Problem Description
You are given a 0-indexed array words containing n strings. You need to perform n - 1 join operations. The join operation concatenates two strings x and y into xy, but if the last character of x is equal to the first character of y, one of them is deleted. Your task is to minimize the length of the final concatenated string.
Key Insights
- The join operation can be performed in two ways: joining the previous string with the current string or joining the current string with the previous string.
- The deletion occurs only when the last character of the first string matches the first character of the second string.
- We need to explore both joining orders at each step to find the optimal solution that minimizes the final string length.
Space and Time Complexity
Time Complexity: O(n * max_length), where n is the number of strings and max_length is the maximum length of the strings (up to 50). Space Complexity: O(n), for storing the lengths of the resulting strings during the join operations.
Solution
To solve this problem, we can use a dynamic programming approach. We maintain an array dp where dp[i] represents the minimum length of the concatenated string after performing joins up to the i-th string. For each string, we calculate the possible lengths when joined with the previous string in both orders (i.e., join(dp[i-1], words[i]) and join(words[i], dp[i-1])). We update the dp array with the minimum lengths found.