Hamming Distance

Hamming Distance

What is this problem about?

The Hamming Distance coding problem asks you to calculate the number of positions at which the corresponding bits of two integers $x$ and $y$ are different. In the world of information theory, the Hamming distance between two strings of equal length is the number of substitutions required to change one string into the other. For integers, this translates to looking at their binary representations and counting the "flips."

Why is this asked in interviews?

This is a standard "Easy" level question frequently asked by companies like Google and Microsoft to test a candidate's proficiency with the bit manipulation interview pattern. It evaluations whether you understand bitwise operators like XOR, AND, and shifts. It is a foundational problem that checks if you can handle low-level data representation, which is critical for optimization, networking, and cryptography tasks.

Algorithmic pattern used

This problem relies on the XOR (Exclusive OR) operator. The XOR of two bits is 1 if the bits are different and 0 if they are the same. By performing x ^ y, you get a new integer where every set bit (1) represents a position where $x$ and $y$ differed. The problem then reduces to counting the number of set bits in the result (also known as the "Population Count" or "Hamming Weight").

Example explanation

Suppose $x = 1$ and $y = 4$.

1. Binary of 1: 0001
2. Binary of 4: 0100
3. $x \oplus y$: 0101 (Binary)
4. The result 0101 has two 1s (at the first and third positions from the right). Result: 2.

Common mistakes candidates make

• Manual Binary Conversion: Trying to convert the integers to strings or arrays of binary digits. While this works, it is highly inefficient and shows a lack of comfort with bitwise operators.
• Inefficient Counting: Not knowing efficient ways to count set bits, such as Brian Kernighan’s algorithm (n & (n - 1)) or built-in language functions.
• Ignoring Overflow: Not considering the bit-width of the integers (though standard 32-bit integers are usually implied).

Interview preparation tip

Master the core bitwise tricks. Specifically, know that x ^ y identifies differences and n & (n - 1) clears the least significant set bit. Being able to explain these operations clearly shows you have a deep understanding of computer architecture.