Walls and Gates
Given an m x n grid where:
- -1 = wall
- 0 = gate
- 2147483647 = empty room
Fill each empty room with the distance to its nearest gate. If impossible, leave it as 2147483647.
Output the grid, each row on a new line, values space-separated.
Example:
2147483647,-1,0,2147483647 2147483647,2147483647,2147483647,-1 2147483647,-1,2147483647,-1 0,-1,2147483647,2147483647
3 -1 0 1 2 2 1 -1 1 -1 2 -1 0 -1 3 4
- The algorithm starts by identifying the gates in the grid, which are the cells with a value of 0.
- It then performs a breadth-first search (BFS) from each gate, incrementing the distance by 1 as it moves to adjacent empty rooms.
- During the BFS, the algorithm updates the distance of each empty room to be the minimum distance from any gate, effectively filling in the grid with the distance to the nearest gate.
- The final output is the resulting grid, where each empty room contains its distance to the nearest gate, and walls remain as −1.
Constraints:
- 1 <= rows, cols <= 250
Background Knowledge
The "Walls and Gates" problem involves working with a grid data structure, which is a two-dimensional array of elements. In this case, the grid represents a physical space with walls, gates, and empty rooms. The problem requires finding the shortest distance from each empty room to its nearest gate, which is a classic problem in graph theory and search algorithms. To solve this problem, you need to understand how to represent the grid as a graph, where each cell is a node, and the edges represent the connections between adjacent cells.
The concept of distance or shortest path is crucial in this problem. Since we're dealing with a grid, we can use Breadth-First Search (BFS) or Depth-First Search (DFS) algorithms to traverse the graph and find the shortest distance to the nearest gate. However, BFS is more suitable for this problem because it explores all the nodes at a given depth level before moving on to the next level, which ensures that we find the shortest distance to the nearest gate.
In the context of this problem, it's essential to understand how to handle boundaries and obstacles (walls) in the grid. We need to ensure that our algorithm doesn't try to access cells outside the grid or attempt to traverse through walls. This requires careful consideration of the grid's dimensions and the values of each cell.
Algorithm/Approach
The algorithm pattern that can be applied to this problem is Breadth-First Search (BFS) with a queue data structure. The general approach involves:
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