Maximum Bitwise AND Value of a Pair in an Array in C++

Problem statement

Given an array of n positive elements. we need to find the maximum bitwise AND value generated by any pair of element from the array.

Example

If input array is {10, 12, 15, 18} then maximum value of bitwise AND is 12.

Algorithm

The result of bitwise AND operations on single bit is maximum when both bits are 1. Considering this property −

• Start from the MSB and check whether we have minimum of two elements of array having set value
• If yes, then that MSB will be part of our solution and be added to result otherwise we will discard that bit
• Similarly, iterating from MSB to LSB (32 to 1) for bit position we can easily check which bit will be part of our solution and will keep adding all such bits to our solution

Example

Let us now see an example −

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int checkBits(int *arr, int n, int pattern) {
   int cnt = 0;
   for (int i = 0; i < n; ++i) {
      if ((pattern & arr[i]) == pattern) {
         ++cnt;
      }
   }
   return cnt;
}
int getMaxBitwiseAnd(int *arr, int n) {
   int result = 0;
   int count;
   for (int i = 31; i >= 0; --i) {
      count = checkBits(arr, n, result | (1 << i));
      if (count >= 2) {
         result |= (1 << i);
      }
   }
   return result;
}
int main() {
   int arr[] = {10, 12, 15, 18};
   int n = sizeof(arr) / sizeof(arr[0]);
   cout << "Maximum bitwise AND = " << getMaxBitwiseAnd(arr, n) << endl;
   return 0;
}

Output

Maximum bitwise AND = 12