Minimum Flips to Make a OR b Equal to c

Problem Description

Given 3 positive numbers a, b, and c, return the minimum flips required in some bits of a and b to make ( a OR b == c ). A flip operation consists of changing any single bit 1 to 0 or changing the bit 0 to 1 in their binary representation.

Key Insights

• The goal is to determine how many bits need to be flipped in a and b so that their bitwise OR equals c.
• If a bit is set to 1 in c, at least one of the corresponding bits in a or b must also be set to 1.
• If a bit is set to 0 in c, both corresponding bits in a and b must be 0.
• We can iterate through each bit position and evaluate the necessary flips based on the values of a, b, and c.

Space and Time Complexity

Time Complexity: O(1) - The approach iterates over a fixed number of bits (32 bits for integers), hence the time complexity is constant.

Space Complexity: O(1) - We use a constant amount of space regardless of the input size.

Solution

To solve the problem, we can use a bitwise approach:

1. Iterate over each bit position from 0 to 31 (since the maximum value is 10^9, which fits in 32 bits).
2. For each bit position, we check the corresponding bits in a, b, and c.
3. Depending on the values of these bits, we determine how many flips are required:
   • If the bit in c is 1 and both bits in a and b are 0, we need 1 flip.
   • If the bit in c is 0, we need to ensure that both bits in a and b are 0; if one or both are 1, we need to flip them.
4. Count the total number of flips required and return that count.

Code Solutions