Given two integers A and B. The task is to choose an integer X such that (A xor X) + (B xor X) is minimum possible.
Input: A = 2, B = 3
Output: X = 2, Sum = 1
Input: A = 7, B = 8
Output: X = 0, Sum = 15
A simple solution is to generate all possible sum by taking xor of A and B with all possible value of X ≤ min(A, B). To generate all possible sums it would take O(N) time where N = min(A, B).
An efficient solution is based on the fact that the number X will contain the set bits only at that index where both A and B contains a set bit such that after xor operation with X that bit will be unset. This would take only O(Log N) time.
Other cases: If at a particular index one or both the numbers contain 0 (unset bit) and the number X contains 1 (set bit) then 0 will be set after xor with X in A and B then the sum couldn't be minimized .
Below is the implementation of the above approach:
X = 2, Sum = 1
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