Minimum Bit Flips to Convert Number

Minimum Bit Flips to Convert Number

What is this problem about?

The Minimum Bit Flips to Convert Number problem asks for the minimum number of bits you need to flip in the binary representation of a number start to transform it into another number goal. A "flip" means changing a 0 to a 1 or a 1 to a 0. This is essentially asking for the Hamming Distance between the two numbers.

Why is this asked in interviews?

This is a standard Minimum Bit Flips interview question at companies like Microsoft and IBM. It tests fundamental Bit Manipulation knowledge. Interviewers want to see if you know about the XOR operation and how to count the number of set bits (1s) in an integer, which are core low-level programming skills.

Algorithmic pattern used

The XOR and Bit Counting interview pattern is the standard approach.

1. Compute xor_result = start ^ goal. The XOR operation results in a 1 only in positions where the bits of start and goal are different.
2. Count the number of set bits in xor_result. This can be done using built-in functions (like bin(x).count('1') or __builtin_popcount) or Brian Kernighan’s algorithm for better efficiency.

Example explanation

start = 10 (binary 1010), goal = 7 (binary 0111).

1. 1010 ^ 0111 = 1101.
2. The result 1101 has three 1 bits (at positions 0, 2, and 3).
3. Minimum bit flips = 3. You need to flip the bits at those three positions to turn 10 into 7.

Common mistakes candidates make

• Iterating through strings: Converting numbers to binary strings and comparing them character by character. While correct, it's much slower and less idiomatic than bitwise operations.
• Not handling different lengths: Strings like "10" and "110" need careful padding. Bitwise operations handle this automatically.
• Inefficient bit counting: Using a loop that runs 32 times instead of just the number of set bits.

Interview preparation tip

Learn Brian Kernighan’s Algorithm: n = n & (n - 1). This trick removes the rightmost set bit in each step, making bit counting much faster. It's an "expert" touch that impresses interviewers during Bit Manipulation interview patterns.