LeetCode 286: Walls And Gates — Step-by-Step Visual Trace

#leetcode #python #algorithms

Medium — BFS | Matrix | Graph

The Problem

Fill each empty room with the distance to its nearest gate, where rooms are represented by a 2D grid with gates (0), walls (-1), and empty rooms (INF).

Approach

Use multi-source BFS starting from all gates simultaneously. For each gate, perform BFS to explore neighboring empty rooms, updating each room with the minimum distance to any gate encountered so far.

Time: O(m * n * g) · Space: O(m * n)

Code

class Solution:
    def wallsAndGates(self, rooms: List[List[int]]) -> None:
        if not rooms:
            return

        rows, cols = len(rooms), len(rooms[0])
        gates = [(i, j) for i in range(rows) for j in range(cols) if rooms[i][j] == 0]
        directions = [(1, 0), (-1, 0), (0, 1), (0, -1)]

        for gate_row, gate_col in gates:
            visited = set()  # To track visited cells in BFS
            queue = deque([(gate_row, gate_col, 0)])

            while queue:
                row, col, distance = queue.popleft()
                rooms[row][col] = min(rooms[row][col], distance)
                visited.add((row, col))

                for dr, dc in directions:
                    new_row, new_col = row + dr, col + dc

                    if (
                        0 <= new_row < rows
                        and 0 <= new_col < cols
                        and rooms[new_row][new_col] != -1
                        and (new_row, new_col) not in visited
                    ):
                        queue.append((new_row, new_col, distance + 1))
                        visited.add((new_row, new_col))