In English, we have a concept called root
, which can be followed by some other words to form another longer word - let's call this word successor
. For example, the root an
, followed by other
, which can form another word another
.
Now, given a dictionary consisting of many roots and a sentence. You need to replace all the successor
in the sentence with the root
forming it. If a successor
has many roots
can form it, replace it with the root with the shortest length.
You need to output the sentence after the replacement.
Example 1:
Input: dict = ["cat", "bat", "rat"] sentence = "the cattle was rattled by the battery" Output: "the cat was rat by the bat"
Note:
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
.
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.