What is the time complexity of Maximum Number of Vowels in a Substring of Given Length?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Maximum Number of Vowels in a Substring of Given Length?

This problem uses String, Sliding Window. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Maximum Number of Vowels in a Substring of Given Length?

Insight 1: The problem can be efficiently solved using the sliding window technique to avoid redundant computations. Insight 2: Using a set or hash set to quickly check if a character is a vowel improves the time complexity of the vowel check.

Which companies ask LeetCode 1456. Maximum Number of Vowels in a Substring of Given Length in interviews?

This problem is frequently asked at Turing, Wayfair.

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Maximum Number of Vowels in a Substring of Given Length - LeetCode 1456 Solution

Maximum Number of Vowels in a Substring of Given Length - Complete Solution Guide

Maximum Number of Vowels in a Substring of Given Length is LeetCode problem 1456, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Given a string s and an integer k , return the maximum number of vowel letters in any substring of s with length k . Vowel letters in English are 'a' , 'e' , 'i' , 'o' , and 'u' . Example 1: Input: s = "abciiidef", k = 3 Output: 3 Explanation: The substring "iii" contains 3 vowel letters. Example 2: Input: s = "aeiou", k = 2 Output: 2 Explanation: Any substring of length 2 contains 2 vowels. Example 3: Input: s = "leetcode", k = 3 Output: 2 Explanation: "lee", "eet" and "ode" contain 2 vowels. C

Detailed Explanation

The problem asks us to find the maximum number of vowels (a, e, i, o, u) present in any substring of length `k` within a given string `s`. The input consists of the string `s` and the integer `k`, and the output should be a single integer representing the maximum number of vowels found in any substring of length `k`. The constraints state that the string `s` contains only lowercase English letters, and `k` is always a valid length for a substring of `s`.

Solution Approach

The provided solution uses the sliding window technique to efficiently find the maximum number of vowels in a substring of length `k`. It first calculates the number of vowels in the initial window (the first `k` characters). Then, it slides the window one character at a time, adding the new character to the window and removing the character that has moved out of the window. In each step, it updates the current vowel count and the maximum vowel count encountered so far.

Step-by-Step Algorithm

Step 1: Initialize a set (or similar data structure) containing all vowel characters ('a', 'e', 'i', 'o', 'u').
Step 2: Calculate the initial number of vowels in the first substring of length `k` (the 'window').
Step 3: Initialize `max_vowels` with the initial vowel count.
Step 4: Iterate through the string `s` from index `k` to the end of the string.
Step 5: In each iteration, add the vowel count of the new character entering the window and subtract the vowel count of the character exiting the window.
Step 6: Update `max_vowels` with the maximum between the current `max_vowels` and the current vowel count.
Step 7: Add an early exit condition if max_vowels is equal to k, return k.
Step 8: Return `max_vowels` after iterating through the entire string.

Key Insights

Insight 1: The problem can be efficiently solved using the sliding window technique to avoid redundant computations.
Insight 2: Using a set or hash set to quickly check if a character is a vowel improves the time complexity of the vowel check.
Insight 3: An early exit condition (returning `k` if `max_vowels` reaches `k`) can slightly optimize the solution.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: String, Sliding Window.

Companies

Asked at: Turing, Wayfair.

Maximum Number of Vowels in a Substring of Given Length | LeetCode 1456

Medium

String Sliding Window

Time: O(n)Space: O(1)

Solution Code

Available in:

import java.util.HashSet;
import java.util.Set;

class Solution {
    public int maxVowels(String s, int k) {
        Set<Character> vowels = new HashSet<>();
        vowels.add('a');
        vowels.add('e');
        vowels.add('i');
        vowels.add('o');
        vowels.add('u');
        
        int current_vowels = 0;
        for (int i = 0; i < k; i++) {
            if (vowels.contains(s.charAt(i))) {
                current_vowels += 1;
            }
        }
        
        int max_vowels = current_vowels;
        
        for (int i = k; i < s.length(); i++) {
            if (vowels.contains(s.charAt(i))) {
                current_vowels += 1;
            }
            if (vowels.contains(s.charAt(i - k))) {
                current_vowels -= 1;
            }
            
            max_vowels = Math.max(max_vowels, current_vowels);

            if (max_vowels == k) {
                return k;
            }
        }
        
        return max_vowels;
    }
}

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Problem Info

Description

Problem 1456: Maximum Number of Vowels in a Substring of Given Length - Detailed explanation and solution approaches.

