Total Hamming Distance is an example of math problems. In this post we will see how we can solve it in Javascript.

Problem Description

The Hamming distance between two integers is the number of positions at which the corresponding bits are different.

Now your job is to find the total Hamming distance between all pairs of the given numbers.


Input: 4, 14, 2
Output: 6


In binary representation, the 4 is 0100, 14 is 1110, and 2 is 0010 (just showing the four bits relevant in this case). So the answer will be:

HammingDistance(4, 14) + HammingDistance(4, 2) + HammingDistance(14, 2) = 2 + 2 + 2 = 6.


  • Elements of the given array are in the range of 0 to 10^9
  • Length of the array will not exceed 10^4.


  •  For each bit position 1-32 in a 32-bit integer, we count the number of integers in the array which have that bit set.
  • Then, if there are n integers in the array and k of them have a particular bit set and (n-k) do not, then that bit contributes
  • k*(n-k) hamming distance to the total.

Implementation: Please check the main.js snippet for the solution. If you have different approach in mind or have any suggestion for this implementation feel free to share in the comment below. Thanks!

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