Use BFS to find the shortest path in an unweighted grid, treating each cell as a node and moves to adjacent open cells as edges. Start from the top-left, explore level by level, and return the distance when reaching the bottom-right or -1 if unreachable. Then prove correctness by arguing BFS explores nodes in non-decreasing distance order, and analyze time and space as O(mn).
Pro tip: Explicitly state that BFS is optimal for unweighted shortest paths, and mention that you'd handle edge cases like start or end being blocked. Also, note that you can optimize space by using a visited matrix or modifying the grid in-place if allowed.
Confirm grid dimensions, movement directions, and that start/end are open. Discuss handling of blocked start/end and empty grid.
Explain that BFS is ideal for unweighted shortest path. Initialize a queue with start cell and distance 0, and a visited set or matrix.
While queue not empty, dequeue cell, check if it's the target, and if not, enqueue all valid unvisited neighbors with distance+1. Mark visited when enqueuing.
Argue that BFS explores nodes in order of increasing distance, so the first time we reach the target, the distance is minimal. Also, if target not reached, no path exists.
Time: O(mn) since each cell is enqueued at most once. Space: O(mn) for queue and visited matrix in worst case.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Propose a systematic exploration algorithm like DFS with backtracking, using relative coordinate tracking and a stack to record the path. After finding the target, compute the shortest path by BFS on the discovered graph or by analyzing the backtracking path to eliminate cycles.
Pro tip: Emphasize that while DFS guarantees finding the target, BFS on the discovered graph ensures the minimum step count; mention that the robot's limited sensing (only move, turn, atTarget) means you must build the map incrementally.
Establish a relative coordinate system with the start as origin and initial direction as north. Track the robot's position and orientation as it moves, updating coordinates based on moves and turns.
Perform a depth-first search to explore all reachable cells. Use a stack to remember the path and backtrack when hitting dead ends, marking visited cells to avoid revisiting.
When atTarget() returns true, record the current path from start to target. This path may not be optimal due to backtracking.
Construct a graph of discovered cells and edges, then run BFS from start to target to find the minimum number of steps. Alternatively, analyze the DFS path to remove cycles.
The exploration visits each reachable cell at most twice (once forward, once backtrack), so time complexity is O(R). Space complexity is O(R) for the stack and visited set.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.