prob1

#include <bits/stdc++.h>

using namespace std;

#define cin fin
#define cout fout
ifstream fin("prob.in");
ofstream fout("prob.out");

int n;
float a[100][100];

void out() {
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++)
            cout << setw(7) << a[i][j];
        cout << endl;
    }
    cout << endl;
}

float determinant() {
    int flag = 0;

    float det = 1;
    for (int i = 1; i <= n; i++)
        for (int k = i + 1; k <= n; k++)
            if (abs(a[i][i]) < abs(a[k][i])) {
                flag++;
                for (int j = 1; j <= n; j++)
                    swap(a[i][j], a[k][j]);
            }
    for (int i = 1; i <= n - 1; i++) // loopul principal a lu gauss
        for (int k = i + 1; k <= n; k++) {
            float t = a[k][i] / a[i][i];
            for (int j = 1; j <= n; j++)
                a[k][j] = a[k][j] - t * a[i][j];
        }
    for (int i = 1; i <= n; i++)
        det = det * a[i][i];
    if (flag % 2 == 0)
        det = det;
    else
        det = -det;
    return det;
}

bool prim(int m) {
    if (m < 2) return false;
    for (int i = 2; i < m; i++)
        if (m % i == 0)
            return false;
    return true;
}

int main() {

    std::vector<int> prime;

    cout << "Dati n: "; cin >> n;
    cout << "Dati matricea:\n";

    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= n; j++) {
            cin >> a[i][j];
            if (i == j) prime.push_back(a[i][j]);
        }

    cout << "Avem matricea:\n"; out();

    double det = determinant();
    cout << "Det(A) = " << setw(6) << setprecision(4) << determinant() << endl;

    if (det != 0) {
        int index = 0;
        while (index < prime.size()) {
            if (!prim(prime[index])) {
                prime.erase(prime.begin()+index);
            } else {
                index++;
            }
        }
        if (prime.size() == 0)
            cout << "Nu avem numere prime pe diagonala principala\n";
        else {
            cout << "Numere prime pe diagonala principala: " << prime.size() << ":" << endl;
            for (auto &it: prime) cout << it << " ";
            cout << endl;
        }
    } else {
        cout << "De la diagonala in jos e zero" << endl;
    }




    return 0;
}