Z Algorithm: When to Use It

Start with the idea

A problem is a good match for Z Algorithm when it asks for pattern search, repetitions, prefix matches. Here the concrete task is: Return the Z array. The visible input aabcaabxaaaz is an example, not a definition of the whole problem. Ask what operations the solution must support and what the input guarantees. Look for repeated prefix queries or pattern matching before choosing a trie or preprocessing; a one-off short search may not need either. The right choice follows from those guarantees, not from a familiar noun in the prompt.

The decisive invariant is: Reuse the rightmost prefix-matching box to compute how much of the prefix matches at every position. Try to say why it applies to the task without quoting the implementation. Which fact becomes known after one update, and which possible answers remain? 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. If that claim cannot be maintained on a legal input, the pattern is wrong or one of its preconditions is missing. A counterexample is more useful than a vague warning: change one property of the sample, trace the first two steps, and identify the exact claim that fails.

Compare costs before committing. The advertised bound is O(n) time · O(n) space; identify the operation responsible for it and the extra memory it needs.