Find the K-Beauty of a Number

Find the K-Beauty of a Number

1. What is this problem about?

The Find the K-Beauty of a Number coding problem combines string manipulation with mathematical divisibility. The "k-beauty" of a number is defined as the number of substrings of length $k$ (when the number is treated as a string) that are divisors of the original number. You are given an integer and a length $k$, and you must count how many such "beautiful" substrings exist. Note that a substring cannot be a divisor if it is zero.

2. Why is this asked in interviews?

This is a popular Sliding Window and Math interview question for entry-level roles at companies like Quora. It tests a candidate's ability to convert between data types (integer to string and back) and their familiarity with the sliding window technique. It also checks for attention to detail, such as handling division-by-zero errors and leading zeros in substrings.

3. Algorithmic pattern used

The core pattern is the Fixed-Size Sliding Window. You convert the number into its string representation and then iterate through all possible substrings of length $k$. For each substring, you convert it back into an integer and check if the original number is divisible by it. This ensures you visit each "window" exactly once.

4. Example explanation

Number = 120, $k$ = 2. String representation: "120".

• Substring 1: "12" -> Integer 12. Does 120 / 12 have a remainder of 0? Yes. (Count = 1)
• Substring 2: "20" -> Integer 20. Does 120 / 20 have a remainder of 0? Yes. (Count = 2) Total K-Beauty: 2.

5. Common mistakes candidates make

• Division by Zero: Not checking if the substring integer is 0 before performing the modulo operation. This will cause the program to crash.
• Type Conversion Overhead: Repeatedly converting strings in a way that is inefficient, although for standard integer sizes, this is rarely a bottleneck.
• Off-by-one in loop: Missing the last substring in the string representation.

6. Interview preparation tip

Always be mindful of the constraints. If the number is very large, consider if you can use a mathematical sliding window (using modulo and division) instead of string conversion to keep the window updated. For this specific problem, string conversion is usually the most readable and accepted approach.