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 10^9 + 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.

Difficulty: MEDIUM_HARD
Tags: String algorithms

Dynamic programming
Skill types: Dynamic programming

Starter code:
class Solution:
    def findGoodStrings(self, n: int, s1: str, s2: str, evil: str) -> int:
        

Solutions:
from functools import lru_cache

def failure(pat):
	(i, target, n) = (1, 0, len(pat))
	res = [0]
	while i < n:
		if pat[i] == pat[target]:
			target += 1
			res.append(target)
			i += 1
		elif target:
			target = res[target - 1]
		else:
			res.append(0)
			i += 1
	return res

class Solution:

	def findGoodStrings(self, n: int, s1: str, s2: str, evil: str) -> int:
		f = failure(evil)

		@lru_cache(None)
		def dfs(idx, max_matched=0, lb=True, rb=True):
			if max_matched == len(evil):
				return 0
			if idx == n:
				return 1
			l = s1[idx] if lb else 'a'
			r = s2[idx] if rb else 'z'
			candidates = [chr(i) for i in range(ord(l), ord(r) + 1)]
			res = 0
			for (i, c) in enumerate(candidates):
				next_matched = max_matched
				while next_matched and evil[next_matched] != c:
					next_matched = f[next_matched - 1]
				res += dfs(idx + 1, next_matched + (evil[next_matched] == c), lb and i == 0, rb and i == len(candidates) - 1)
			return res
		return dfs(0) % (10 ** 9 + 7)


class Solution:

	def findGoodStrings(self, N, *args):
		from functools import lru_cache
		(s1, s2, evil) = [list(map(ord, i)) for i in args]
		mod = 10 ** 9 + 7

		def kmp(l, c):
			while l and evil[l] != c:
				l = f[l - 1]
			if evil[l] == c:
				l += 1
			return l
		f = [0] * len(evil)
		for i in range(1, len(evil)):
			f[i] = kmp(f[i - 1], evil[i])

		@lru_cache(None)
		def dp(i=0, lcp=0, f1=False, f2=False):
			if lcp == len(evil):
				return 0
			if i == N:
				return 1
			ans = 0
			for char in range(f1 and 97 or s1[i], f2 and 123 or s2[i] + 1):
				ans += dp(i + 1, kmp(lcp, char), f1 or char > s1[i], f2 or char < s2[i])
				ans %= mod
			return ans
		return dp()


class Solution:

	def findGoodStrings(self, n: int, s1: str, s2: str, evil: str) -> int:

		@lru_cache(None)
		def dfs(k, j, b1, b2):
			if k == n:
				return 1
			start = ord(s1[k]) if b1 else ord('a')
			end = ord(s2[k]) if b2 else ord('z')
			res = 0
			for x in range(start, end + 1):
				c = chr(x)
				l = j
				while l > 0 and c != evil[l]:
					l = lps[l - 1]
				nevil = True
				if c == evil[l]:
					l += 1
					if l == m:
						nevil = False
				if nevil:
					res += dfs(k + 1, l, b1 and c == s1[k], b2 and c == s2[k])
					res %= mod
			return res
		m = len(evil)
		lps = [0] * m
		for i in range(1, m):
			j = lps[i - 1]
			while j > 0 and evil[j] != evil[i]:
				j = lps[j - 1]
			if evil[j] == evil[i]:
				lps[i] = j + 1
		mod = 10 ** 9 + 7
		return dfs(0, 0, True, True)


class Solution:

	def findGoodStrings(self, n: int, s1: str, s2: str, evil: str) -> int:
		M = 10 ** 9 + 7
		table = [-1]
		(pos, cnd) = (1, 0)
		while pos < len(evil):
			if evil[pos] == evil[cnd]:
				table.append(table[cnd])
			else:
				table.append(cnd)
				cnd = table[cnd]
				while cnd >= 0 and evil[pos] != evil[cnd]:
					cnd = table[cnd]
			pos += 1
			cnd += 1
		table.append(cnd)

		@lru_cache(None)
		def dfs(i, j, u, b):
			if j == len(evil):
				return 0
			if i == n:
				return 1
			r = 0
			for c in range(ord(s1[i]) if b else 97, ord(s2[i]) + 1 if u else 123):
				if c == ord(evil[j]):
					t = dfs(i + 1, j + 1, u and c == ord(s2[i]), b and c == ord(s1[i]))
				else:
					p = j
					while p >= 0:
						if c == ord(evil[p]):
							break
						p = table[p]
					t = dfs(i + 1, p + 1, u and c == ord(s2[i]), b and c == ord(s1[i]))
				r += t
			return r % M
		return dfs(0, 0, True, True)


class Solution:

	def findGoodStrings(self, n: int, s1: str, s2: str, evil: str) -> int:
		e_len = len(evil)
		par = [0] * e_len
		for i in range(1, e_len):
			j = par[i - 1]
			while j and evil[i] != evil[j]:
				j = par[j - 1]
			j += int(evil[i] == evil[j])
			par[i] = j
		mod = 10 ** 9 + 7

