Pattern

Bit Manipulation

Leverage binary operations for space and time efficiency.

7 Problems

5 Easy

2 Medium

0 Hard

How Bit Manipulation Works

Bit manipulation operates directly on the binary representation of numbers using bitwise operators: AND (&), OR (|), XOR (^), NOT (~), and shifts (<<, >>). XOR is especially powerful: a ^ a = 0 and a ^ 0 = a, so XORing all elements cancels out pairs, leaving the unique element. Common tricks include n & (n-1) to clear the lowest set bit, n & (-n) to isolate the lowest set bit, and bit masks to track state in O(1) space. This enables solving certain problems without extra data structures.

When to Use Bit Manipulation

Pattern Recognition

Look for these trigger words in problem statements:

single number bit-manipulation number of 1 bits counting bits reverse bits missing number sum of two integers reverse integer

Common Mistakes

Operator precedence errors — bitwise operators have lower precedence than comparison operators in most languages
Not considering signed vs unsigned integers (negative numbers have different bit patterns)
Assuming 32-bit integers when the problem uses different sizes
Overcomplicating solutions — bit manipulation should simplify, not obscure the logic

When NOT to Use Bit Manipulation

When a hash set or hash map solution is clearer and equally efficient
When the numbers are too large for fixed-width bit operations
When the bit manipulation trick is obscure and makes the code unreadable

Practice Problems

Easy (5) Medium (2) Hard (0)

Single Number easy Number of 1 Bits easy Counting Bits easy Reverse Bits easy Missing Number easy Sum of Two Integers medium Reverse Integer medium

Master Bit Manipulation

Build pattern recognition with interactive MCQs. Understand why to use Bit Manipulation, not just how.

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