Using Siamese method fill a Magic Square Matrix

buildMagic.cpp

// buildMagic.cpp
// juanfc 2018-01-17
// Using Siamese method fill a Magic Square Matrix,
// odd fixed size.
// We have used a big square matrix, but used
// an extra parameter to restrict to that size
// 
// Testing it building magic matrices up to a size
// checking they really are magic and printing them
// https://gist.github.com/6db44e77b75d3aacdfa70bdfb7972ef1
#include <iostream>
#include <iomanip>
#include <array>
using namespace std;

const int NMAX = 15;
typedef array<int, NMAX> TRow;
typedef array<TRow, NMAX> TSqMat;

TSqMat buildMagicSquare (int N);
void testAndPrintMagicSq(TSqMat m, int N);

int main()
{
    for (int size = 1; size <= NMAX; size += 2)
        testAndPrintMagicSq(buildMagicSquare(size), size);
    return 0;
}

TSqMat buildMagicSquare (int N)
{
    TSqMat m;
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            m[i][j] = 0;

    int i, j;
    int key = 1;
    int NN = N * N;
    i = 0;
    j = (N - 1) / 2;
    m[i][j] = key++;  // middle of the top row
    while (key <= NN) {
        int ii, jj;  // try, look ahead beforehand

        if (i > 0) ii = i-1;
        else       ii = N-1;

        if (j < N-1) jj = j+1;
        else         jj = 0;

        if (m[ii][jj] != 0)  // taken cell
            i = (i+1) % N;   // go down
        else {
            i = ii;  // alright, take them
            j = jj;
        }
        m[i][j] = key++;
    }
    return m;
}

bool isMagic(TSqMat m, int N);

void testAndPrintMagicSq(TSqMat m, int N)
{
    cout << endl << "Magic Square of size: " << N;
    int s = 0;
    for (int i = 0; i < N; i++)
        s += m[i][0];
    cout << ". Sum: " << s << endl;
    cout << (isMagic(m, N)? "IS":"is NOT")
         << " magic" << endl;
    // display it
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++)
            cout << setw(4) << m[i][j];
        cout << endl << endl;
    }
}

int sumRow(TSqMat m, int row, int N);
int sumCol(TSqMat m, int col, int N);

bool isMagic(TSqMat m, int N)
{
    bool ok = true;
    int magic = sumRow(m, 0, N);
    int i = 1;
    while (i<N and ok)
        ok = (magic == sumRow(m, i++, N));

    i = 0;
    while (i<N and ok)
        ok = (magic == sumCol(m, i++, N));

    if (ok) {
        int s = 0;
        for (int i = 0; i < N; ++i)
            s += m[i][i];
        ok = magic == s;
    }
    if (ok) {
        int s = 0;
        for (int i = 0; i < N; ++i)
            s += m[i][N-1-i];
        ok = magic == s;
    }
    return ok;
}

int sumRow(TSqMat m, int row, int N)
{
    int s = 0;
    for (int i = 0; i < N; ++i)
        s += m[row][i];
    return s;
}

int sumCol(TSqMat m, int col, int N)
{
    int s = 0;
    for (int i = 0; i < N; ++i)
        s += m[i][col];
    return s;
}