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Find the K-Beauty of a Number

Difficulty: Easy

Problem Description

The k-beauty of an integer num is defined as the number of substrings of num when it is read as a string that meet the following conditions:

It has a length of k.
It is a divisor of num.

Given integers num and k, return the k-beauty of num.

Key Insights

A substring is defined as a contiguous sequence of characters in a string.
Leading zeros are allowed in the substrings.
The number 0 is not considered a divisor of any value.
We need to extract all substrings of length k from the string representation of num and check if they divide num evenly.

Space and Time Complexity

Time Complexity: O(n) where n is the length of the string representation of num, since we need to check each substring of length k once.

Space Complexity: O(1) for storing the count of k-beautiful substrings as we only need a few variables regardless of the input size.

Solution

To solve this problem, we will:

Convert the integer num into its string representation to easily access substrings.
Iterate through the string and extract all possible substrings of length k.
Convert each substring back into an integer and check if it is a divisor of num (excluding the case where the substring is "0").
Count how many of these valid substrings meet the divisor condition.

We will use a simple loop to generate substrings and a variable to count valid divisors.

Code Solutions

def k_beauty(num: int, k: int) -> int:
    num_str = str(num)
    count = 0
    
    for i in range(len(num_str) - k + 1):
        substring = num_str[i:i + k]
        if substring[0] == '0':
            continue  # Skip substrings with leading zeros
        divisor = int(substring)
        if num % divisor == 0:
            count += 1
            
    return count

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