What is the time complexity of Sort Characters By Frequency?

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

What data structures are used to solve Sort Characters By Frequency?

This problem uses Hash Table, String, Sorting, Heap (Priority Queue), Bucket Sort, Counting. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Sort Characters By Frequency?

Insight 1: Counting character frequencies is essential. A hash table (dictionary/map) is an efficient data structure for this purpose. Insight 2: Sorting the characters based on their frequencies is crucial. We need a sorting algorithm or data structure that can efficiently arrange the characters by their counts.

Which companies ask LeetCode 451. Sort Characters By Frequency in interviews?

This problem is frequently asked at Nvidia, Wipro, tcs.

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Sort Characters By Frequency - LeetCode 451 Solution

Sort Characters By Frequency - Complete Solution Guide

Sort Characters By Frequency is LeetCode problem 451, 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 , sort it in decreasing order based on the frequency of the characters. The frequency of a character is the number of times it appears in the string. Return the sorted string . If there are multiple answers, return any of them . Example 1: Input: s = "tree" Output: "eert" Explanation: 'e' appears twice while 'r' and 't' both appear once. So 'e' must appear before both 'r' and 't'. Therefore "eetr" is also a valid answer. Example 2: Input: s = "cccaaa" Output: "aaaccc" Explanatio

Detailed Explanation

The problem requires sorting a given string such that characters appear in decreasing order based on their frequency in the string. The frequency of a character is the number of times it occurs. The output should be a string where characters with higher frequencies appear earlier, and if characters have the same frequency, their order does not matter as long as they are grouped together. Uppercase and lowercase characters are treated as distinct.

Solution Approach

The solution involves three main steps: counting character frequencies, sorting the characters by frequency, and reconstructing the sorted string. A hash map (dictionary/map) is used to efficiently count the occurrences of each character. Then, the character-frequency pairs are sorted based on frequency in descending order. Finally, the sorted characters are appended to build the resulting string based on their respective frequencies.

Step-by-Step Algorithm

Step 1: **Count Character Frequencies:** Iterate through the input string and store the frequency of each character in a hash map (dictionary). If a character is already present, increment its count; otherwise, add it to the map with a count of 1.
Step 2: **Sort by Frequency:** Convert the hash map into a list of (character, frequency) pairs. Sort this list in descending order based on the frequency. This step leverages a sorting algorithm (or specialized data structure like a heap).
Step 3: **Reconstruct Sorted String:** Iterate through the sorted list of (character, frequency) pairs. For each pair, append the character to the result string as many times as its frequency indicates.

Key Insights

Insight 1: Counting character frequencies is essential. A hash table (dictionary/map) is an efficient data structure for this purpose.
Insight 2: Sorting the characters based on their frequencies is crucial. We need a sorting algorithm or data structure that can efficiently arrange the characters by their counts.
Insight 3: Reconstructing the sorted string from the frequency-sorted characters.
Insight 4: The problem explicitly allows for multiple valid outputs, meaning that any arrangement of characters with the same frequency is acceptable.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(n)

Topics

This problem involves: Hash Table, String, Sorting, Heap (Priority Queue), Bucket Sort, Counting.

Companies

Asked at: Nvidia, Wipro, tcs.

Sort Characters By Frequency | LeetCode 451

Medium

Hash Table String Sorting Heap (Priority Queue)Bucket Sort Counting

Time: O(n log n)Space: O(n)

Solution Code

Available in:

import java.util.HashMap;
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Map;

class Solution {
    public String frequencySort(String s) {
        // Count the frequency of each character in the string.
        // e.g., s = "tree" -> counts = {'e': 2, 't': 1, 'r': 1}
        Map<Character, Integer> counts = new HashMap<>();
        for (char c : s.toCharArray()) {
            counts.put(c, counts.getOrDefault(c, 0) + 1);
        }

        // Convert the map to a list of (element, count) pairs.
        List<Map.Entry<Character, Integer>> sortedChars = new ArrayList<>(counts.entrySet());

        // Sort the list by count in descending order.
        Collections.sort(sortedChars, (a, b) -> b.getValue() - a.getValue());

        // Build the result string by repeating each character by its frequency.
        StringBuilder result = new StringBuilder();
        for (Map.Entry<Character, Integer> entry : sortedChars) {
            char character = entry.getKey();
            int frequency = entry.getValue();
            for (int i = 0; i < frequency; i++) {
                result.append(character);
            }
        }

        return result.toString();
    }
}

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Problem Info

Description

Problem 451: Sort Characters By Frequency - Detailed explanation and solution approaches.

Topics

Hash Table String Sorting Heap (Priority Queue)Bucket Sort Counting

Companies

NvidiaWiprotcs

Stats

Difficulty:Medium

Languages:4

Companies:3

Problem #:451

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

3 steps

1
Step 1: **Count Character Frequencies:** Iterate through the input string and store the frequency of each character in a hash map (dictionary). If a character is already present, increment its count; otherwise, add it to the map with a count of 1.
2
Step 2: **Sort by Frequency:** Convert the hash map into a list of (character, frequency) pairs. Sort this list in descending order based on the frequency. This step leverages a sorting algorithm (or specialized data structure like a heap).
3
Step 3: **Reconstruct Sorted String:** Iterate through the sorted list of (character, frequency) pairs. For each pair, append the character to the result string as many times as its frequency indicates.

