Problem Description
You are given an array of words where each word consists of lowercase English letters. A word A is a predecessor of word B if we can insert exactly one letter anywhere in word A without changing the order of the other characters to make it equal to word B. Return the length of the longest possible word chain with words chosen from the given list of words.
Key Insights
- A word can be extended to a longer word by inserting exactly one letter.
- The problem can be approached using dynamic programming.
- Sorting the words by length helps in efficiently finding potential predecessors.
- A hash map can be used to store the longest chain length for each word.
Space and Time Complexity
Time Complexity: O(n * m^2) where n is the number of words and m is the average length of the words.
Space Complexity: O(n) for storing the longest chain lengths in a hash map.
Solution
To solve the problem, we can use a dynamic programming approach. First, we sort the words based on their lengths. For each word, we check all possible predecessors by removing one character at a time and see if it exists in our hash map. We update the longest chain length for the current word based on the maximum chain length of its predecessors. Finally, the maximum value in our hash map will be the length of the longest word chain.