Challenge: Interval Stabbing

Start with the idea

Solve the exact task, not just the visible example: Return the minimum points needed to hit all intervals. On input [(10,16),(2,8),(1,6),(7,12)], 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: Sort by interval end and place a point only when the next interval starts after the current point. Decide what state represents that claim, how it is initialized, what a single update does, and when the algorithm stops. A greedy step commits to a local choice. Give the exchange or dominance reason that an optimal solution can still include that choice. 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. Keep interval endpoint conventions explicit where they apply.