String Transformation

Problem Description

You are given two strings s and t of equal length n. You can perform the following operation on the string s: Remove a suffix of s of length l where 0 < l < n and append it at the start of s. Given an integer k, return the number of ways in which s can be transformed into t in exactly k operations. Since the answer can be large, return it modulo 10^9 + 7.

Key Insights

• The operation allows any non-empty suffix of s to be moved to the front.
• The transformation can be viewed as cyclic shifts of the string.
• To find the number of ways to transform s into t in k operations, we can leverage the properties of string rotations.
• The number of distinct rotations that lead to t can be determined by comparing substrings of s and t.

Space and Time Complexity

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

Solution

To solve the problem, we can follow these steps:

1. Identify Rotations: For each possible rotation of the string s, check if it matches the string t. This can be done using string concatenation (i.e., check if t is a substring of s + s).

2. Counting Valid Operations: Each valid rotation can be achieved in multiple ways, depending on the value of k. Specifically, if we have m valid rotations, then the number of ways to reach t in k operations is m if k is odd, or m if k is even.

3. Modulo Operation: Since the result can be large, return the answer modulo 10^9 + 7.

Code Solutions