Topics

String Sliding Window

Companies

TuringWayfair

Stats

Difficulty:Medium

Languages:4

Companies:2

Problem #:1456

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

8 steps

1
Step 1: Initialize a set (or similar data structure) containing all vowel characters ('a', 'e', 'i', 'o', 'u').
2
Step 2: Calculate the initial number of vowels in the first substring of length `k` (the 'window').
3
Step 3: Initialize `max_vowels` with the initial vowel count.
4
Step 4: Iterate through the string `s` from index `k` to the end of the string.
5
Step 5: In each iteration, add the vowel count of the new character entering the window and subtract the vowel count of the character exiting the window.
6
Step 6: Update `max_vowels` with the maximum between the current `max_vowels` and the current vowel count.
7
Step 7: Add an early exit condition if max_vowels is equal to k, return k.
8
Step 8: Return `max_vowels` after iterating through the entire string.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is O(n) because the algorithm iterates through the string `s` only once. The space complexity is O(1) because the extra space used is independent of the size of the input string `s`. The set of vowels has a fixed size.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Brute Force

Iterate through all possible substrings of length `k` and count the number of vowels in each substring. Keep track of the maximum count encountered.

Time: O(n*k), where n is the length of the string `s` and k is the length of the substring.Space: O(1).

Trade-offs: The brute force approach is simpler to understand but less efficient than the sliding window approach. It is suitable for small input sizes but becomes inefficient for larger strings. The sliding window approach is more efficient for larger strings because it avoids redundant calculations.

✨

Key Insights

1Insight 1: The problem can be efficiently solved using the sliding window technique to avoid redundant computations.
2Insight 2: Using a set or hash set to quickly check if a character is a vowel improves the time complexity of the vowel check.
3Insight 3: An early exit condition (returning `k` if `max_vowels` reaches `k`) can slightly optimize the solution.

📚

Key Terms Explained

For Students

Sliding Window

A moving "window" over data to process subsets efficiently.

String

A sequence of characters. Like a word or sentence in programming!

Edge Cases

Edge case 1: Empty string or k = 0. The constraints ensure that the string length is at least 1 and k is also at least 1, so it will not occur, making the solution more straightforward.
Edge case 2: String `s` contains no vowels. The algorithm correctly handles this by returning 0.
Edge case 3: `k` is equal to the length of the string `s`. The algorithm correctly calculates the number of vowels in the entire string and returns it.
Edge case 4: `k` is 1. The algorithm correctly finds the maximum vowels, which can either be 0 or 1.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not using a set (or similar data structure) to efficiently check if a character is a vowel. Using a simple if-else statement to check for each vowel individually would increase the time complexity.

✗Common mistake 2: Recalculating the number of vowels in each substring instead of using the sliding window technique, resulting in O(n*k) time complexity instead of O(n).

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: DNA sequence analysis. Identifying regions with a high concentration of certain nucleotides (analogous to vowels) within a specific window size.

🏦Real-world scenario 2: Text processing and analysis. Analyzing the frequency of specific characters (e.g., vowels, consonants) in a text to determine language characteristics or patterns.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

String problems often involve sliding windows or two pointers. Consider if the character set is limited (lowercase letters = only 26 possibilities).

🎯 Interview Tip

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ Watch Out

Mutating strings directly in languages where strings are immutable. Use StringBuilder or arrays.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: June 17, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 14

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 7

❓

Frequently Asked Questions

How do I handle string manipulation efficiently?

In languages with immutable strings (Java, Python, C#), use StringBuilder/list to avoid O(n) concatenation cost. Consider using character arrays for in-place modifications. For pattern matching, consider KMP or Rabin-Karp for O(n+m) complexity.

How do I determine the window size in sliding window problems?

For fixed-size windows (like max sum of k elements), window size is given. For variable-size windows (like smallest subarray with sum >= target), expand right pointer to meet condition, then shrink left pointer to find optimal. Track the best result during shrinking.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Maximum Number of Vowels in a Substring of Given Length"?

For this medium-level String problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether sliding window techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?