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#include <iostream>
#include <vector>
using namespace std;

void printSolution(int path[], int V);

bool hamCycleUtil(const vector<vector<bool>>& graph, int path[], int pos, int V) {
    if (pos == V) {
        if (graph[path[pos - 1]][path[0]] == 1)
            return true;
        else
            return false;
    }

    for (int v = 1; v < V; v++) {
        if (graph[path[pos - 1]][v] == 1 && path[v] == -1) {
            path[pos] = v;
            if (hamCycleUtil(graph, path, pos + 1, V))
                return true;
            path[pos] = -1;
        }
    }

    return false;
}

bool hamCycle(const vector<vector<bool>>& graph, int V) {
    int* path = new int[V];
    for (int i = 0; i < V; i++)
        path[i] = -1;

    path[0] = 0;
    if (hamCycleUtil(graph, path, 1, V) == false) {
        cout << "\nSolution does not exist";
        delete[] path;
        return false;
    }

    cout << "Solution Exists: Following are all Hamiltonian Cycles \n";
    printSolution(path, V);

    delete[] path;
    return true;
}

void printSolution(int path[], int V) {
    for (int i = 0; i < V; i++)
        cout << path[i] << " ";
    cout << path[0] << " ";
    cout << endl;
}

int main() {
    int V;
    cout << "Enter the number of vertices (V): ";
    cin >> V;

    vector<vector<bool>> graph(V, vector<bool>(V, false));

    cout << "Enter the adjacency matrix for the graph (0 or 1):\n";
    for (int i = 0; i < V; i++) {
        for (int j = 0; j < V; j++) {
            cin >> graph[i][j];
        }
    }

    hamCycle(graph, V);

    return 0;
}