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Check if bits in Range L to R of Two Numbers are Complement of Each other or Not in C++

To check if the bits in a given range [L, R] of two numbers are complements of each other in C++, you can use bitwise operations. The XOR (^) operator is particularly useful for this task because XORing two bits results in 1 if the bits are different (complements) and 0 if they are the same.

Here’s a C++ function to check if the bits in the specified range [L, R] of two numbers are complements:

C++
#include <iostream>

bool areBitsComplements(int num1, int num2, int L, int R) {
    // Create a mask with 1s in the range [L, R]
    int mask = ((1 << (R - L + 1)) - 1) << L;

    // Extract the bits in the specified range from both numbers
    int bits1 = (num1 & mask) >> L;
    int bits2 = (num2 & mask) >> L;

    // Check if the bits are complements by XORing them
    return (bits1 ^ bits2) == ((1 << (R - L + 1)) - 1);
}

int main() {
    int num1 = 12; // Binary: 1100
    int num2 = 3;  // Binary: 0011
    int L = 0;
    int R = 3;

    bool result = areBitsComplements(num1, num2, L, R);

    if (result) {
        std::cout << "Bits in range [" << L << ", " << R << "] are complements." << std::endl;
    } else {
        std::cout << "Bits in range [" << L << ", " << R << "] are not complements." << std::endl;
    }

    return 0;
}

In this example:

  • The areBitsComplements function takes two numbers, num1 and num2, as well as the range [L, R] to check.
  • It creates a mask with 1s in the specified range [L, R] using bitwise operations.
  • It extracts the bits in the specified range from both num1 and num2 using bitwise AND and shifting.
  • It XORs the extracted bits and checks if the result is a sequence of 1s, which would indicate that the bits in the range are complements.
  • Finally, the main function demonstrates how to use this function to check if the bits in the range [L, R] of num1 and num2 are complements.

Keep in mind that this code assumes that the range [L, R] is valid and within the bit-width of the integers being checked.

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