💡

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 log n)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The dominant operations are the sorting step which utilizes a comparison-based sort, and allocating space for the hash map and the result string. The number of distinct characters 'k' can be, in the worst case, equal to 'n', the length of the input string.

📖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

Bucket Sort

Using Bucket Sort, create buckets based on the frequencies, with the most frequent characters at the end. Iterate through the frequencies from largest to smallest, appending characters in each bucket to the result.

Time: O(n), where n is the length of the input string if we assume the character set is limited to ASCII or similar. In this case, the character frequency will be limited to n.Space: O(n), where n is the length of the input string. We need space to store the character counts, buckets, and result string.

Trade-offs: Bucket sort can be faster (linear time) than O(n log n) sorting if the range of character frequencies is limited. However, if the range is very large, the space complexity may become a concern, and the constant factors might make it slower in practice for reasonable input sizes.

Heap (Priority Queue)

Use a max-heap (priority queue) to store the characters based on their frequencies. The character with the highest frequency will be at the root of the heap. Repeatedly extract the character with the highest frequency from the heap and append it to the result string.

Time: O(n log k), where n is the length of the input string and k is the number of distinct characters. Building the heap takes O(n) time, and extracting and appending each character takes O(log k) time, repeated for each of the n characters to build the result.Space: O(k), where k is the number of distinct characters. This is the space needed to store the characters and their frequencies in the heap.

Trade-offs: Using a heap provides a good balance between time and space complexity. It can be more efficient than the initial approach if the number of distinct characters is significantly smaller than the length of the string.

✨

Key Insights

1Insight 1: Counting character frequencies is essential. A hash table (dictionary/map) is an efficient data structure for this purpose.
2Insight 2: Sorting the characters based on their frequencies is crucial. We need a sorting algorithm or data structure that can efficiently arrange the characters by their counts.
3Insight 3: Reconstructing the sorted string from the frequency-sorted characters.
4Insight 4: The problem explicitly allows for multiple valid outputs, meaning that any arrangement of characters with the same frequency is acceptable.

📚

Key Terms Explained

For Students

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

String

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

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: **Empty String:** If the input string is empty, the solution should return an empty string. The provided solutions handle this implicitly as loops won't execute and an empty string will be returned.
Edge case 2: **String with Only One Character:** If the input string contains only one character, the solution should return the same string. The algorithm handles this case correctly because the frequency count will be 1, and after sorting, it will simply append the character once to the result.
Edge case 3: **String with All Unique Characters:** If the input string contains all unique characters (e.g., "abcdefg"), the sorting step will determine the order, and the reconstruction step will append each character once. The order is unspecified, so any order is a valid answer as the frequencies are all 1.
Edge case 4: **String with Mixed Case and Digits:** The problem statement specifies that the string can contain uppercase and lowercase English letters and digits. The solutions correctly handle this by treating each character as a distinct entity when counting frequencies.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: **Incorrectly Handling Case Sensitivity:** Failing to distinguish between uppercase and lowercase characters. Make sure the code treats 'A' and 'a' as different characters.

✗Common mistake 2: **Not Grouping Characters Correctly:** Failing to ensure that characters with the same frequency appear together in the result string. The sorting step must ensure that characters are grouped by frequency, and the reconstruction phase must maintain that grouping.

✗Common mistake 3: **Premature Optimization:** Trying to use extremely complex data structures for optimization before fully understanding the problem or performance bottlenecks. Starting with a clear and simple approach is often more productive.

✅

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: **Data Compression:** Frequency analysis is used in data compression algorithms like Huffman coding, where more frequent characters are assigned shorter codes.

🏦Real-world scenario 2: **Text Analysis and NLP:** Determining the most frequent words in a document can be useful for text summarization, keyword extraction, and sentiment analysis.

🎮Real-world scenario 3: **Database Indexing:** Understanding the frequency distribution of values in a database column can help optimize indexing strategies.

📱Real-world scenario 4: **Bioinformatics:** Analyzing the frequency of nucleotides (A, C, G, T) in DNA sequences.

💡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

Hash tables trade space for time. Before using one, consider if the problem constraints allow the extra memory. In interviews, always mention this trade-off.

🎯 Interview Tip

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

⚠️ Watch Out

Don't forget to handle key collisions and null/undefined keys. Consider what happens with duplicate values.

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: August 31, 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

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJun 30

❓

Frequently Asked Questions

How do I choose between a hash map and a hash set?

Use a hash set when you only need to track presence/absence of elements (like detecting duplicates). Use a hash map when you need to associate values with keys (like counting frequencies or storing indices). Hash sets use less memory since they only store keys.

What is the sliding window technique for string problems?

Sliding window maintains a "window" of characters with two pointers. Expand the right pointer to include characters, shrink from left when window violates constraints. Useful for substring problems, anagrams, and longest/shortest substring with properties.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Sort Characters By Frequency"?

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

🤖 Need help with this problem?