Start by tracking the frequency of each character in the original string. Apply state transition dynamic programming to simulate transformations efficiently without rebuilding the string. Use modular arithmetic to handle large results and ensure the calculation scales with high t values.
Problem Statement
You are given a lowercase string s and an integer t representing the number of transformations. In one transformation, each character in s is replaced according to a fixed set of rules, and the process repeats for t transformations.
Return the length of the string after exactly t transformations, computed modulo 10^9 + 7. Optimize your approach to handle strings and transformations of length up to 10^5 efficiently.
Examples
Example 1
Input: s = "abcyy", t = 2
Output: 7
Example 2
Input: s = "azbk", t = 1
Output: 5
Constraints
- 1 <= s.length <= 105
- s consists only of lowercase English letters.
- 1 <= t <= 105
Solution Approach
Frequency Mapping
Create a hash table to store the count of each character in the initial string. This allows constant-time access for updating counts during each transformation.
Dynamic Programming Transitions
Use state transition dynamic programming to compute how counts of each character evolve after each transformation. Avoid reconstructing the string, updating only the frequencies per character.
Modulo Summation
After all t transformations, sum the counts of all characters and take modulo 10^9 + 7. This ensures the result stays within integer limits while reflecting the total string length.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | O(n + t |
| Space | O( |
Time complexity is O(n + t|Σ|) where n is the initial string length and |Σ| is the alphabet size, since each transformation updates character counts. Space complexity is O(|Σ|) for storing frequency counts of all lowercase letters.
What Interviewers Usually Probe
- Notice how naive string reconstruction fails for large t due to exponential growth.
- Tracking frequencies instead of actual strings is key for optimal performance.
- State transition dynamic programming is expected; watch for off-by-one or modulo errors.
Common Pitfalls or Variants
Common pitfalls
- Attempting to build the full string at each transformation, causing memory overflow.
- Forgetting to apply modulo after each addition, leading to integer overflow.
- Mismanaging frequency updates and double-counting characters in transitions.
Follow-up variants
- Return the actual transformed string instead of its length for small t.
- Allow custom transformation rules defined per character.
- Compute the maximum character frequency after t transformations rather than total length.
How GhostInterview Helps
- GhostInterview quickly simulates character frequency transitions without full string construction.
- It identifies correct state transitions and modulo usage to avoid overflow mistakes.
- The tool highlights common off-by-one and frequency counting pitfalls for this exact problem pattern.
Topic Pages
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- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What pattern does Total Characters in String After Transformations I follow?
It follows a state transition dynamic programming pattern where character frequencies evolve over t transformations.
Can this approach handle very large t efficiently?
Yes, by tracking frequencies and applying transitions without reconstructing the string, it scales to t up to 10^5.
Why is modulo 10^9 + 7 needed?
The string length can grow exponentially with t, so modulo ensures the result stays within integer limits.
Is it necessary to store the entire string during transformations?
No, storing only character counts is sufficient and prevents memory overflow.
What common mistakes should I avoid in this problem?
Avoid rebuilding the string, forgetting modulo operations, and incorrectly updating character frequencies in transitions.
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Calculate the length of a string after repeated transformations using state transition dynamic programming for large t values efficiently.
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