Decremental String Concatenation — LeetCode 2746 Python Solution

The problem

You are given a 0-indexed array words containing n strings. Let's define a join operation join(x, y) between two strings x and y as concatenating them into xy.

Example

Input

words = ["aa","ab","bc"]

Output

4

Explanation

In this example, we can perform join operations in the following order to minimize the length of str2:

Python solution

class Solution:
    def minimizeConcatenatedLength(self, words: List[str]) -> int:
        @cache
        def dfs(i: int, a: str, b: str) -> int:
            if i >= len(words):
                return 0
            s = words[i]
            x = dfs(i + 1, a, s[-1]) - int(s[0] == b)
            y = dfs(i + 1, s[0], b) - int(s[-1] == a)
            return len(s) + min(x, y)

        return len(words[0]) + dfs(1, words[0][0], words[0][-1])

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 2746. Decremental String Concatenation is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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