#3335

Medium

auto_awesomeState transition dynamic programming

LeetCode Problem Workspace

Total Characters in String After Transformations I

Calculate the total number of characters in a string after repeated transformations using dynamic programming and frequency tracking.

hash table math string dynamic programming counting

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.

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.

terminal

Solution

Solution 1: Recurrence

We define $f[i][j]$ to represent the count of the $j$-th letter in the alphabet after $i$ transformations. Initially, $f[0][j]$ is the count of the $j$-th letter in the string $s$.

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class Solution:
    def lengthAfterTransformations(self, s: str, t: int) -> int:
        f = [[0] * 26 for _ in range(t + 1)]
        for c in s:
            f[0][ord(c) - ord("a")] += 1
        for i in range(1, t + 1):
            f[i][0] = f[i - 1][25]
            f[i][1] = f[i - 1][0] + f[i - 1][25]
            for j in range(2, 26):
                f[i][j] = f[i - 1][j - 1]
        mod = 10**9 + 7
        return sum(f[t]) % mod

Continue Practicing

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