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Bit manipulation

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Basic bit operators

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Common tricks

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1. Check odd or even

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2. Swap two numbers without a temporary variable

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3. Check whether the k-th bit is 1

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4. Set the k-th bit to 1

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5. Set the k-th bit to 0

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6. Flip the k-th bit

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7. Extract the lowest 1 bit

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8. Remove the lowest 1 bit

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9. Check whether a number is a power of two

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10. Count the number of 1 bits in binary

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Classic problems

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LeetCode 136. Single Number

class Solution:
    def singleNumber(self, nums: List[int]) -> int:
        ans = 0
        for num in nums:
            ans ^= num
        return ans

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LeetCode 191. Number of 1 Bits

class Solution:
    def hammingWeight(self, n: int) -> int:
        count = 0
        while n:
            n &= n - 1
            count += 1
        return count

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LeetCode 231. Power of Two

class Solution:
    def isPowerOfTwo(self, n: int) -> bool:
        return n > 0 and (n & (n - 1)) == 0

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LeetCode 338. Counting Bits

class Solution:
    def countBits(self, n: int) -> List[int]:
        dp = [0] * (n + 1)
        for i in range(1, n + 1):
            dp[i] = dp[i >> 1] + (i & 1)
        return dp

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Typical use cases

• State compression: represent multiple boolean states with one integer
• Set operations: implement intersection, union, and complement through bit masks
• Permission systems: store different permissions as bits
• Performance optimization: use fast bitwise operations to replace some multiply/divide cases