Problem Description

Analysts have determined that people often use personal information in their passwords, which is insecure. A new feature is needed to address this issue.

The feature will:

1. Search for the presence of a reference string as a subsequence in any permutation of the password.
2. If the reference string is found as a subsequence, determine the minimum cost to remove characters from the password so that no permutation contains the reference string as a subsequence.

Details:

• The cost of removing any character is specified in an array cost, with 26 elements.
  • cost[0] corresponds to the cost of removing 'a'.
  • cost[25] corresponds to the cost of removing 'z'.

Inputs:

1. string password: The password string.
2. string reference: The string that should not appear as a subsequence in any permutation of the password.
3. int cost[26]: The costs to remove each character in the lowercase English alphabet.

Output:

• long int: The minimum total cost to remove characters from the password such that no permutation contains the reference string as a subsequence.

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Example

Input:

password = "adefgh"
reference = "hf"
cost = [1, 0, 0, 2, 4, 4, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Explanation:

• Removing either 'h' or 'f' will ensure that reference no longer appears as a subsequence in any permutation.
• Removing 'h' has a cost of 1, while removing 'f' has a cost of 4.
• The minimum cost is 1 (removing 'h').

Output:

1

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Function Signature

def minCost(password: str, reference: str, cost: List[int]) -> int:
    pass

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Plan for Implementation

1. Character Frequency Count:
   • Count the frequency of each character in the password.
   • Use these counts to determine the minimum removals required.
2. Subsequence Check:
   • Iterate over the characters in the reference to determine their presence in the password frequency.
3. Cost Calculation:
   • Compute the cost of removing each required character.
   • Use a greedy approach to minimize the total cost.
4. Output the Minimum Cost:
   • Return the minimum cost to modify the password.

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