Minimum Flips to Make a OR b Equal to c

The least-significant bit (LSB) is the rightmost bit in a binary number, with the most significant bit (MSB) being on the left. Bitwise operations are frequently used to manipulate individual bits within binary numbers. One common application is solving problems that involve finding the minimum number of bit flips required to satisfy a specific condition. In this article, we’ll explore a solution to the minimum flips problem using bitwise operations in C++.

Problem Description:
In this problem, we are given three positive numbers: a, b, and c. The goal is to determine the minimum number of bit flips needed in the binary representations of numbers a and b in order to make their bitwise OR operation equal to c. A flip operation involves changing any single bit from 1 to 0 or from 0 to 1. The output should be the minimum number of flips required to achieve the desired condition (a OR b == c).

Solution Approach:
The solution approach involves using bitwise operations to iterate through the binary representations of the numbers a, b, and c, and counting the minimum number of flips needed to ensure that the bitwise OR operation of a and b equals c.

1. Iterating through Binary Representations:
   We start by using a while loop to iterate through the binary representations of the numbers a, b, and c. This is achieved by examining the individual bits of these numbers in a bitwise manner.
2. Counting Flips:
   Within the iteration, we use bitwise AND and OR operations to compare the individual bits of a, b, and c. Depending on the conditions met during the iteration, we increment the flips variable to keep track of the minimum number of flips required.
3. Bitwise AND and OR Operations:
   By utilizing bitwise AND and OR operations, we can compare the individual bits of the numbers and determine the necessary flips to ensure that the bitwise OR of a and b equals c. This involves examining the binary representation of each number and performing bitwise operations on corresponding bits.
4. Shifting Bits:
   As we iterate through the binary representations, we use the right shift (>>) operator to move to the next bit for each number a, b, and c. This allows us to sequentially evaluate the bits from right to left and continue the comparison process.
5. Returning the Result:
   Once the iteration is complete, the total number of flips required is returned as the result, providing the minimum number of bit flips needed to satisfy the condition (a OR b == c).

By employing bitwise operations and carefully examining the binary representations of the numbers, we can efficiently determine the minimum number of bit flips required to achieve the desired bitwise OR condition. This approach allows for a systematic evaluation of individual bits and an effective calculation of the minimum flips needed.

C++ Code:

#include <iostream>
int main() {
    int a = 5; // Binary: 0101
    int b = 10; // Binary: 1010
    int c = 7; // Binary: 0111

    int flips  = 0;
    while(a || b || c) {
        if(c & 1) {
            if ((a & 1) == 0 & (b & 1) == 0)
                flips ++;
        } else {
            if (a & 1)
                flips ++;
            if(b & 1)
                flips ++;
        }
        a >>=1, b >>= 1, c >>= 1;
    }
    return flips ;
}

In a binary representation, each digit, or bit, represents a power of 2, starting from 2⁰ on the rightmost side and increasing to higher powers of 2 as we move to the left. For example, the binary number 10110 represents (1 * 2⁴) + (0 * 2³) + (1 * 2²) + (1 * 2¹) + (0 * 2⁰), which simplifies to 22.

Conclusion:
In conclusion, we have presented a solution to the minimum flips problem using bitwise operations in C++. Through this approach, we have illustrated how bitwise operations can be effectively utilized to manipulate individual bits and solve problems related to binary representations. By leveraging these techniques, we can efficiently navigate and manipulate binary data, providing an effective means of addressing problems that involve bitwise operations and bit manipulation.

Understanding and applying these bitwise operations and techniques can be valuable not only for solving similar problems but also for optimizing code for efficiency. By employing bitwise operations, developers can handle binary data and perform bit-level manipulations in an efficient and precise manner.

More Reads:
The program solves a LeetCode problem that involves finding the minimum number of bit flips needed in two given numbers to make their bitwise OR equal to a third number.

The solution can be accessed through the link provided.