Determine the -th character in a string built through repeated expansion rules without constructing the full string.
Problem
You are given a starting string and a sequence of expansion rules that repeatedly transform it into a much longer string. Your task is to determine the character at position in the final string.
The final string can become extremely large, so a correct solution should avoid explicitly building the entire result when possible. Instead, reason about how positions map through each expansion step and trace the query position back through the transformations until the answer is found.
Goal
Return the character that appears at the 1-indexed position after all transformations have been applied.
Notes
- The exact transformation details are encoded by the input for the platform problem.
- The intended challenge is to locate a single character in a recursively defined generated string.
- Efficient solutions usually work by following the ancestry of position through the construction process rather than simulating the full string.
Input Format
- The input describes the generation rules for the string and a query index .
- Assume the position is 1-indexed.
- The generated string may be too large to materialize directly.
Output Format
- Return a single character: the character located at position in the final generated string.
Constraints
- The generated string may grow exponentially across steps.
- is within the length of the final string.
- An efficient solution should use sublinear extra space and avoid constructing the full string.
Example 1
Input
s = "a" operations = ["ab", "bc"] k = 2
Output
b
Explanation
After the first expansion, the string becomes "ab". The second expansion changes it according to the given rule set, and the character at position 2 is still 'b'.
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