Count Set Bits / Reverse Bits

Problem
Two related bit-manipulation tasks. First, count the number of set (1) bits in an integer (the Hamming weight). Second, reverse the bits of a 32-bit unsigned integer so the least-significant bit becomes the most-significant and vice versa.

Input / Output

• Input: a 32-bit unsigned integer n.
• Output: for the first task, the count of 1-bits; for the second, the integer whose bit pattern is the reverse of n.

Constraints

• n is a 32-bit unsigned integer.
• Aim for time better than a naive 32-iteration scan where possible, and discuss a constant-time lookup-table variant.

Example

• countBits(0b1011) -> 3
• reverse(0b00000000000000000000000000000001) -> 0b10000000000000000000000000000000