Maze solver: fix the failing search, then add one-way gates and the route

Context

Welcome to the robotics team. maze/ finds the robots' paths; the rules are in README.md. Start by running the tests: the search itself fails on some floors, and that comes first. Then add the one-way gates the new floor plan uses, then the route the robots actually follow.

You have 40 minutes. The checks are graded one by one, so each part you get working counts even if the rest is not done. Use the AI assistant if you like, but check what it gives you against the README and the tests.

MZ-1: The search fails on floors that are not square

Report

On a floor 5 cells wide and 3 tall the solver says the exit cannot be reached; on a tall, narrow floor it crashes.

Acceptance criteria

• steps() is correct on floors of any shape.

MZ-2: One-way gates (level 2)

Acceptance criteria

• >, <, ^ and v are entered and left only by their own move, as the README describes.
• steps() follows the gate rules.

MZ-3: The route (level 3)

Acceptance criteria

• route() returns the letters of a shortest route, alphabetical first when there is a tie, and "" when there is none.

Notes

• Run pytest tests/visible. Four tests fail on the current code.
• The hidden checks include large floors.
• Practice task modelled on candidate reports of Meta's AI-enabled coding round, where a core problem was a maze search with directional gates. Original StackYard code, not the actual question; not affiliated with Meta.