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Sync LeetCode submission Runtime - 5257 ms (23.43%), Memory - 154.8 MB (29.86%)
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‎1931-shortest-path-in-a-hidden-grid/README.md‎

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<p>This is an <strong>interactive problem</strong>.</p>
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<p>There is a robot in a hidden grid, and you are trying to get it from its starting cell to the target cell in this grid. The grid is of size <code>m x n</code>, and each cell in the grid is either empty or blocked. It is <strong>guaranteed</strong> that the starting cell and the target cell are different, and neither of them is blocked.</p>
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<p>You want to find the minimum distance to the target cell. However, you <strong>do not know</strong> the grid&#39;s dimensions, the starting cell, nor the target cell. You are only allowed to ask queries to the <code>GridMaster</code> object.</p>
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<p>Thr <code>GridMaster</code> class has the following functions:</p>
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<ul>
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<li><code>boolean canMove(char direction)</code> Returns <code>true</code> if the robot can move in that direction. Otherwise, it returns <code>false</code>.</li>
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<li><code>void move(char direction)</code> Moves the robot in that direction. If this move would move the robot to a blocked cell or off the grid, the move will be <strong>ignored</strong>, and the robot will remain in the same position.</li>
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<li><code>boolean isTarget()</code> Returns <code>true</code> if the robot is currently on the target cell. Otherwise, it returns <code>false</code>.</li>
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</ul>
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<p>Note that <code>direction</code> in the above functions should be a character from <code>{&#39;U&#39;,&#39;D&#39;,&#39;L&#39;,&#39;R&#39;}</code>, representing the directions up, down, left, and right, respectively.</p>
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<p>Return <em>the <strong>minimum distance</strong> between the robot&#39;s initial starting cell and the target cell. If there is no valid path between the cells, return </em><code>-1</code>.</p>
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<p><strong>Custom testing:</strong></p>
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<p>The test input is read as a 2D matrix <code>grid</code> of size <code>m x n</code> where:</p>
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<ul>
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<li><code>grid[i][j] == -1</code> indicates that the robot is in cell <code>(i, j)</code> (the starting cell).</li>
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<li><code>grid[i][j] == 0</code> indicates that the cell <code>(i, j)</code> is blocked.</li>
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<li><code>grid[i][j] == 1</code> indicates that the cell <code>(i, j)</code> is empty.</li>
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<li><code>grid[i][j] == 2</code> indicates that the cell <code>(i, j)</code> is the target cell.</li>
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</ul>
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<p>There is exactly one <code>-1</code> and <code>2</code> in <code>grid</code>. Remember that you will <strong>not</strong> have this information in your code.</p>
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<p>&nbsp;</p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> grid = [[1,2],[-1,0]]
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<strong>Output:</strong> 2
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<strong>Explanation:</strong> One possible interaction is described below:
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The robot is initially standing on cell (1, 0), denoted by the -1.
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- master.canMove(&#39;U&#39;) returns true.
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- master.canMove(&#39;D&#39;) returns false.
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- master.canMove(&#39;L&#39;) returns false.
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- master.canMove(&#39;R&#39;) returns false.
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- master.move(&#39;U&#39;) moves the robot to the cell (0, 0).
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- master.isTarget() returns false.
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- master.canMove(&#39;U&#39;) returns false.
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- master.canMove(&#39;D&#39;) returns true.
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- master.canMove(&#39;L&#39;) returns false.
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- master.canMove(&#39;R&#39;) returns true.
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- master.move(&#39;R&#39;) moves the robot to the cell (0, 1).
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- master.isTarget() returns true.
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We now know that the target is the cell (0, 1), and the shortest path to the target cell is 2.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> grid = [[0,0,-1],[1,1,1],[2,0,0]]
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<strong>Output:</strong> 4
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<strong>Explanation:</strong>&nbsp;The minimum distance between the robot and the target cell is 4.</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> grid = [[-1,0],[0,2]]
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<strong>Output:</strong> -1
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<strong>Explanation:</strong>&nbsp;There is no path from the robot to the target cell.</pre>
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<p>&nbsp;</p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 &lt;= n, m &lt;= 500</code></li>
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<li><code>m == grid.length</code></li>
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<li><code>n == grid[i].length</code></li>
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<li><code>grid[i][j]</code> is either <code>-1</code>, <code>0</code>, <code>1</code>, or <code>2</code>.</li>
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<li>There is <strong>exactly one</strong> <code>-1</code> in <code>grid</code>.</li>
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<li>There is <strong>exactly one</strong> <code>2</code> in <code>grid</code>.</li>
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</ul>

‎1931-shortest-path-in-a-hidden-grid/solution.py‎

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# Approach: DFS + BFS
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# Time: O(m * n)
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# Space: O(m * n)
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# """
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# This is GridMaster's API interface.
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# You should not implement it, or speculate about its implementation
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# """
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#class GridMaster(object):
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# def canMove(self, direction: str) -> bool:
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#
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#
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# def move(self, direction: str) -> None:
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#
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#
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# def isTarget(self) -> bool:
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#
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#
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class Solution(object):
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def findShortestPath(self, master: 'GridMaster') -> int:
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directions = {
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'U': (0, 1),
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'D': (0, -1),
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'L': (-1, 0),
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'R': (1, 0)
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}
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opposite = {
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'U': 'D',
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'D': 'U',
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'L': 'R',
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'R': 'L'
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}
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# Store all reachable cells and target location
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visited = set()
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target = None
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# DFS to map the grid (Phase 1)
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def dfs(x, y):
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nonlocal target
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visited.add((x, y))
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if master.isTarget():
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target = (x, y)
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for dir_char, (dx, dy) in directions.items():
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next_x, next_y = x + dx, y + dy
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# If we can move in this direction and haven't visited the next cell
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if master.canMove(dir_char) and (next_x, next_y) not in visited:
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master.move(dir_char) # Move forward
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dfs(next_x, next_y) # Explore from new position
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master.move(opposite[dir_char]) # Move back
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# Start DFS from (0, 0)
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dfs(0, 0)
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# If target is not found, return -1
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if target is None:
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return -1
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# BFS to find the shortest path to target (Phase 2)
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queue = [(0, 0, 0)] # (x, y, distance)
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visited_bfs = {(0, 0)}
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while queue:
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x, y, dist = queue.pop(0)
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if (x, y) == target:
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return dist
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for dx, dy in directions.values():
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next_x, next_y = x + dx, y + dy
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# Only consider cells that were found reachable in first phase (DFS)
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if (next_x, next_y) in visited and (next_x, next_y) not in visited_bfs:
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visited_bfs.add((next_x, next_y))
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queue.append((next_x, next_y, dist + 1))
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return -1
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