Total Hamming Distance

MediumBit Manipulationbit manipulation

Solve this the way you would in the interview: out loud, on a timer, with an AI interviewer asking follow-ups while you code. You get a scored report at the end.

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Problem

The **Hamming distance** between two integers is the number of bit positions at which their binary representations differ. Given an integer array nums, return the sum of the Hamming distances over **all unordered pairs** (i, j) with i < j. Aim for O(n * B) time where B is the number of bits, instead of comparing every pair.

Examples

Input: nums = [4,14,2]
Output: 6
4 = 0100, 14 = 1110, 2 = 0010. Distances: (4,14) = 2, (4,2) = 2, (14,2) = 2, total 6.
Input: nums = [4,14,4]
Output: 4
(4,14) = 2, (4,4) = 0, (14,4) = 2.

Constraints

  • 1 <= nums.length <= 10^4
  • 0 <= nums[i] <= 10^9
  • The answer fits in a 32-bit signed integer

What the interviewer grades

A correct solution is one of five scores. The report also grades problem understanding (did you clarify inputs and edge cases before coding), problem solving, communication while you work, code quality, and testing. See a sample report, or read up on the pattern in the lessons.

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