Challenge: Quickselect

Start with the idea

Solve the exact task, not just the visible example: Return the third smallest value. On input [7,10,4,3,20,15], 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: Partition like quicksort but recurse only into the side containing the requested rank. Decide what state represents that claim, how it is initialized, what a single update does, and when the algorithm stops. Sorting establishes global order; selection asks only for a rank or partition. Explain which comparisons make progress toward that goal. 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.