Master Group Anagrams with Leetcode 49

Table of Contents

• Introduction
• Understanding the Problem
• Naive Solution Approach
• Optimal Solution Approach
• Implementation in Python
• Time Complexity Analysis
• Conclusion

Introduction

In this article, we will explore the problem of grouping anagrams. Anagrams are words or phrases that can be formed by rearranging the letters of another word or phrase. The task is to group all the anagrams together from a given list of strings. We will discuss the problem in detail, analyze different approaches to solve it, and implement the optimal solution using Python. Additionally, we will provide a time complexity analysis and conclude with key takeaways.

Understanding the Problem

To begin, let us understand the problem statement. Given a list of strings, we need to group all the anagrams together. Two strings are considered anagrams of each other if they have the same characters, irrespective of their order.

For example, consider the strings "tan" and "nat." These two strings are anagrams of each other because we can rearrange the letters to form the same word. In the output, we should group them together into a sub-list.

It is worth noting that the problem specifies that each character in the input strings will be lowercase alphabet letters (from 'a' to 'z'). This information provides us with a useful insight that we can leverage to improve the efficiency of our solution.

Naive Solution Approach

A naive approach to solving this problem would be to sort each string in the input list. We can then compare the sorted strings to identify anagrams. However, this approach has a time complexity of O(m * n log n), where m is the number of input strings and n is the average length of each string. The sorting operation has a time complexity of O(n log n), and we need to perform it for each string.

Optimal Solution Approach

Fortunately, there exists a more efficient solution for this problem. Since we know that all the characters in the strings will be lowercase alphabets, we can use a hashmap to count the occurrence of each character in a string. We can then use this character count as a key in the hashmap and group all the anagrams together.

By leveraging this approach, the overall time complexity of our solution becomes O(m * n), where m is the number of input strings and n is the average length of each string. This improvement is significant compared to the naive solution.

Implementation in Python

Now let's implement the optimal solution using Python. We will create a hashmap called result, where we will map the character count of each string to a list of anagrams. We will iterate through each string in the input list and count the occurrence of each character. We will use an array of size 26, initialized with zeros, to store the character count. The index of each character will be determined by subtracting the ASCII value of 'a'. We will increment the count for each character encountered. Finally, we will append the string to the corresponding list of anagrams in the result dictionary. If the character count does not exist yet, we will handle it using a default dictionary with a default value of a list.

Time Complexity Analysis

The time complexity of our optimal solution is O(m * n), where m is the number of input strings and n is the average length of each string. We need to iterate through each string to count the occurrence of each character.

Conclusion

In this article, we explored the problem of grouping anagrams. We discussed different approaches to solve the problem, including a naive solution and an optimal solution that leverages a hashmap. We implemented the optimal solution using Python and analyzed its time complexity. By using the optimal solution, we can significantly improve the efficiency of grouping anagrams.