1397. Find All Good Strings

Problem Link

Description

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Given the strings s1 and s2 of size n and the string evil, return the number of good strings.

A good string has size n, it is alphabetically greater than or equal to s1, it is alphabetically smaller than or equal to s2, and it does not contain the string evil as a substring. Since the answer can be a huge number, return this modulo 109 + 7.

 

Example 1:

Input: n = 2, s1 = "aa", s2 = "da", evil = "b"
Output: 51 
Explanation: There are 25 good strings starting with 'a': "aa","ac","ad",...,"az". Then there are 25 good strings starting with 'c': "ca","cc","cd",...,"cz" and finally there is one good string starting with 'd': "da". 

Example 2:

Input: n = 8, s1 = "leetcode", s2 = "leetgoes", evil = "leet"
Output: 0 
Explanation: All strings greater than or equal to s1 and smaller than or equal to s2 start with the prefix "leet", therefore, there is not any good string.

Example 3:

Input: n = 2, s1 = "gx", s2 = "gz", evil = "x"
Output: 2

 

Constraints:

• s1.length == n
• s2.length == n
• s1 <= s2
• 1 <= n <= 500
• 1 <= evil.length <= 50
• All strings consist of lowercase English letters.

Solution

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Python3

class Solution:
    def _kmp(self, pattern: str):
        tab = [0] * len(pattern)
        j = 0
        for i in range(1, len(pattern)):
            while j and pattern[i] != pattern[j]:
                j = tab[j - 1]
            if pattern[i] == pattern[j]:
                j += 1
            tab[i] = j
        return tab
 
    def findGoodStrings(self, n: int, s1: str, s2: str, evil: str) -> int:
        M = 10 ** 9 + 7
        E = len(evil)
        s1 = [ord(x) - ord('a') for x in s1]
        s2 = [ord(x) - ord('a') for x in s2]
        kmp = self._kmp(evil)
        evil = [ord(x) - ord('a') for x in evil]
 
        @cache
        def go(index, evilIndex, tight1, tight2):
            if evilIndex == E: return 0
 
            if index == n: return 1
 
            low = s1[index] if tight1 else 0
            high = s2[index] if tight2 else 25
            res = 0
 
            for char in range(low, high + 1):
                nxtTight1 = tight1 and char == s1[index]
                nxtTight2 = tight2 and char == s2[index]
 
                j = evilIndex
                while j > 0 and evil[j] != char:
                    j = kmp[j - 1]
                
                if evil[j] == char:
                    j += 1
                
                res += go(index + 1, j, nxtTight1, nxtTight2)
                res %= M
            
            return res
 
        return go(0, 0, True, True)