Maximum Number of Vowels in a Substring of Given Length

Maximum Number of Vowels in a Substring of Given Length - Problem

Given a string s and an integer k, find the maximum number of vowel letters in any substring of s with length exactly k.

The vowel letters in English are: 'a', 'e', 'i', 'o', and 'u'.

For example, if s = "abciiidef" and k = 3, you need to examine all substrings of length 3: "abc" (1 vowel), "bci" (1 vowel), "cii" (2 vowels), "iii" (3 vowels), "iid" (2 vowels), "ide" (2 vowels), "def" (1 vowel). The maximum is 3 vowels.

This problem tests your understanding of the sliding window technique - a powerful pattern for solving substring problems efficiently!

Input & Output

example_1.py — Basic Case

$ Input: s = "abciiidef", k = 3

› Output: 3

💡 Note: The substring "iii" contains 3 vowels, which is the maximum possible for any substring of length 3.

example_2.py — No Vowels Case

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

› Output: 0

💡 Note: No substring of length 2 contains any vowels, so the maximum is 0.

example_3.py — All Vowels Case

$ Input: s = "aeiouaei", k = 4

› Output: 4

💡 Note: Multiple substrings contain 4 vowels: "aeio", "eiou", "ioua", "ouae", "uaei".

Constraints

1 ≤ s.length ≤ 10⁵
s consists of lowercase English letters
1 ≤ k ≤ s.length
Vowels are: 'a', 'e', 'i', 'o', 'u'

Visualization

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Understanding the Visualization

Initialize Window

Count vowels in the first k characters

Slide Window

Move one position right, update count incrementally

Track Maximum

Keep track of the highest vowel count encountered

Continue Until End

Process all possible windows of size k

Key Takeaway

🎯 Key Insight: The sliding window technique transforms an O(n*k) problem into O(n) by avoiding redundant work and reusing previous calculations.

Asked in

a Amazon 45 ⊞ Microsoft 38 G Google 32 f Meta 28

The optimal solution uses the sliding window technique to achieve O(n) time complexity. Instead of recounting vowels for each substring, we maintain a running count and adjust it as characters enter and leave our window of size k.

Common Approaches

Approach	Time	Space	Notes
✓ Sliding Window (Optimal)	O(n)	O(1)	Use sliding window technique to efficiently track vowels
Brute Force (Check All Substrings)	O(n*k)	O(1)	Check every possible substring of length k and count vowels in each

Sliding Window (Optimal) — Algorithm Steps

Count vowels in the first window (indices 0 to k-1)
Set this count as the initial maximum
Slide the window one position at a time
For each slide: subtract the leaving character (if vowel), add the entering character (if vowel)
Update maximum if current window has more vowels
Return the maximum count found

Visualization

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Step-by-Step Walkthrough

Initial window

Count vowels in first k characters

Slide right

Remove left character, add right character

Update count

Adjust count based on what entered/left

Track maximum

Keep track of the highest count seen

Code -

solution.c — C

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

bool isVowel(char c) {
    return c == 'a' || c == 'e' || c == 'i' || c == 'o' || c == 'u';
}

int maxVowels(char* s, int k) {
    int n = strlen(s);
    
    // Count vowels in first window
    int currentCount = 0;
    for (int i = 0; i < k; i++) {
        if (isVowel(s[i])) {
            currentCount++;
        }
    }
    
    int maxCount = currentCount;
    
    // Slide the window
    for (int i = k; i < n; i++) {
        // Remove the leftmost character of previous window
        if (isVowel(s[i - k])) {
            currentCount--;
        }
        // Add the rightmost character of current window
        if (isVowel(s[i])) {
            currentCount++;
        }
        if (currentCount > maxCount) {
            maxCount = currentCount;
        }
    }
    
    return maxCount;
}

int main() {
    char s[100001];
    int k;
    scanf("\"%[^\"]\" %d", s, &k);
    printf("%d\n", maxVowels(s, k));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

We visit each character at most twice - once when entering window, once when leaving

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables regardless of input size

✓ Linear Space

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High Frequency

~15 min Avg. Time

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Sliding Window (Optimal) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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