Count_Lucky_Permutation.cpp

class Solution {
  public:
    long long int luckyPermutations(int N, int M, vector<int> arr,vector<vector<int>> graph) {

        vector<vector<long long int>> dp(N, vector<long long int>(1<<N, 0));
        for (int i = 0; i < N; i++) {
            dp[i][1 << i] = 1;   
        }
        vector<vector<int>> adj(N, vector<int>(N, 0));
        for (vector<int> edge : graph) {
            adj[edge[0] - 1][edge[1] - 1] = 1;
            adj[edge[1] - 1][edge[0] - 1] = 1;
        }
        
        for (int bitmask = 1; bitmask < (1 << N); bitmask++) {
            for (int i = 0; i < N; i++) {
                if ((1 & (bitmask >> i))) {
                    for (int j = 0; j < N; j++) {
                        if (j!= i && arr[j]!=arr[i] &&
                            (1 & (bitmask >> j)) && adj[arr[i]-1][arr[j] - 1]) {
                                dp[i][bitmask] += dp[j][bitmask ^ (1 << i)];
                        }
                    }
                }
            }
        }
        
        long long int ans = 0;
        for (int i = 0; i < N; i++) {
            ans += dp[i][(1 << N) - 1];            
        }
        return ans;
    }
};