Find the K-Beauty of a Number - Practice Coding Problems

Find the K-Beauty of a Number - Problem

The k-beauty of an integer is a fascinating concept that combines string manipulation with mathematical divisibility!

Given an integer num and a positive integer k, we need to find how many k-length substrings of num (when treated as a string) are actual divisors of the original number.

Rules:

Each substring must have exactly k characters
The substring (as an integer) must divide num evenly
Leading zeros are allowed in substrings
Zero is never considered a divisor

Example: For num = 240 and k = 2, we check substrings "24", "40". Since 240 ÷ 24 = 10 and 240 ÷ 40 = 6 (both integers), the k-beauty is 2.

Input & Output

example_1.py — Basic Case

$ Input: num = 240, k = 2

› Output: 2

💡 Note: The 2-length substrings of "240" are "24" and "40". Both 24 and 40 divide 240 evenly (240÷24=10, 240÷40=6), so the k-beauty is 2.

example_2.py — Single Digit

$ Input: num = 430, k = 3

› Output: 2

💡 Note: The only 3-length substring of "430" is "430" itself. Since 430÷430=1, it divides evenly, so the k-beauty is 1.

example_3.py — With Zeros

$ Input: num = 1012, k = 3

› Output: 0

💡 Note: The 3-length substrings are "101" and "012". 1012÷101≈10.02 (not integer) and "012"=12, but 1012÷12≈84.33 (not integer). No valid divisors, so k-beauty is 0.

Constraints

1 ≤ num ≤ 10⁹
1 ≤ k ≤ num.length
Leading zeros in substrings are allowed
Zero is never considered a valid divisor

Visualization

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Understanding the Visualization

Setup

Convert number to string for easy character access

Slide Window

Move window of size k from left to right

Extract & Test

Extract substring, convert to int, test divisibility

Count Valid

Increment counter for each valid divisor found

Key Takeaway

🎯 Key Insight: The sliding window approach efficiently checks all possible k-length substrings in linear time, making it perfect for this divisibility problem.

Asked in

G Google 15 a Amazon 12 ⊞ Microsoft 8 f Meta 5

The optimal approach uses a sliding window technique to extract all k-length substrings from the number string, then checks each substring for divisibility. Time complexity is O((n-k+1) × k) where n is the number of digits. Key insight: convert to string for easy substring extraction, but remember to handle zero substrings as invalid divisors.

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force (Sliding Window)	O((n-k+1) * k)	O(1)	Generate all k-length substrings and check each for divisibility

Brute Force (Sliding Window) — Algorithm Steps

Convert num to string
Iterate through all possible starting positions
Extract k-length substring at each position
Convert substring to integer
Check if non-zero and divides num evenly
Count valid divisors

Visualization

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Step-by-Step Walkthrough

Convert to String

Convert number 240 to string "240"

Position 0

Extract substring "24", check if 240 % 24 == 0 ✓

Position 1

Extract substring "40", check if 240 % 40 == 0 ✓

Count Result

Found 2 valid divisors, return count = 2

Code -

solution.c — C

#include <stdio.h>
#include <string.h>
#include <stdlib.h>

int divisorSubstrings(int num, int k) {
    char numStr[20];
    sprintf(numStr, "%d", num);
    int len = strlen(numStr);
    int count = 0;
    
    // Sliding window of size k
    for (int i = 0; i <= len - k; i++) {
        char substring[20];
        strncpy(substring, numStr + i, k);
        substring[k] = '\0';
        int substringVal = atoi(substring);
        
        // Check if it's a valid divisor
        if (substringVal != 0 && num % substringVal == 0) {
            count++;
        }
    }
    
    return count;
}

int main() {
    int num, k;
    scanf("%d %d", &num, &k);
    printf("%d\n", divisorSubstrings(num, k));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O((n-k+1) * k)

We check (n-k+1) substrings, each requiring O(k) time for string-to-int conversion

✓ Linear Growth

Space Complexity

O(1)

Only using constant extra space for variables

✓ Linear Space

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Brute Force (Sliding Window) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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