		@lru_cache(None)
		def rec(cur, ei, sm, bg):
			if ei == e_len:
				return 0
			if cur == n:
				return 1
			ans = 0
			st = ord('a') if bg else ord(s1[cur])
			ed = ord('z') if sm else ord(s2[cur])
			for i in range(st, ed + 1):
				if i == ord(evil[ei]):
					new_ei = ei + 1
				else:
					new_ei = ei
					while new_ei and evil[new_ei] != chr(i):
						new_ei = par[new_ei - 1]
					if evil[new_ei] == chr(i):
						new_ei += 1
				ans += rec(cur + 1, new_ei, sm | (i < ord(s2[cur])), bg | (i > ord(s1[cur])))
			return ans % mod
		return rec(0, 0, False, False) % mod


from functools import lru_cache
from itertools import takewhile

class Solution:

	def findGoodStrings(self, n: int, A: str, B: str, evil: str) -> int:
		MOD = 10 ** 9 + 7
		evil_checker = KMPTable(evil)

		@lru_cache(None)
		def DP(i=0, startswith_A=True, startswith_B=True, match_evil=0):
			if match_evil == len(evil):
				return 0
			if i == n:
				return 1
			start = A[i] if startswith_A else 'a'
			end = B[i] if startswith_B else 'z'
			return sum((DP(i + 1, startswith_A and c == A[i], startswith_B and c == B[i], match_evil=evil_checker.match(c, idx=match_evil)) for c in map(chr, list(range(ord(start), ord(end) + 1))))) % MOD
		return DP()

class KMPTable:

	def __init__(self, s):
		self.s = s
		self._init_table()

	def _init_table(self):
		self.table = [0, 0]
		for i in range(1, len(self.s)):
			self.table.append(self.match(self.s[i], idx=self.table[-1]))

	def match(self, c, idx):
		if c == self.s[idx]:
			return idx + 1
		return self.match(c, self.table[idx]) if idx > 0 else 0


class Solution:

	def findGoodStrings(self, n: int, s1: str, s2: str, evil: str) -> int:
		MOD = 1000000000 + 7
		K = len(evil)
		umap = [[[[0 for x in range(2)] for j in range(2)] for k in range(K)] for l in range(n)]
		lps = list()

		def computeLPS(s: str) -> List[int]:
			N = len(s)
			dp = [0 for i in range(N)]
			j = 0
			for i in range(1, N):
				while j > 0 and s[i] != s[j]:
					j = dp[j - 1]
				if s[i] == s[j]:
					j += 1
				dp[i] = j
			return dp

		def dfs(sp, ep, leftB, rightB) -> int:
			if ep >= K:
				return 0
			if sp >= n:
				return 1
			if umap[sp][ep][leftB][rightB] == 0:
				i = s1[sp] if leftB == 1 else 'a'
				j = s2[sp] if rightB == 1 else 'z'
				while ord(i) <= ord(j):
					nxt = ep
					while nxt > 0 and i != evil[nxt]:
						nxt = lps[nxt - 1]
					res = umap[sp][ep][leftB][rightB] + dfs(sp + 1, nxt + 1 if evil[nxt] == i else 0, 1 if leftB == 1 and i == s1[sp] else 0, 1 if rightB == 1 and i == s2[sp] else 0)
					umap[sp][ep][leftB][rightB] = res % MOD
					i = chr(ord(i) + 1)
			return umap[sp][ep][leftB][rightB]
		lps = computeLPS(evil)
		return dfs(0, 0, 1, 1)


import functools

class Solution:

	def findGoodStrings(self, n: int, s1: str, s2: str, evil: str) -> int:

		def calc(k, char):
			i = 0
			while i <= k and (not evil[i:k] + char == evil[:k - i + 1]):
				i += 1
			return k - i + 1

		@functools.lru_cache(None)
		def dp(i, k, limit_low, limit_high):
			if k == len(evil):
				return 0
			if i == n:
				return 1
			ans = 0
			min_char = s1[i] if limit_low else 'a'
			max_char = s2[i] if limit_high else 'z'
			for o in range(ord(min_char), ord(max_char) + 1):
				curr = chr(o)
				if curr == evil[k]:
					ans += dp(i + 1, k + 1, limit_low and curr == min_char, limit_high and curr == max_char)
				else:
					ans += dp(i + 1, calc(k, curr), limit_low and curr == min_char, limit_high and curr == max_char)
			return ans % (10 ** 9 + 7)
		return dp(0, 0, True, True) % (10 ** 9 + 7)