What is the optimal time complexity of solving Swim In Rising Water?

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 Swim In Rising Water?

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 Swim In Rising Water?

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 Swim In Rising Water?

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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Swim In Rising Water

Learn how to solve the 'Swim In Rising Water' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

You are given an n x n integer matrix grid where each value grid[i][j] represents the elevation at that point (i, j). Rain starts to fall. At time t, the depth of the water everywhere is t. You can swim from a square to another 4-directionally adjacent square if and only if both elevations in the squares are at most t.

You start at the top left square (0, 0). What is the least time until you can reach the bottom right square (n-1, n-1)?

Write a function swimInWater(grid: List[List[int]]) -> int.

Constraints

•n == len(grid) == len(grid[i])
•1 <= n <= 50
•0 <= grid[i][j] < n^2
•Each value grid[i][j] is unique

Examples

Example 1

Input

grid = [[0,2],[1,3]]

Output

Explanation

At time 3, you are permitted to swim all the way from (0,0) to (1,1). The path is 0 -> 1 -> 3.

Example 2

Input

grid = [[0,1,2,3,4],[24,23,22,21,5],[12,13,14,15,16],[11,17,18,19,20],[10,9,8,7,6]]

Output

Explanation

The final path is 0-1-2-3-4-5-16-15-14-13-12-11-10-9-8-7-6. The maximum height along this path is 16.

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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