Prim minimum spanning trees

Implement prototype(costs) and solve(costs). Input must be a square symmetric matrix. Number entries are undirected edge costs, null means no edge, and zero/negative costs are valid. Ignore diagonal edges only after shape/symmetry validation.

Return the MST total or null if disconnected. [] returns 0. [[0, 2, 8], [2, 0, 1], [8, 1, 0]] returns 3. Nonsquare or asymmetric matrices throw RangeError.

Prototype: convert to edges and use an MST method. Final: dense array-frontier Prim in O(V²) time/O(V) auxiliary space. Preserve every input row, including on failure.

All numeric inputs and finite arithmetic results in this lesson are safe-integer Numbers. Use null for documented absence, not undefined or a numeric sentinel. Return actual booleans where the contract requires them. Do not add validation requirements beyond the documented inputs.

Run with Node.js 20+ from this directory:

node main.mjs --stage prototype
node main.mjs --stage final

Edit exercise.mjs; keep main.mjs unchanged. Both stages begin as unfinished learner functions. The website uses the same test functions in a separate browser worker. Tests check deterministic examples, boundaries, documented validation, input preservation, and stage-specific cases. Passing tests does not prove the required time complexity.