#### Approach #1: Prefix Hash [Accepted]

Intuition

For each word in the sentence, we'll look at successive prefixes and see if we saw them before.

Algorithm

Store all the roots in a Set structure. Then for each word, look at successive prefixes of that word. If you find a prefix that is a root, replace the word with that prefix. Otherwise, the prefix will just be the word itself, and we should add that to the final sentence answer.

Complexity Analysis

• Time Complexity: where is the length of the -th word. We might check every prefix, the -th of which is work.

• Space Complexity: where is the length of our sentence; the space used by rootset.

#### Approach #2: Trie [Accepted]

Intuition and Algorithm

Put all the roots in a trie (prefix tree). Then for any query word, we can find the smallest root that was a prefix in linear time.

Complexity Analysis

• Time Complexity: where is the length of the sentence. Every query of a word is in linear time.

• Space Complexity: , the size of our trie.

Analysis written by: @awice.