check_finitary_relation(MS)

#include <iostream>
#include <algorithm>
#include <vector>
#include <utility>

using namespace std;

void printMatrix(vector<auto> v) {
    cout << '\n';
    for (auto i : v) {
        for (auto j : i)
            cout << j << ' ';
        cout << '\n';
    }
}

void printAnswer(int ref, int sym, bool tran) {
    cout << "Finitary relation is: ";
    if (ref == 1) cout << "Reflexive, ";
    else if (ref == 0) cout << "AntiReflexive, ";
    else cout << "Not-Reflexive, ";

    if (sym == 1) cout << "Symmetric, ";
    else if (sym == 0) cout << "AntiSymmetric, ";
    else cout << "Not-Symmetric, ";

    tran ? cout << "Transitive.\n" : cout << "Not-Transitive.\n";
}

vector<vector<bool>> transparency(vector<auto> v) {
    for (int i = 0; i < v.size(); i++) {
        for (int j = i; j < v.size(); j++)
            swap(v[i][j], v[j][i]);
    }
    return v;
}

int is_reflexsity(vector<auto>& v) {
    int cnt = 0;
    for (int i = 0; i < v.size(); i++)
        if (v[i][i] == 1) cnt++;
    return cnt == v.size() ? 1 : cnt == 0 ? 0 : -1; // 1 - Рефлексивность, 0 - Антиреф., -1 - Нерефлексивность
}

int is_symmetry(vector<auto>& v) {
    vector<vector<bool>> v2 = v;
    v2 = transparency(v2);
    //printMatrix(v2);
    int cnt = 0;
    for (int i = 0; i < v.size(); i++) {
        for (int j = 0; j < v.size(); j++) {
            if (i != j && (v[i][j] * v2[i][j])) cnt++;
        }
    }
    if (v == v2 && cnt != 0) return 1; // Симметрия
    if (cnt > 0) return -1; // Несимметрия
    return 0; // Антисимметрия
}

bool is_transit(vector<auto>& v) {
    bool ans = 1;
    for (int i = 0; i < v.size(); i++) {
        for (int j = 0; j < v.size(); j++) {
            for (int u = 0; u < v.size(); u++) {
                ans = v[i][j] >= min(v[i][u], v[u][j]);

                if (!ans) return ans; // Нетранзитивно
            }
        }

    }
    return ans; // Транзитивно
}

int main() {
    int n, dim, reflex, sym, transit;
    cout << "Input dimensions of set and count of pairs the finitary relation:\n";
    cin >> dim >> n;
    vector <pair<int,int>> vec(n);
    cout << "Input pairs:\n";
    for (int i = 0; i < n; i++)
        cin >> vec[i].first >> vec[i].second;

    vector <vector<bool>> matrix(dim, vector<bool>(dim));
    for (int i = 0; i < n; i++) {
        matrix[vec[i].first-1][vec[i].second-1] = 1;
    }

    printMatrix(matrix);
    reflex = is_reflexsity(matrix);
    sym = is_symmetry(matrix);
    transit = is_transit(matrix);

    printAnswer(reflex, sym, transit);
    system("Pause");
    return 0;
}