Challenge: Z Algorithm

Start with the idea

Solve the exact task, not just the visible example: Return the Z array. On input aabcaabxaaaz, predict the output before opening the answer reveal. The revealed output is a test oracle for this case, while private checks exercise other legal cases. Start by stating the input grammar and output format in your own words. Parse the complete input, including surrounding whitespace, before relying on any convenient positions in the example.

Build the solution around one maintained claim: Reuse the rightmost prefix-matching box to compute how much of the prefix matches at every position. Decide what state represents that claim, how it is initialized, what a single update does, and when the algorithm stops. String algorithms compare symbols or prefixes, but a Rust String is UTF-8 bytes. State whether the task means bytes, scalar values, or grapheme clusters. Trace the visible input by hand and record at least two intermediate states, not only the final answer. If the trace cannot justify your predicted output, there is a gap between the idea and the implementation.

Use the Rust sketch as a guide, not a substitute for a complete solve function. The supplied Rust sketch is a starting point. Identify what it stores, how one iteration changes it, and whether it already solves the exact task or only demonstrates a related operation. Use bytes only when the input contract permits byte-wise matching.