Maximum Deletions on a String

Problem Description

You are given a string s consisting of only lowercase English letters. In one operation, you can:

• Delete the entire string s, or
• Delete the first i letters of s if the first i letters of s are equal to the following i letters in s, for any i in the range 1 <= i <= s.length / 2.

Return the maximum number of operations needed to delete all of s.

Key Insights

• The task requires finding repeated substrings within the string to maximize deletion operations.
• Deleting the entire string counts as one operation.
• We need to identify the longest prefixes that can be removed based on the conditions provided.
• The problem can be approached using dynamic programming or greedy strategies to optimize the number of deletions.

Space and Time Complexity

Time Complexity: O(n^2), where n is the length of the string. Each potential prefix is compared with its corresponding substring. Space Complexity: O(n), for storing results in the DP array (if used).

Solution

The solution involves iterating through the string and checking for valid prefixes that can be removed, while counting the number of operations. A dynamic programming approach can be employed where we maintain an array that tracks the maximum number of operations possible from each index in the string.

1. Initialize a DP array where dp[i] represents the maximum operations needed to delete the substring starting from index i.
2. For each index i, check potential prefixes and their matches in the remaining substring.
3. Update the DP array based on valid deletions.
4. The result will be stored in dp[0], which will represent the maximum operations needed to delete the entire string.

Code Solutions