Challenge: BST Search and Insert

Start with the idea

Solve the exact task, not just the visible example: Insert 5 and return inorder values. On input BST=[4,2,7,1,3], 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: Use the ordering invariant to follow one child and preserve it at insertion. Decide what state represents that claim, how it is initialized, what a single update does, and when the algorithm stops. A tree result is built from a node and its children. Decide whether information flows downward, upward, or in level order. 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.