2223 - Sum of Scores of Built Strings (Hard)

Problem Link

https://leetcode.com/problems/sum-of-scores-of-built-strings/

Problem Statement

You are building a string s of length n one character at a time, prepending each new character to the front of the string. The strings are labeled from 1 to n, where the string with length i is labeled si.

• For example, for s = "abaca", s1 == "a", s2 == "ca", s3 == "aca", etc.

The score of si is the length of the longest common prefix between si and sn (Note that s == sn).

Given the final string s, return the sum of the score of every si.

Example 1:

Input: s = "babab"
Output: 9
Explanation:
For s1 == "b", the longest common prefix is "b" which has a score of 1.
For s2 == "ab", there is no common prefix so the score is 0.
For s3 == "bab", the longest common prefix is "bab" which has a score of 3.
For s4 == "abab", there is no common prefix so the score is 0.
For s5 == "babab", the longest common prefix is "babab" which has a score of 5.
The sum of the scores is 1 + 0 + 3 + 0 + 5 = 9, so we return 9.

Example 2:

Input: s = "azbazbzaz"
Output: 14
Explanation: 
For s2 == "az", the longest common prefix is "az" which has a score of 2.
For s6 == "azbzaz", the longest common prefix is "azb" which has a score of 3.
For s9 == "azbazbzaz", the longest common prefix is "azbazbzaz" which has a score of 9.
For all other si, the score is 0.
The sum of the scores is 2 + 3 + 9 = 14, so we return 14.

Constraints:

• 1 <= s.length <= 10^5
• s consists of lowercase English letters.

Approach 1: Z Algorithm

The sum of the score of every $s_i$ would be the sum of the values in $Z$ array.

Written by @wingkwong

class Solution {
public:
    template <typename T>
    vector<int> z_function(int n, const T &s) {
      vector<int> z(n, n);
      int l = 0, r = 0;
      for (int i = 1; i < n; i++) {
        z[i] = (i > r ? 0 : min(r - i + 1, z[i - l]));
        while (i + z[i] < n && s[z[i]] == s[i + z[i]]) {
          z[i]++;
        }
        if (i + z[i] - 1 > r) {
          l = i;
          r = i + z[i] - 1;
        }
      }
      return z;
    }

    template <typename T>
    vector<int> z_function(const T &s) {
      return z_function((int)s.size(), s);
    }

    long long sumScores(string s) {
        long long ans = 0;
        vector<int> z = z_function(s);
        for (auto x : z) ans += x;
        return ans; 
    }
};