using namespace std;

void getCfactor(vector<vector<float >> &M, vector<vector<float >> &t, int p, int q, int n) {
    int i = 0, j = 0;
    for (int r = 0; r < n; r++) {
        for (int c = 0; c < n; c++) //Copy only those elements which are not in given row r and column c: {
            if (r != p && c != q) {
                t[i][j++] = M[r][c]; //If row is filled increase r index and reset c index
                if (j == n - 1) {
                    j = 0;
                    i++;
                }
            }
    }
}

float DET(vector<vector<float >> &matrix, int n) {
    float D = 0;
    if (n == 1)
        return matrix[0][0];

    vector<vector<float>> t = vector<vector<float>> (matrix.size());
    for (int i = 0; i < matrix.size(); i++) {
        t[i] = vector<float > (matrix.size());
    }
    float s = 1; //store sign multiplier //
    for (int f = 0; f < n; f++) {
        getCfactor(matrix, t, 0, f, n);
        D += s * matrix[0][f] * DET(t, n - 1);
        s = -s;
    }
    return D;
}

void ADJ(vector<vector<float >> &M, vector<vector<float >> &adj) {
    if (M.size() == 1) {
        adj[0][0] = 1;
        return;
    }
    float s = 1;
    vector<vector<float>> t = vector<vector<float>> (M.size());
    for (int i = 0; i < M.size(); i++) {
        t[i] = vector<float > (M.size());
    }
    for (int i = 0; i < M.size(); i++) {
        for (int j = 0; j < M.size(); j++) {
            getCfactor(M, t, i, j, M.size());
            s = ((i + j) % 2 == 0) ? 1 : -1; //sign of adj[j][i] positive if sum of row and column indexes is even.
            adj[j][i] = (s) * (DET(t, M.size() - 1)); //Interchange rows and columns to get the transpose of the cofactor matrix
        }
    }
}

bool INV(vector<vector<float>> &matrix, vector<vector<float>> &res) {
    float det = DET(matrix, matrix.size());
    if (det == 0) {
        cout << "can't find its inverse";
        return false;
    }
    vector<vector<float>> adj = vector<vector<float>>(matrix.size());
    for (int i = 0; i < matrix.size(); i++) {
        adj[i] = vector<float > (matrix.size());
    }
    ADJ(matrix, adj);
    for (int i = 0; i < matrix.size(); i++) for (int j = 0; j < matrix.size(); j++) res[i][j] = adj[i][j] / float(det);
    return true;
}