Group Anagrams

Grouping anagrams is a common problem in computer science and programming that involves sorting or categorizing a list of strings into groups where each group contains words that are anagrams of each other. An anagram is a word or phrase formed by rearranging the letters of a different word or phrase, typically using all the original letters exactly once. For example, "listen" and "silent" are anagrams of each other.

Understanding Anagrams

To understand how to group anagrams, it's crucial to recognize that anagrams share a fundamental characteristic: when the letters of anagrams are sorted alphabetically, they produce the same string. For instance, sorting the letters of both "listen" and "silent" alphabetically yields "eilnst". This property serves as the basis for grouping anagrams.

The Basic Approach

The basic approach to solving the group anagrams problem involves the following steps:

  1. Normalize each word: Transform each word in the input list into a standardized form that represents its anagram group. This is typically done by sorting the letters of the word alphabetically. For example, both "listen" and "silent" would be normalized to "eilnst".

  2. Group words by their normalized form: Use a data structure, such as a hash map or dictionary, to group words by their normalized forms. In this dictionary, the keys would be the normalized forms, and the values would be lists of words that, when normalized, match the key.

  3. Extract the groups: Once the input list has been processed, the values of the dictionary represent the groups of anagrams.

Detailed Explanation with an Example

Let's consider an example input list of words: ["listen", "silent", "enlist", "hello", "ohlle"]. Here's how we would group these words into anagrams:

  1. Normalize each word:

    • "listen" -> "eilnst"
    • "silent" -> "eilnst"
    • "enlist" -> "eilnst"
    • "hello" -> "ehllo"
    • "ohlle" -> "ehllo"
  2. Group words by their normalized form:

    • "eilnst": ["listen", "silent", "enlist"]
    • "ehllo": ["hello", "ohlle"]
  3. Extract the groups: The final groups of anagrams would be:

    • Group 1: ["listen", "silent", "enlist"]
    • Group 2: ["hello", "ohlle"]

Implementation Considerations

When implementing this solution, key considerations include:

  • Choosing the right data structure for grouping: A hash map or dictionary is ideal because it allows efficient grouping and retrieval by the normalized forms.

  • Efficiency of normalization: Sorting the letters of each word is a straightforward way to normalize, but it has a computational cost. The time complexity for sorting each word is O(n log n), where n is the length of the word. Thus, the overall time complexity depends on the total number of letters across all words.

  • Handling case sensitivity: Depending on the requirements, you might need to consider whether "Listen" and "silent" should be grouped together, which would involve converting all letters to the same case before normalization.

  • Dealing with duplicates: If the input list contains duplicates (e.g., two instances of "listen"), the implementation should ensure that these duplicates are correctly handled according to the problem's requirements.

This approach can be implemented in various programming languages using their respective data structures and sorting functions. The choice of data structures and algorithms can affect the performance and efficiency of the solution.