Minimum Time to Revert Word to Initial State II

Problem Description

You are given a 0-indexed string word and an integer k. At every second, you must perform the following operations:

• Remove the first k characters of word.
• Add any k characters to the end of word.

Return the minimum time greater than zero required for word to revert to its initial state.

Key Insights

• The problem revolves around understanding how the operations affect the state of the string over time.
• The length of the string is n, and the operations involve manipulating the first k characters and appending k characters.
• The string can be reverted to its initial state if the changes made in the operations allow the string to cycle back to its original configuration.
• The main task is to find the smallest number of operations (or seconds) required to achieve this.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

To solve this problem, we can use a combination of string manipulation and cyclic analysis. The key is to track how the string transforms with each operation and determine when it returns to its original state.

1. Track the positions: As we remove and add characters, we can track the state of the string using a combination of pointers or indices.
2. Cyclic nature: Since we are removing and adding the same amount of characters (k), we need to calculate the effective transformation of the string after each second.
3. Detect cycles: We can use a hash or a simple comparison to check when the string reverts to its original state.

The algorithm iterates through the string, applying the operations until the string matches its initial configuration, counting the number of seconds taken.

Code Solutions