What is the optimal time complexity of solving Walls And Gates?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Walls And Gates?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Walls And Gates?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Walls And Gates?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Walls And Gates

Learn how to solve the 'Walls And Gates' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

You are given an m x n grid rooms initialized with these three possible values:

- -1: A wall or an obstacle.

- 0: A gate.

- INF (represented by 2147483647): An empty room.

Fill each empty room with the distance to its nearest gate. If it is impossible to reach a gate, it should be filled with INF.

Write a function wallsAndGates(rooms: List[List[int]]) -> List[List[int]] that returns the modified rooms grid.

Constraints

•m == len(rooms)
•n == len(rooms[i])
•1 <= m, n <= 250
•rooms[i][j] is -1, 0, or 2147483647

Examples

Example 1

Input

rooms = [[2147483647,-1,0,2147483647],[2147483647,2147483647,2147483647,-1],[2147483647,-1,2147483647,-1],[0,-1,2147483647,2147483647]]

Output

[[3,-1,0,1],[2,2,1,-1],[1,-1,2,-1],[0,-1,3,4]]

Explanation

The empty rooms are filled with the shortest distance to their nearest gate.

Need a Hint?

Represent graph node connections as an adjacency list/matrix, then use standard BFS or DFS graph traversal.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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