Swim in Rising Water

Explore how to determine the minimum time to swim across an n by n grid with rising water levels. Learn to navigate matrix-based constraints and implement a solution that checks elevation conditions for movement. This lesson helps you understand key problem-solving strategies involving matrices for coding interviews.

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Statement

Given an $n \times n$ grid (2D matrix) where each cell grid[i][j] represents the elevation at position (i, j).

Once it starts to rain, the water level rises over time. At any given time t, the water depth across the grid equals t. A swimmer can move from one cell to an adjacent cell (up, down, left, or right) if both cells have elevations less than or equal to the current water level t.

If the elevation condition is satisfied, a swimmer can swim any distance instantly. However, he cannot move outside the grid boundaries.

Return the minimum time t at which it becomes possible to swim from the top-left cell $(0$ ...