Question

Java Magic Square:
A n x n matrix that is filled with the numbers 1, 2, 3,.... n^2 is a magic square if the sum of the elements in each row, in each column, and in the two diagonals is the same value.
I need to write an application that gets 16 values as user input, in any order. Store these values in an ArrayList. When the numbers are put into a square, this would be a 4x4 two-dimensional array.

Here's an example where n 4: 16 32 13 5 10 11 8 9 67 12 4 15 14 Let's look to see if it's a magic square. 34 34 8 34 12 34 34 34 10 11 6 15 14 7 4 34 34 34 34

Then test the following features to see if the numbers entered make a magic square:

1. Does each of the numbers 1 - 16 occur in the input? Note: I must perform this check from the ArrayList using the "contains" method.
2. Are the sums of the rows, columns, and diagonals equal to each other? If possible: when you store the number in the ArrayList, store it in a two-dimensional array too.

Here’s a sample run (user input in bold): Enter the numbers 1 - 16 in any order: 12 13 2 7 6 3 16 9 15 10 5 4 1 8 11 14 - You found a magic square! -
Here’s another example: This time it’s not going to work: Enter the numbers 1 - 16 in any order: 2 3 7 10 9 16 4 5 12 8 1 15 14 11 13 6 - The numbers you have entered are not a magic square.
And one more that won’t work: Enter the numbers 1 - 16 in any order: 12 13 2 7 6 3 16 9 16 10 5 4 1 8 11 14 - The numbers you have entered are not a magic

Answer 1

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

#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;
cout<<"Enter order of square: ";
cin>>n;

vector<vector<int> > matrix(n, vector<int> (n, 0));

MagicSquare(matrix, n);

//Print results

PrintMagicSquare(matrix, n);

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++)
cout<<" "<<" "<<matrix[i][j];

cout<<("\n");
}

cout<<"\n\n";
}

Kindly revert for any queries

Thanks.