='Y' || again=='y');
	
	system("pause");
    return 0;
}

void MagicSquare(vector<vector<int> > &matrix,int n)
{
    if (n%2==1)        //n is Odd
        OddMagicSquare(matrix, n);
    else          //n is even
        if (n%4==0)    //doubly even order
            DoublyEvenMagicSquare(matrix, n);
        else      //singly even order
            SinglyEvenMagicSquare(matrix, n);
}

void OddMagicSquare(vector<vector<int> > &matrix, int n)
{
    int nsqr = n * n;
    int i=0, j=n/2;     // start position
    
    for (int k=1; k<=nsqr; ++k)
    {
        matrix[i][j] = k;
        
        i--;
        j++;
        
        if (k%n == 0)
        {
            i += 2;
            --j;
        }
        else
        {
            if (j==n)
                j -= n;
            else if (i<0)
                i += n;
        }
    }
}

void DoublyEvenMagicSquare(vector<vector<int> > &matrix, int n)
{
    vector<vector<int> > I(n, vector<int> (n, 0));
    vector<vector<int> > J(n, vector<int> (n, 0));
    
    int i, j;
    
    //prepare I, J
    int index=1;
    for (i=0; i<n; i++)
        for (j=0; j<n; j++)
        {
            I[i][j]=((i+1)%4)/2;
            J[j][i]=((i+1)%4)/2;
            matrix[i][j]=index;
            index++;
        }
    
    for (i=0; i<n; i++)
        for (j=0; j<n; j++)
        {
            if (I[i][j]==J[i][j])
                matrix[i][j]=n*n+1-matrix[i][j];
        }
}

void SinglyEvenMagicSquare(vector<vector<int> > &matrix, int n)
{
    int p=n/2;
    
    vector<vector<int> > M(p, vector<int> (p, 0));
    MagicSquare(M, p);
    
    int i, j, k;
    
    for (i=0; i<p; i++)
        for (j=0; j<p; j++)
        {
            matrix[i][j]=M[i][j];
            matrix[i+p][j]=M[i][j]+3*p*p;
            matrix[i][j+p]=M[i][j]+2*p*p;
            matrix[i+p][j+p]=M[i][j]+p*p;
        }
    
    if (n==2)
        return;
    
    vector<int> I(p, 0);
    vector<int> J;
    
    for (i=0; i<p; i++)
        I[i]=i+1;
    
    k=(n-2)/4;
    
    for (i=1; i<=k; i++)
        J.push_back(i);
    
    for (i=n-k+2; i<=n; i++)
        J.push_back(i);
    
    int temp;
    for (i=1; i<=p; i++)
        for (j=1; j<=J.size(); j++)
        {
            temp=matrix[i-1][J[j-1]-1];
            matrix[i-1][J[j-1]-1]=matrix[i+p-1][J[j-1]-1];
            matrix[i+p-1][J[j-1]-1]=temp;
        }
    
    //j=1, i
    //i=k+1, k+1+p
    i=k;
    j=0;
    temp=matrix[i][j]; matrix[i][j]=matrix[i+p][j]; matrix[i+p][j]=temp;
    
    j=i;
    temp=matrix[i+p][j]; matrix[i+p][j]=matrix[i][j]; matrix[i][j]=temp;
}


void PrintMagicSquare(vector<vector<int> > &matrix, int n)
{
    for (int i=0; i<n; i++)
    {
        for (int j=0; j<n; j++)
            
            printf(" |%3d ", matrix[i][j]);
        
        cout<<"|\n\n";
    }
    
    cout<<"\n\n";
}
Last edited on
codewalker (394)
Duthomhas (13206)
Props actually on doing a very good job.

I don't know enough about generating magic squares, but it appears there are several hundred 4-squares at least.

There are only eight different 3-squares, and they are all some simple transformation of the same thing (rotation or reflection).

Unfortunately, the methods to generate magic squares seem fairly deterministic. The random function won't help much with that...

You might want to ask 'him' (your professor?) to review your code as-is and make a real suggestion on how to generate a different magic square.

Sorry I can't be of more help.
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