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#include <iostream>
#include <vector>

using namespace std;

namespace HamiltonianCycle {

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

    bool hamCycleUtil(const vector<vector<int>>& 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<int>>& 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;
    }

}  // namespace HamiltonianCycle

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

    vector<vector<int>> graph(V, vector<int>(V, 0));

    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];
        }
    }

    HamiltonianCycle::hamCycle(graph, V);

    return 0;
}
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