You are given an array words of size n consisting of non-empty strings.
We define the score of a string word as the number of strings words[i] such that word is a prefix of words[i].
For example, if words = ["a", "ab", "abc", "cab"], then the score of "ab" is 2, since "ab" is a prefix of both "ab" and "abc".
Return an array answer of size n where answer[i] is the sum of scores of every non-empty prefix of words[i].
Note that a string is considered as a prefix of itself.
Example 1:
Input: words = ["abc","ab","bc","b"]
Output: [5,4,3,2]
Explanation: The answer for each string is the following:
- "abc" has 3 prefixes: "a", "ab", and "abc".
- There are 2 strings with the prefix "a", 2 strings with the prefix "ab", and 1 string with the prefix "abc".
The total is answer[0] = 2 + 2 + 1 = 5.
- "ab" has 2 prefixes: "a" and "ab".
- There are 2 strings with the prefix "a", and 2 strings with the prefix "ab".
The total is answer[1] = 2 + 2 = 4.
- "bc" has 2 prefixes: "b" and "bc".
- There are 2 strings with the prefix "b", and 1 string with the prefix "bc".
The total is answer[2] = 2 + 1 = 3.
- "b" has 1 prefix: "b".
- There are 2 strings with the prefix "b".
The total is answer[3] = 2.
Example 2:
Input: words = ["abcd"]
Output: [4]
Explanation:
"abcd" has 4 prefixes: "a", "ab", "abc", and "abcd".
Each prefix has a score of one, so the total is answer[0] = 1 + 1 + 1 + 1 = 4.
Constraints:
1 <= words.length <= 1000
1 <= words[i].length <= 1000
words[i] consists of lowercase English letters.
Solutions
Solution 1: Trie
Use a trie to maintain the prefixes of all strings and the occurrence count of each prefix.
Then, traverse each string, accumulating the occurrence count of each prefix.
The time complexity is $O(n \times m)$. Here, $n$ and $m$ are the length of the string array words and the maximum length of the strings in it, respectively.