Group Anagrams

Background Knowledge

The problem of grouping anagrams together involves understanding the concept of anagrams, which are words or phrases formed by rearranging the letters of another word or phrase, typically using all the original letters exactly once. To solve this problem, we need to understand how to identify anagrams and group them together. This requires knowledge of hash maps (also known as dictionaries or associative arrays), which are data structures that store key-value pairs and allow for efficient lookup, insertion, and deletion of elements.

In the context of this problem, we can use hash maps to store the anagrams together. One way to do this is by using a sorted string as the key in the hash map. For example, the words "listen" and "silent" can be sorted to form the key "eilnst", which can be used to group these anagrams together. This approach requires understanding of string sorting and how to use it to create a unique key for each group of anagrams.

Another important concept in this problem is time and space complexity. We need to consider how our solution will scale with the size of the input array and how much memory it will use. This requires understanding of big O notation, which is used to describe the complexity of algorithms. We should aim to find a solution that has a reasonable time and space complexity, such as $O(nm\log m)$, where $n$ is the number of strings and $m$ is the maximum length of a string.

Algorithm/Approach

The general approach to solve this problem involves using a hash map to store the anagrams together. We can iterate through the input array, sort each string, and use the sorted string as the key in the hash map. The value associated with each key can be a list of anagrams that correspond to that key. This approach requires understanding of hash map operations, such as insertion, lookup, and deletion.

Step-by-Step Strategy

To implement the solution, we can follow these steps:

• Create an empty hash map to store the anagrams.
• Iterate through the input array, and for each string:

• Sort the characters in the string to create a unique key.
• Use the sorted string as the key in the hash map.
• If the key is not already in the hash map, add it with an empty list as the value.
• Append the original string to the list of anagrams associated with the key.

• Iterate through the hash map, and for each key-value pair:

• Sort the list of anagrams associated with the key.
• Print the sorted list of anagrams.

Common Pitfalls

Some common pitfalls to watch out for when implementing this solution include:

• Not handling the case where two strings are not anagrams of each other.
• Not sorting the characters in the string correctly.
• Not using a hash map efficiently, resulting in poor time complexity.
• Not handling the case where the input array is empty.

Time & Space Complexity

The expected time complexity of this solution is $O(nm\log m)$, where $n$ is the number of strings and $m$ is the maximum length of a string. This is because we are sorting each string, which takes $O(m\log m)$ time, and we are doing this for $n$ strings. The space complexity is $O(nm)$, as we are storing all the characters of the input strings in the hash map.