Find Subsequences with Maximum Bitwise AND and Bitwise OR in Python

Suppose we have an array of n elements, we have to show the maximum sum by choosing two subsequences of the array (they may or may not be different) so that the sum of bit-wise AND operation of all elements of the first subsequence and bit-wise OR operation of all the elements of the second subsequence is maximum.

So, if the input is like A = {4, 6, 7, 2}, then the output will be 14 as we are getting maximum AND value by selecting 7 only and maximum OR value by selecting all (4 | 6 | 7 | 2) = 7. So, the result will be 7 + 7 = 14.

To solve this, we will follow these steps −

• and_max := maximum of arr

• or_max := 0

• for i in range 0 to size of arr, do

  • or_max := or_max OR arr[i]

• return and_max + or_max

Example 

Let us see the following implementation to get better understanding −

 Live Demo

def get_max_sum(arr):
   and_max = max(arr)
   or_max = 0
   for i in range(len(arr)):
      or_max|= arr[i]
   return and_max + or_max
a = [4,6,7,2]
print(get_max_sum(a))

Input

[4,6,7,2]

Output

14