Find a Repeating Vehicle Program Under Fuel and Memory Limits

Find a short program for a vehicle on a grid. The vehicle starts at a specified interior cell with 100 fuel units. It can move up, down, left, or right, spending one unit per move, or refuel at a station to gain 50 units. Obstacles cannot be crossed. The vehicle can store at most ten commands and repeats that same program until it reaches any cell in the final column. Return any program that succeeds, or report that none exists under the stated rules. No shortest program or minimum number of moves is required. ### Constraints & Assumptions The source leaves execution details open. Use these explicit practice rules: - Grid cells are free, blocked, or refueling stations. The supplied start is unblocked and not already in the last column. The map is finite and intended to be small enough for bounded-program search. - Programs have length 1 through 10 over U, D, L, R, F. The instruction pointer wraps to zero after the last command. - A move outside the grid, into an obstacle, or with zero fuel makes that candidate program fail. It does not cause the vehicle to wait or choose another direction. - F is legal only at a refueling station, adds exactly 50 fuel, and does not move. No upper fuel capacity is imposed in this practice version because the source gives only initial fuel and refill amount. - Reaching the last column succeeds immediately. A program that repeats forever without reaching it fails. ### Clarifying Questions Is the storage limit at most ten commands or exactly ten? Is fuel capacity capped? Are illegal moves fatal or ignored? Can a station be reused? Does the program have conditional branches? ### What a Strong Answer Covers A complete search space, faithful simulation, a termination argument despite possible loops, output validation, and an honest exponential complexity bound. ### Follow-up Questions How would you prune invalid command prefixes or avoid equivalent repeated programs? Which additional constraints would justify a more sophisticated search? Why is ordinary shortest-path BFS insufficient when one fixed program must repeat?