720. Longest Word in Dictionary

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https://leetcode.com/problems/longest-word-in-dictionary/

Given a list of strings words representing an English Dictionary, find the longest word in words that can be built one character at a time by other words in words. If there is more than one possible answer, return the longest word with the smallest lexicographical order.
If there is no answer, return the empty string.
Example 1:
Input: 
words = ["w","wo","wor","worl", "world"]
Output: "world"
Explanation: 
The word "world" can be built one character at a time by "w", "wo", "wor", and "worl".
Example 2:
Input: 
words = ["a", "banana", "app", "appl", "ap", "apply", "apple"]
Output: "apple"
Explanation: 
Both "apply" and "apple" can be built from other words in the dictionary. However, "apple" is lexicographically smaller than "apply".
Note:

  • All the strings in the input will only contain lowercase letters.
  • The length of words will be in the range [1, 1000].
  • The length of words[i] will be in the range [1, 30].
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    Intuition
    Prefixes of string ~ Trie
    BFS => Each time we try next level, we have longer string. Traverse in reverse to get lexicographically smallest string

    DFS => Each time we reach a word node, check if length is longer or its lexicographically smaller
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    Time - O(w) - Build the trie
    Space - O(w) - Trie storage
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