Triples with Bitwise AND Equal To Zero in C++

Suppose we have an array of integers A. We have to find the number of triples of indices (i, j, k) such that −

• 0 <= i < size of A

• 0 <= j < size of A

• 0 <= k < size of A

A[i] AND A[j] AND A[k] is 0, where AND represents the bitwise-AND operator.

So, if the input is like [3,1,2], then the output will be 12

• To solve this, we will follow these steps −

• Define one map m

• ret := 0

• n := size of A

• for initialize i := 0, when i < n, update (increase i by 1), do −

  • for initialize j := 0, when j < n, update (increase j by 1), do −

    • for initialize j := 0, when j < n, update (increase j by 1), do −

• for initialize i := 0, when i < n, update (increase i by 1), do −

  • x := A[i]

  • for all key-value pairs a in m

    • if (a.key AND x) is same as 0, then −

      • ret := ret + a.value

• return ret

Let us see the following implementation to get better understanding −

Example

 Live Demo

#include <bits/stdc++.h> using namespace std; class Solution {    public:    int countTriplets(vector<int>& A){       unordered_map<int, int> m;       int ret = 0;       int n = A.size();       for (int i = 0; i < n; i++) {          for (int j = 0; j < n; j++) {             m[A[i] & A[j]]++;          }       }       for (int i = 0; i < n; i++) {          int x = A[i];          for (auto& a : m) {             if ((a.first & x) == 0) {                ret += a.second;             }          }       }       return ret;    } }; main(){    Solution ob;    vector<int> v = {3,1,2};    cout << (ob.countTriplets(v)); }

Input

{3,1,2}

Output

12