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3361. Shift Distance Between Two Strings

Description

You are given two strings s and t of the same length, and two integer arrays nextCost and previousCost.

In one operation, you can pick any index i of s, and perform either one of the following actions:

  • Shift s[i] to the next letter in the alphabet. If s[i] == 'z', you should replace it with 'a'. This operation costs nextCost[j] where j is the index of s[i] in the alphabet.
  • Shift s[i] to the previous letter in the alphabet. If s[i] == 'a', you should replace it with 'z'. This operation costs previousCost[j] where j is the index of s[i] in the alphabet.

The shift distance is the minimum total cost of operations required to transform s into t.

Return the shift distance from s to t.

 

Example 1:

Input: s = "abab", t = "baba", nextCost = [100,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], previousCost = [1,100,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]

Output: 2

Explanation:

  • We choose index i = 0 and shift s[0] 25 times to the previous character for a total cost of 1.
  • We choose index i = 1 and shift s[1] 25 times to the next character for a total cost of 0.
  • We choose index i = 2 and shift s[2] 25 times to the previous character for a total cost of 1.
  • We choose index i = 3 and shift s[3] 25 times to the next character for a total cost of 0.

Example 2:

Input: s = "leet", t = "code", nextCost = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], previousCost = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]

Output: 31

Explanation:

  • We choose index i = 0 and shift s[0] 9 times to the previous character for a total cost of 9.
  • We choose index i = 1 and shift s[1] 10 times to the next character for a total cost of 10.
  • We choose index i = 2 and shift s[2] 1 time to the previous character for a total cost of 1.
  • We choose index i = 3 and shift s[3] 11 times to the next character for a total cost of 11.

 

Constraints:

  • 1 <= s.length == t.length <= 105
  • s and t consist only of lowercase English letters.
  • nextCost.length == previousCost.length == 26
  • 0 <= nextCost[i], previousCost[i] <= 109

Solutions

Solution 1

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class Solution:
    def shiftDistance(
        self, s: str, t: str, nextCost: List[int], previousCost: List[int]
    ) -> int:
        m = 26
        s1 = [0] * (m << 1 | 1)
        s2 = [0] * (m << 1 | 1)
        for i in range(m << 1):
            s1[i + 1] = s1[i] + nextCost[i % m]
            s2[i + 1] = s2[i] + previousCost[(i + 1) % m]
        ans = 0
        for a, b in zip(s, t):
            x, y = ord(a) - ord("a"), ord(b) - ord("a")
            c1 = s1[y + m if y <