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:
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".'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 109 + 7.
Example 1:
Input: s = "abcyy", t = 2, nums = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2]
Output: 7
Explanation:
First Transformation (t = 1):
'a' becomes 'b' as nums[0] == 1'b' becomes 'c' as nums[1] == 1'c' becomes 'd' as nums[2] == 1'y' becomes 'z' as nums[24] == 1'y' becomes 'z' as nums[24] == 1"bcdzz"Second Transformation (t = 2):
'b' becomes 'c' as nums[1] == 1'c' becomes 'd' as nums[2] == 1'd' becomes 'e' as nums[3] == 1'z' becomes 'ab' as nums[25] == 2'z' becomes 'ab' as nums[25] == 2"cdeabab"Final Length of the string: The string is "cdeabab", which has 7 characters.
Example 2:
Input: s = "azbk", t = 1, nums = [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
Output: 8
Explanation:
First Transformation (t = 1):
'a' becomes 'bc' as nums[0] == 2'z' becomes 'ab' as nums[25] == 2'b' becomes 'cd' as nums[1] == 2'k' becomes 'lm' as nums[10] == 2"bcabcdlm"Final Length of the string: The string is "bcabcdlm", which has 8 characters.
Constraints:
1 <= s.length <= 105s consists only of lowercase English letters.1 <= t <= 109nums.length == 261 <= nums[i] <= 25This approach involves directly simulating each transformation step-by-step. For each character in the string, determine the next characters it transforms into based on the nums array. Repeat this process t times and calculate the length of the resulting string.
This approach, while straightforward, can quickly become computationally expensive as the length of the string grows exponentially with each transformation, especially for large values of t.
The function total_transformed_length takes a string s, the number of transformations t, and an array nums. It calculates the length of the resulting string after t transformations. The length is computed by summing up the transformation length for each character in the string and is returned modulo 10^9 + 7.
C++
Time Complexity: O(t * n), where n is the length of the string s.
Space Complexity: O(1), as we only store a few variables for computation.
Instead of simulating each transformation, consider calculating how the length changes character by character and accumulate the total transformation effect. The transformation sequence is uniform, and we can calculate the total theoretical length in one go using matrix exponentiation or pre-computed powers.
This approach directly calculates the expected length based on fixed relationship assumptions, avoiding direct string manipulations and reducing computational complexity significantly.
The method totalTransformedLength calculates the product of transformation lengths raised to the power of t using quick powering technique (fastPower), thereby efficiently computing the final length without simulating each transformation.
JavaScript
Time Complexity: O(log t + n), where n is the length of the input string.
Space Complexity: O(1).
| Approach | Complexity |
|---|---|
| Direct Simulation of Transformations | Time Complexity: |
| Mathematical Calculation Without Simulation | Time Complexity: |
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