Total Hamming Distance - Solution & Explanation

This approach involves calculating the Hamming distance for each pair of numbers by comparing their binary representations. This naive method checks each bit position from the least significant bit to the most significant bit for each pair.

This C code defines a function hammingDistance that calculates the Hamming distance between two integers by XORing them and counting the number of 1s in the result. The totalHammingDistance function calculates the sum of Hamming distances for every pair in the array nums.

For each bit position, count how many numbers have that bit set. The number of pairs from two sets, one having the bit set and the other not, can be computed directly. This reduces the complexity significantly.

This C code iterates through each bit position from 0 to 31. bitCount keeps track of how many numbers have the current bit set. The Hamming distance contribution of this bit is given by bitCount * (numsSize - bitCount).