First, parse the command string into a sequence of primitive operations (move, turn) by expanding repeat blocks. Then simulate one full run to find the final position and heading, and use the final displacement and orientation change to determine if the path is bounded when repeated infinitely. Finally, analyze time and space complexity, considering grid size and command length.
Pro tip: After one run, if the robot's heading is unchanged and it has moved, the path is unbounded; if the heading changes, the path is bounded because the robot will cycle through a finite set of positions and orientations. Also, handle blocked cells by treating them as obstacles that prevent movement, but remember that turns still occur.
Convert the command string into a list of primitive operations (move forward, turn left/right) by recursively expanding repeat blocks (e.g., '3M' becomes 'M M M'). Use a stack or recursion to handle nested repeats.
Starting at (0,0) facing north, execute each primitive operation. For moves, check if the next cell is blocked; if not, update position. For turns, update heading. Record the final position and heading.
After one run, if the robot's heading is unchanged and it has moved (i.e., displacement is non-zero), the path is unbounded. If the heading changed, the path is bounded because the robot will eventually return to a previous state (position and orientation) and cycle.
Time complexity is O(N * L) where N is the number of runs considered (at most 4 for boundedness check) and L is the length of the expanded command string. Space complexity is O(L) for storing the expanded commands or O(1) if simulating on the fly with a stack.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.