Bit Manipulation

Work directly on a number's binary representation using bitwise operators — often turning an O(n) or O(log n) problem into a handful of O(1) operations.

Key concepts

• XOR cancels out identical values (x ^ x = 0), which is why it's used to find a single "odd one out" among pairs.
• AND/OR/shifts are used to check, set, clear, or move individual bits.
• `n & (n - 1)` clears the lowest set bit — a classic trick for counting set bits.

When to use it

• The problem talks about bits directly (count set bits, reverse bits, single number among duplicates).
• You want a constant-time trick instead of a loop for a numeric problem.

Tips

• XOR-ing every element together is the standard trick when "every value appears twice except one."
• `n & (n - 1)` removes the lowest set bit — useful for counting bits or checking if a number is a power of two.
• Watch for language-specific behavior with negative numbers and sign bits when shifting.

Practice problems (7)

Blind 75 (5):

• Number of 1 Bits Easy — Read & practice · LeetCode ↗
• Counting Bits Easy — Read & practice · LeetCode ↗
• Reverse Bits Easy — Read & practice · LeetCode ↗
• Missing Number Easy — Read & practice · LeetCode ↗
• Sum of Two Integers Medium — Read & practice · LeetCode ↗

More from Blind 150 (2):

• Single Number Easy — Read & practice · LeetCode ↗
• Reverse Integer Medium — Read & practice · LeetCode ↗