Bit operation can efficiently implement the underlying operation of integers. 1. Check whether the i-th bit is 1: Use n & (1 0 && (n & (n-1)) == 0; 6. Statistics the number of 1: Use n &= (n-1) to clear the last bit 1 and finally return the count. These techniques are widely used in state compression, algorithm optimization and set operations.
Bit Manipulation is a technology that efficiently handles underlying data operations in C, and is often used to optimize performance, save memory or implement algorithms. The following is a practical example to show common bit operation techniques.

? Example: Common operations to implement integers using bit operations
Suppose we have an integer and want to complete the following tasks through bit operations:
- Check if a certain number is 1
- Set a certain bit to 1
- Clear one
- Flip a certain one
- Determine whether it is a power of 2
- Statistics the number of 1 in binary
#include <iostream> using namespace std; // 1. Check whether the i-th bit is 1 (starting from the 0th bit from the right) bool isBitSet(int n, int i) { return (n & (1 << i)) != 0; } // 2. Set the i-th bit to 1 int setBit(int n, int i) { return n | (1 << i); } // 3. Clear the i-th bit int clearBit(int n, int i) { return n & ~(1 << i); } // 4. Flip the i-th bit int flipBit(int n, int i) { return n ^ (1 << i); } // 5. Determine whether it is a power of 2 (positive number and only one 1) bool isPowerOfTwo(int n) { return n > 0 && (n & (n - 1)) == 0; } // 6. Statistics the number of 1 in binary (Brian Kernighan algorithm) int countSetBits(int n) { int count = 0; while (n) { n &= (n - 1); // Clear the lowest 1 at each time count ; } return count; } int main() { int num = 12; // Binary: 1100 cout << "Number: " << num << " (binary: "; for (int i = 3; i >= 0; --i) { cout << ((num >> i) & 1); } cout << ")\n"; // Check if the second bit is 1 cout << "Bit 2 is set: " << isBitSet(num, 2) << endl; // 1 (true) // Set the 1st bit num = setBit(num, 1); // 1100 -> 1110 (14) cout << "After setting bit 1: " << num << endl; // Clear the 3rd bit num = clearBit(num, 3); // 1110 -> 0110 (6) cout << "After clearing bit 3: " << num << endl; // Flip bit 0 num = flipBit(num, 0); // 0110 -> 0111 (7) cout << "After flipping bit 0: " << num << endl; // determine whether it is a power of 2 cout << "Is power of two: " << isPowerOfTwo(num) << endl; // 7 -> false // Statistics 1 cout << "Number of set bits: " << countSetBits(12) << endl; // 12 -> 1100 -> 2 return 0; }
? Key points description
-
1 : Create a mask with only the i-th bit being 1.
-
&
: Used to detect bits (and operations). -
|
: Used to set bits (or operations). -
~
: Inverse bit by bit, cooperate&
achieve zeroing. -
^
: Exclusive OR, the same is 0, and the difference is 1, suitable for flip. -
n & (n - 1)
: Classic trick, clear the rightmost 1 at each time.
? Application scenarios
- State compression (such as using one int to represent multiple boolean states)
- Hash algorithm, encryption algorithm
- Efficient collection operations (such as bitmaps)
- In algorithm problems, judge odd or even, exchange variables (
a ^= b ^= a ^= b
), deduplication, etc.
Basically that's it. Bit operation seems to be the underlying layer, but after mastering it, you can write more efficient and "cool" code.

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