3591. Shift Distance Between Two Strings

Medium
Array
String
Prefix Sum

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

Hints

Hint 1
- For every unordered pair of characters <code>(a, b)</code>, the cost of turning <code>a</code> into <code>b</code> is equal to the minimum between: <ul> <li>If <code>i < j</code>, <code>nextCost[i] + nextCost[i + 1] + … + nextCost[j - 1]</code>, and <code>nextCost[i] + nextCost[i + 1] + … + nextCost[25] + nextCost[0] + … + nextCost[j - 1]</code> otherwise.</li> <li>If <code>i < j</code>, <code>prevCost[i] + prevCost[i - 1] + … + prevCost[0] + prevCost[25] + … + prevCost[j + 1]</code>, and <code>prevCost[i] + prevCost[i - 1] + … + prevCost[j + 1]</code> otherwise.</li> </ul> Where <code>i</code> and <code>j</code> are the indices of <code>a</code> and <code>b</code> in the alphabet.
Hint 2
The shift distance is the sum of costs of turning <code>s[i]</code> into <code>t[i]</code>.

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