The String Transformation interview question is a complex problem that involves determining the number of ways to transform one string into another using a specific set of operations. Usually, the operation allowed is shifting the string—taking a suffix and moving it to the front. You are asked to find how many ways you can reach the target string from the source string in exactly k operations. Because the number of ways can be very large, the result is typically required modulo 10^9 + 7. It combines string matching with advanced mathematics.
This is a "hard" rated problem asked by companies like Google and Atlassian because it requires a combination of different skills: string searching (to find how many shifts result in the target string) and dynamic programming or matrix exponentiation (to calculate the number of ways to reach a state in k steps). It tests a candidate's ability to simplify a large problem into a mathematical recurrence. It's not just about coding; it's about identifying patterns in state transitions over a large number of iterations.
This problem uses two main patterns. First, String Matching (using KMP or Z-algorithm) is used to find all possible single-shift positions where the source string matches the target. Second, Dynamic Programming or Combinatorics is used to find the number of sequences of k shifts that end at a matching position. Specifically, because all non-matching shifts are equivalent and all matching shifts (other than the identity) are often equivalent, the DP can be reduced to a simple recurrence that can be solved in O(log k) using matrix exponentiation or O(k) using linear DP.
Suppose source = "abcd", target = "cdab", and k = 2.
A major pitfall is trying to simulate all possible shifts for k steps, which is impossible given that k can be as large as 10^15. Failing to recognize that the problem can be modeled as a state transition between "currently at a match" and "currently not at a match" is another common error. Candidates also struggle with the string matching part, especially handling the circular nature of shifts (often solved by concatenating the string with itself).
To master the String Transformation interview question, study how to solve recurrences using matrix exponentiation. Also, ensure you have a solid grasp of the KMP algorithm for finding occurrences of a pattern in a circular string. Practicing "counting ways to reach a state in K steps" problems will help you see the underlying structure of this hard challenge. Focus on reducing the number of states to the absolute minimum.
| Title | Difficulty | Topics | LeetCode |
|---|---|---|---|
| Find All Good Strings | Hard | Solve | |
| Count the Number of Powerful Integers | Hard | Solve | |
| Count of Integers | Hard | Solve | |
| Number of Ways to Divide a Long Corridor | Hard | Solve | |
| Maximum Repeating Substring | Easy | Solve |
