💾 Bit Manipulation

Bit tricks turn $O(n)$ scans into single CPU instructions. The arsenal is small but the payoff is huge — memorize the idioms below and they will appear everywhere.

This category contains 14 problems. Use the patterns below to recognize what's being asked, then jump to the problem list at the bottom.

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🧠 Key Patterns

• XOR for "find unique" — a ^ a = 0, a ^ 0 = a. Single Number family.
• Clear lowest set bit — n & (n - 1) — count set bits, power-of-two check.
• Bitmask DP — State = subset of items, often up to ~20 elements.
• Bit-by-bit reconstruction — Sum each bit position mod 3, mod k, etc.
• Built-ins — BitOperations.PopCount, LeadingZeroCount, TrailingZeroCount (C#).

⚠️ Common Pitfalls

• Signed vs unsigned shifts. >> on negative int keeps the sign bit. Use (uint).
• Operator precedence: (x & 1) == 0 needs the parens.

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📚 Study Resources

📺 Videos

• Errichto — Bitmasks
• NeetCode — Bit Manipulation

📖 Books

• Hacker's Delight — Henry S. Warren — The definitive bit-twiddling reference
• Competitive Programming Handbook — Laaksonen — Ch. 10

🌐 Articles & References

• Bit Twiddling Hacks — Sean Eron Anderson

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💻 All Bit Manipulation Problems

📄️Biggest Single Number

LeetCode 619 | Difficulty: Easy

📄️Bitwise AND of Numbers Range

LeetCode 201 | Difficulty: Medium

📄️Counting Bits

LeetCode 338 | Difficulty: Easy

📄️Hamming Distance

LeetCode 461 | Difficulty: Easy

📄️Missing Number

LeetCode 268 | Difficulty: Easy

📄️Number of 1 Bits

LeetCode 191 | Difficulty: Easy

📄️Power of Four

LeetCode 342 | Difficulty: Easy

📄️Power of Three

LeetCode 326 | Difficulty: Easy

📄️Power of Two

LeetCode 231 | Difficulty: Easy

📄️Reverse Bits

LeetCode 190 | Difficulty: Easy

📄️Single Number

LeetCode 136 | Difficulty: Easy

📄️Single Number II

LeetCode 137 | Difficulty: Medium

📄️Sort Integers by The Number of 1 Bits

LeetCode 1458 | Difficulty: Easy

📄️Total Hamming Distance

LeetCode 477 | Difficulty: Medium