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  1. Prepare
  2. Algorithms
  3. Implementation
  4. Forming a Magic Square
  5. Discussions

Forming a Magic Square

  • eidolon_2003
     + 1 comment

    Probably the simplest solution you could think of

    // All eight possible magic squares
static const vector<vector<int>> squares[8] = {
    {
        { 8, 3, 4 },
        { 1, 5, 9 },
        { 6, 7, 2 }
    },
    {
        { 6, 7, 2 },
        { 1, 5, 9 },
        { 8, 3, 4 }
    },
    {
        { 4, 3, 8 },
        { 9, 5, 1 },
        { 2, 7, 6 }
    },
    {
        { 2, 7, 6 },
        { 9, 5, 1 },
        { 4, 3, 8 }
    },
    {
        { 6, 1, 8 },
        { 7, 5, 3 },
        { 2, 9, 4 }
    },
    {
        { 2, 9, 4 },
        { 7, 5, 3 },
        { 6, 1, 8 }
    },
    {
        { 8, 1, 6 },
        { 3, 5, 7 },
        { 4, 9, 2 }
    },
    {
        { 4, 9, 2 },
        { 3, 5, 7 },
        { 8, 1, 6 }
    }
};

int computeCost(const vector<vector<int>> &a, const vector<vector<int>> &b) {
    int cost = 0;
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            cost += abs(a[i][j] - b[i][j]);
        }
    }
    return cost;
}

int formingMagicSquare(vector<vector<int>> s) {
    int minCost = computeCost(s, squares[0]);
    
    for (int i = 1; i < 8; i++) {
        int c = computeCost(s, squares[i]);
        if (c < minCost) minCost = c;
    }
    
    return minCost;
}