Problem Description
You are given a string s consisting of lowercase English letters, an integer t representing the number of transformations to perform, and an array nums of size 26. In one transformation, every character in s is replaced according to the following rules:
- Replace s[i] with the next nums[s[i] - 'a'] consecutive characters in the alphabet. For example, if s[i] = 'a' and nums[0] = 3, the character 'a' transforms into the next 3 consecutive characters ahead of it, which results in "bcd".
- The transformation wraps around the alphabet if it exceeds 'z'. For example, if s[i] = 'y' and nums[24] = 3, the character 'y' transforms into the next 3 consecutive characters ahead of it, which results in "zab".
Return the length of the resulting string after exactly t transformations. Since the answer may be very large, return it modulo 10^9 + 7.
Key Insights
- Each character transformation depends on its corresponding value in the nums array.
- The transformations can cause exponential growth in the length of the string due to the wrapping around the alphabet.
- Since t can be very large (up to 10^9), simulating each transformation is inefficient, requiring an optimized approach.
- Understanding how the transformations affect the length rather than the actual string is crucial for efficiency.
Space and Time Complexity
Time Complexity: O(n + k), where n is the length of the string s and k is the effective number of transformations based on the cumulative effects of nums. Space Complexity: O(1), as we are using a fixed-size array regardless of input size.
Solution
The solution involves calculating the growth of the string's length after each transformation without explicitly constructing the new string. We can track how each character expands based on the values in the nums array and the total number of transformations. By simulating the growth in lengths iteratively, we can achieve the desired result efficiently.