# 720. 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].

# Solution

Approach 1: use a set to speed up all look ups. Can presort the word list to speed up prefix checks. Time: O(N).

Approach 2: use a trie to keep all words, and later go through either the trie or the word again. Can also presort the word list to reduce the number of times needed to look down the trie. Time: O(NL).

# Code (Python)

Approach 1:

    def longestWord(self, words: 'List[str]') -> 'str':
        words = sorted(words)
        words_can_be_built = set()
        result = ''
        for word in words:
            if len(word) == 1 or word[:-1] in words_can_be_built:
                words_can_be_built.add(word)
                if len(word) > len(result) or (len(word) == len(result) and word < result):
                    result = word
        return result

Approach 2:

class TrieNode:
    def __init__(self):
        self.is_word = False
        self.children = {}

class Trie:
    def __init__(self):
        self.root = TrieNode()
    
    def insert(self, word):
        node = self.root
        for char in word:
            if char not in node.children:
                node.children[char] = TrieNode()
            node = node.children[char]
        node.is_word = True
    
    def can_build(self, word):
        node = self.root
        for char in word:
            if node != self.root and not node.is_word:
                return False
            if char not in node.children:
                return False
            node = node.children[char]
        return True

class Solution:
    def longestWord(self, words: 'List[str]') -> 'str':
        result = ''
        trie = Trie()
        for word in words:
            trie.insert(word)
        for word in words:
            if trie.can_build(word):
                if len(word) > len(result) or (len(word) == len(result) and word < result):
                    result = word
        return result

# Code (C++)

Approach 1:

Approach 2: