When to Use

Look for these signals in the problem:

• "Single number" among pairs: XOR cancels paired numbers, leaving the single one.
• "Power of $2$" check: n & (n-1) equals $0$ only for powers of $2$.
• "Count bits" or Hamming operations: Bit counting techniques like Brian Kernighan's algorithm.
• "Subset" enumeration with bitmask: Each bit represents inclusion/exclusion of an element.
• "No extra space" constraint: Bit manipulation often achieves $O(1)$ space where other approaches need $O(n)$.