[bal7hazar]

Summary

Lot L3 of origami_hexmap: weighted shortest path without a heap, and movement range with costs.

• Dial::search(grid, width, height, from, to, costs): cheapest path, entry cost 1 unless the tile is in costs[k] (cost k + 2, at most 3 classes). A tile in several classes takes the highest cost. Output as Bfs::search (target included, start excluded, empty if unreachable or from == to).
• Dial::field_of_movement(grid, width, height, from, budget, costs) -> felt252 (new public function): tiles reachable with total cost <= budget, start included (hexx semantics).
• Time-expanded buckets: because costs are paid on entering a tile, a tile's first scheduling is final. It goes into bucket t + cost once and leaves the unvisited set at that moment. That means no stale entries, and the search stops when the target is scheduled. The ring is 4 felts, and unions are additions because the scheduled sets are disjoint.
• Separate unit-cost loop when costs is empty. Single-limb u128 path for boards <= 128 bits, sharing code through a private Set<T> trait.
• Edge endpoints are handled locally (interior layer loop, edge tiles only as endpoints). Nothing is taken from L1.

Gas (17x14, CAVE far pair, 2 classes over 30 % of the floor)

	Measured	Target
Dial::search CAVE far	1_427_654	< 1.5M
Per time step (2 classes)	36_806	< 40k
Per time step (0 / 1 / 3 classes)	26_456 / 35_600 / 38_012
Scalar Dijkstra + binary heap (baseline)	25_902_461
origami_map Dijkstra, 18x14 unit costs	22_826_630

All variants from the brief are implemented and measured in tests/bench_dial.cairo (bucket ring as locals / fixed array / Array, per-class masking vs partition, sparse layers, bit-test backtracking, corelib vs local bitwise triple, u128 vs u256, Dijkstra with a heap). The full tables are in the L3 section of GAS.md.

Tests

• Oracle: a scalar Dijkstra (test-only). Total cost is equal and every path is valid, on all fixtures, random caves (17x14, 19x13), 3x3, open edge tiles (corner, adjacent edge pairs, edge to edge) and 0 to 3 pseudo-random cost classes. field_of_movement is checked against the oracle for several budgets.
• With no costs, the path length equals the scalar BFS of tests/variants.cairo.
• Unit tests in dial.cairo: exact paths with printouts, the overlap rule, edges, dimensions, and panics (Dial: too many costs, Dial: position not walkable, asserter errors).

Scope: finders/dial.cairo, tests/bench_dial.cairo, GAS.md (L3 section).

🤖 Generated with Claude Code