Challenge: A* Search

Start with the idea

Solve the exact task, not just the visible example: On a 4x4 empty grid, return shortest moves from (0,0) to (3,2) using Manhattan heuristic. On input start=0,0 goal=3,2, 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: Prioritize distance-so-far plus an admissible estimate that never overstates remaining cost. Decide what state represents that claim, how it is initialized, what a single update does, and when the algorithm stops. Edge weights change what a path means. State whether the objective is minimum distance, a spanning structure, or feasible flow before choosing state. 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 an invariant note rather than a complete program. Turn it into explicit state and transitions before coding. Use numeric types wide enough for distances, weights, or capacities.