Minimum Bit Flips to Convert Number

Problem Description

Given two integers start and goal, return the minimum number of bit flips required to convert start to goal.

Key Insights

• A bit flip changes a bit from 0 to 1 or from 1 to 0.
• To determine the number of bits that differ between two numbers, we can use the XOR operation.
• The result of the XOR operation will have bits set to 1 where the two numbers differ.
• Counting the number of 1s in the XOR result gives the minimum number of flips required.

Space and Time Complexity

Time Complexity: O(1) - The algorithm performs a fixed number of operations regardless of the input size.
Space Complexity: O(1) - Only a constant amount of space is used.

Solution

To solve the problem, we can use the XOR operation to find the differing bits between start and goal. By counting the number of 1s in the resulting binary representation, we can determine the minimum number of bit flips required.

1. Perform start XOR goal to get a number that represents the bits that are different.
2. Count the number of 1s in the binary representation of the result.

The algorithm leverages bit manipulation to achieve this in a highly efficient manner.

Code Solutions