When I started working on this problem, I initially thought about how a human would approach solving a word search puzzle. Typically, as a human, my first instinct is to scan the matrix and start by looking at the first letter of the word I’m trying to find. Once I spot the first letter, I can start exploring possible directions for the rest of the word—either horizontally or vertically. It’s a fairly straightforward process for a human, but when it comes to scaling up this idea for a large dataset or for performance, it becomes less feasible.
At first, I thought of using a linear search to find each word in the matrix. However, this approach would involve checking every possible word and searching through the entire matrix for every potential match, which would be computationally expensive, especially as the number of words grows.
This is where I realized I needed to rethink the approach. Instead of searching through the entire matrix every time, I needed to optimize the search process. I needed a more efficient data structure that could help me organize the search process while making it much faster to find words and prefixes.
The idea behind using a Trie is that it’s optimized for scenarios where multiple strings share common prefixes. Instead of storing the entire word each time, the Trie stores characters at each node. This means that common prefixes are stored once, which greatly reduces redundancy and memory usage.
For example, if you have words like "apple", "app", and "application", rather than storing "apple", "app", and "application" as separate strings, the Trie stores the common prefix "app" once, followed by the unique parts of each word. This structure allows us to efficiently look up any word or prefix with minimal processing.
When searching for a word in the Trie, we can start at the root node and follow the characters of the word, one by one, down the tree. Each character corresponds to a specific node, and we move from node to node in sequence. If we reach the end of the word and the last node marks the end of the word, we have successfully found the word in the Trie. If we hit a dead end (i.e., a character node doesn't exist), the word isn’t present in the Trie.
The primary reason for using a Trie in this case was to optimize for both search efficiency and memory usage:
Searching for a word or prefix in a Trie is done in O(m) time complexity, where m is the length of the word. This is because each character is processed sequentially in constant time. This is far faster than a linear search, especially when dealing with large datasets of words.
By storing shared prefixes only once, the Trie reduces memory consumption, especially when working with a large number of words that share common beginnings. This is ideal for word search puzzles, where many words can have the same prefix.