LeetCode #2269 — EASY

Find the K-Beauty of a Number

Build confidence with an intuition-first walkthrough focused on math fundamentals.

Solve on LeetCode
The Problem

Problem Statement

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.

Note:

  • Leading zeros are allowed.
  • 0 is not a divisor of any value.

A substring is a contiguous sequence of characters in a string.

Example 1:

Input: num = 240, k = 2
Output: 2
Explanation: The following are the substrings of num of length k:
- "24" from "240": 24 is a divisor of 240.
- "40" from "240": 40 is a divisor of 240.
Therefore, the k-beauty is 2.

Example 2:

Input: num = 430043, k = 2
Output: 2
Explanation: The following are the substrings of num of length k:
- "43" from "430043": 43 is a divisor of 430043.
- "30" from "430043": 30 is not a divisor of 430043.
- "00" from "430043": 0 is not a divisor of 430043.
- "04" from "430043": 4 is not a divisor of 430043.
- "43" from "430043": 43 is a divisor of 430043.
Therefore, the k-beauty is 2.

Constraints:

  • 1 <= num <= 109
  • 1 <= k <= num.length (taking num as a string)
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: 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. Note: Leading zeros are allowed. 0 is not a divisor of any value. A substring is a contiguous sequence of characters in a string.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Math · Sliding Window

Example 1

240
2

Example 2

430043
2
Step 02

Core Insight

What unlocks the optimal approach

  • We should check all the substrings of num with a length of k and see if it is a divisor of num.
  • We can more easily obtain the substrings by converting num into a string and converting back to an integer to check for divisibility.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2269: Find the K-Beauty of a Number
class Solution {
    public int divisorSubstrings(int num, int k) {
        int ans = 0;
        String s = "" + num;
        for (int i = 0; i < s.length() - k + 1; ++i) {
            int t = Integer.parseInt(s.substring(i, i + k));
            if (t != 0 && num % t == 0) {
                ++ans;
            }
        }
        return ans;
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(log num × k)
Space
O(log num + k)

Approach Breakdown

BRUTE FORCE
O(n × k) time
O(1) space

For each starting index, scan the next k elements to compute the window aggregate. There are n−k+1 starting positions, each requiring O(k) work, giving O(n × k) total. No extra space since we recompute from scratch each time.

SLIDING WINDOW
O(n) time
O(k) space

The window expands and contracts as we scan left to right. Each element enters the window at most once and leaves at most once, giving 2n total operations = O(n). Space depends on what we track inside the window (a hash map of at most k distinct elements, or O(1) for a fixed-size window).

Shortcut: Each element enters and exits the window once → O(n) amortized, regardless of window size.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Overflow in intermediate arithmetic

Wrong move: Temporary multiplications exceed integer bounds.

Usually fails on: Large inputs wrap around unexpectedly.

Fix: Use wider types, modular arithmetic, or rearranged operations.

Shrinking the window only once

Wrong move: Using `if` instead of `while` leaves the window invalid for multiple iterations.

Usually fails on: Over-limit windows stay invalid and produce wrong lengths/counts.

Fix: Shrink in a `while` loop until the invariant is valid again.