Swim in Rising Water

Swim in Rising Water is a Hard Data Structures and Algorithms interview problem you can solve, run and submit on Thita.ai. It belongs to the Graph Traversal Patterns (DFS & BFS) pattern, in the Shortest Path (Dijkstra's Algorithm) subpattern.

Problem statement

You are given an n x n integer matrix grid where each value grid[i][j] represents the elevation at that point (i, j).

The 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 the elevation of both squares individually are at most t. You can swim infinite distances in zero time. Of course, you must stay within the boundaries of the grid during your swim.

Return the least time until you can reach the bottom right square (n - 1, n - 1) if you start at the top left square (0, 0).

Example 1:

Input: grid = [[0,2],[1,3]] Output: 3 Explanation: At time 0, you are in grid location (0, 0). You cannot go anywhere else because 4-directionally adjacent neighbors have a higher elevation than t = 0. You cannot reach point (1, 1) until time 3. When the depth of water is 3, we can swim anywhere inside the grid.

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: 16 Explanation: The final route is shown. We need to wait until time 16 so that (0, 0) and (4, 4) are connected.

Constraints:

- n == grid.length

- n == grid[i].length

- 1 <= n <= 50

- 0 <= grid[i][j] < n2

- Each value grid[i][j] is unique.

Topics and companies

Topics: Array, Binary Search, Depth-First Search, Breadth-First Search, Union Find, Heap (Priority Queue), Matrix.

Reported in interviews at Facebook.

How to practise Swim in Rising Water on Thita.ai

Starter code is provided in C, C#, C++, Go, Java, JavaScript and Python. Your solution runs against 4 test cases for this problem, with the AI coach available for a hint when you are stuck rather than a finished answer. The reference solution runs in O(n^2) time and O(n^2) space.

Open Swim in Rising Water in the code editor, or read the Swim in Rising Water editorial for a worked solution with its approach and complexity analysis.

Where Swim in Rising Water sits in the DSA pattern sheet

Problems related to Swim in Rising Water

Other problems that use the same Shortest Path (Dijkstra's Algorithm) and Graph Traversal Patterns (DFS & BFS) techniques:

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