# Solution Alignment The prompt asks for an implementation-level answer. The safest way to present it is to define the state, maintain clear invariants, then walk through complexity and tests. ## Problem Restatement ##### Question Implement a URL routing matcher that supports adding route patterns and matching request paths, using a trie (prefix tree) as the core data structure. Paths are split into `/`-delimited segments. Support static segments (e.g., `/a/b/c`) and a single-segment wildcard `*` that matches exactly one segment (e.g., `/a/*/c`). Design and implement the following: 1. **APIs.** Provide `addRoute(pattern, handler)`, `removeRoute(pattern)`, and `match(path) -> (matchedHandler, matchedPattern)`. Routes must be addable and removable at runtime. 2. **Wildcard matching.** `*` matches exactly one path segment. For example, `/a/*/c` matches `/a/x/c` and `/a/y/c` but not `/a/c` or `/a/x/y/c`. 3.... ## Recommended Approach Choose traversal based on the required view or aggregate. DFS is natural for subtree computations and reconstruction; BFS is natural for level order or side views. Keep per-depth or per-position state when the output depends on columns, rows, or depths. ## Correctness The implementation should maintain an invariant after each loop or operation that directly matches the problem statement. At termination, that invariant implies the returned value has considered every valid candidate exactly once, or has preserved the required data-structure state after every API call. ## Complexity Most tree traversals are O(n) time and O(h) recursion stack for DFS or O(w) queue space for BFS, where h is height and w is maximum width. ## Edge Cases and Tests Empty tree, one node, skewed tree, duplicate values when reconstruction assumes uniqueness, deep recursion, and tie-breaking for same row/column nodes.

Rubric: the candidate should (1) choose a segment-keyed trie with a dedicated wildcard edge per node (not a character trie); (2) implement addRoute/removeRoute/match cleanly, including path normalization for leading/trailing slashes and the root path; (3) get precedence right — static beats wildcard via a DFS that tries the exact branch first and BACKTRACKS to the wildcard, since a greedy exact-first walk fails on inputs like /a/x/c with patterns {/a/x/d, /a/*/c}; (4) enforce single-segment wildcard semantics (matches exactly one segment); (5) analyze complexity (O(S) add/remove, O(S) match without wildcards, with the wildcard-backtracking caveat) and prune empty nodes on removal; and (6) discuss thread safety, ideally landing on copy-on-write with an atomic root swap for lock-free reads in a read-heavy router, or at minimum a read-write lock. Strong answers also state a duplicate-route policy and write tests for the listed edge cases.