Longest Substring with At Most K Distinct Characters

Longest Substring with At Most K Distinct Characters - Problem

Given a string s and an integer k, return the length of the longest substring of s that contains at most k distinct characters.

A substring is a contiguous sequence of characters within a string. The goal is to find the maximum possible length while ensuring the substring has no more than k unique characters.

Example: If s = "eceba" and k = 2, the longest substring with at most 2 distinct characters is "ece" with length 3.

Input & Output

Example 1 — Basic Case

$ Input: s = "eceba", k = 2

› Output: 3

💡 Note: The longest substring with at most 2 distinct characters is "ece" with length 3. It contains only 'e' and 'c'.

Example 2 — All Same Characters

$ Input: s = "aaaa", k = 1

› Output: 4

💡 Note: The entire string contains only 1 distinct character 'a', so the answer is 4.

Example 3 — Edge Case k=0

$ Input: s = "abc", k = 0

› Output: 0

💡 Note: When k=0, no characters are allowed, so the longest valid substring has length 0.

Constraints

1 ≤ s.length ≤ 5 × 10⁴
0 ≤ k ≤ 50
s consists of lowercase English letters

Visualization

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Asked in

G Google 45 f Facebook 38 a Amazon 32 M Microsoft 28

The sliding window approach is optimal. Use two pointers and a hash map to maintain a window with at most k distinct characters. Key insight: expand right when possible, shrink left when necessary. Time: O(n), Space: O(k)

Common Approaches

✓ Brute Force - Check All Substrings

⏱️ Time: O(n³) Space: O(min(k, 26))

Generate all possible substrings of the input string. For each substring, count the number of distinct characters. Keep track of the maximum length among all valid substrings (those with at most k distinct characters).

Sliding Window with Hash Map

⏱️ Time: O(n) Space: O(min(k, 26))

Maintain a sliding window using two pointers (left and right). Expand the window by moving right pointer and adding characters to a hash map. When we have more than k distinct characters, shrink the window from left until we have at most k distinct characters again.

Brute Force - Check All Substrings — Algorithm Steps

Step 1: Generate all possible substrings using nested loops
Step 2: For each substring, count distinct characters using a set
Step 3: If distinct count ≤ k, update maximum length
Step 4: Return the maximum length found

Visualization

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Step-by-Step Walkthrough

Generate Substrings

Create all possible substrings using nested loops

Count Distinct

For each substring, count unique characters

Track Maximum

Keep the longest valid substring length

Code -

solution.c — C

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

int solution(char* s, int k) {
    if (k == 0) return 0;
    
    int maxLen = 0;
    int n = strlen(s);
    
    // Check all possible substrings
    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            // Count distinct characters in substring s[i...j]
            int charCount[256] = {0}; // ASCII characters
            int distinctCount = 0;
            
            for (int p = i; p <= j; p++) {
                if (charCount[(unsigned char)s[p]] == 0) {
                    distinctCount++;
                }
                charCount[(unsigned char)s[p]]++;
            }
            
            // If distinct characters <= k, update max length
            if (distinctCount <= k) {
                int currentLen = j - i + 1;
                if (currentLen > maxLen) {
                    maxLen = currentLen;
                }
            }
        }
    }
    
    return maxLen;
}

int main() {
    char s[10001];
    int k;
    
    fgets(s, sizeof(s), stdin);
    s[strcspn(s, "\n")] = 0; // Remove newline
    
    scanf("%d", &k);
    
    int result = solution(s, k);
    printf("%d\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n³)

Outer loop O(n) for start, inner loop O(n) for end, O(n) to count distinct chars in each substring

⚠ Quadratic Growth

Space Complexity

O(min(k, 26))

Set to store distinct characters, at most k characters or 26 for lowercase letters

⚡ Linearithmic Space

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High Frequency

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Related Problems

Common Approaches

Brute Force - Check All Substrings — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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