Replace Words

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In English, we have a concept called root, which can be followed by some other word to form another longer word — let’s call this word successor. For example, when the root "an" is followed by the successor word "other", we can form a new word "another".

Given a dictionary consisting of many roots and a sentence consisting of words separated by spaces, replace all the successors in the sentence with the root forming it. If a successor can be replaced by more than one root, replace it with the root that has the shortest length.

Return the sentence after the replacement.

Example 1:

Input: dictionary = ["cat","bat","rat"], sentence = "the cattle was rattled by the battery"
Output: "the cat was rat by the bat"

Example 2:

Input: dictionary = ["a","b","c"], sentence = "aadsfasf absbs bbab cadsfafs"
Output: "a a b c"

Example 3:

Input: dictionary = ["a", "aa", "aaa", "aaaa"], sentence = "a aa a aaaa aaa aaa aaa aaaaaa bbb baba ababa"
Output: "a a a a a a a a bbb baba a"

Example 4:

Input: dictionary = ["catt","cat","bat","rat"], sentence = "the cattle was rattled by the battery"
Output: "the cat was rat by the bat"

Example 5:

Input: dictionary = ["ac","ab"], sentence = "it is abnormal that this solution is accepted"
Output: "it is ab that this solution is ac"

Constraints:

• 1 <= dictionary.length <= 1000
• 1 <= dictionary[i].length <= 100
• dictionary[i] consists of only lower-case letters.
• 1 <= sentence.length <= 10^6
• sentence consists of only lower-case letters and spaces.
• The number of words in sentence is in the range [1, 1000]
• The length of each word in sentence is in the range [1, 1000]
• Each two consecutive words in sentence will be separated by exactly one space.
• sentence does not have leading or trailing spaces.

Algorithm

Store all the roots in a HashSet data 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 : O(∑wi2​) where wi​ is the length of the i-th word. We might check every prefix, the i-th of which is O(wi2​) work.
• Space Complexity : O(N) where NN is the length of our sentence; the space used by rootset.