Swim in Rising Water
<p>You are given an <code>n x n</code> integer matrix <code>grid</code> where each value <code>grid[i][j]</code> represents the elevation at that point <code>(i, j)</code>.</p>

<p>It starts raining, and water gradually rises over time. At time <code>t</code>, the water level is <code>t</code>, meaning <strong>any</strong> cell with elevation less than equal to <code>t</code> is submerged or reachable.</p>

<p>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 <code>t</code>. You can swim infinite distances in zero time. Of course, you must stay within the boundaries of the grid during your swim.</p>

<p>Return <em>the minimum time until you can reach the bottom right square </em><code>(n - 1, n - 1)</code><em> if you start at the top left square </em><code>(0, 0)</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0700-0799/0778.Swim%20in%20Rising%20Water/images/swim1-grid.jpg" style="width: 164px; height: 165px;" />
<pre>
<strong>Input:</strong> grid = [[0,2],[1,3]]
<strong>Output:</strong> 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.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0700-0799/0778.Swim%20in%20Rising%20Water/images/swim2-grid-1.jpg" style="width: 404px; height: 405px;" />
<pre>
<strong>Input:</strong> 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]]
<strong>Output:</strong> 16
<strong>Explanation:</strong> The final route is shown.
We need to wait until time 16 so that (0, 0) and (4, 4) are connected.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 50</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;&nbsp;n<sup>2</sup></code></li>
	<li>Each value <code>grid[i][j]</code> is <strong>unique</strong>.</li>
</ul>
Depth-First Search; Breadth-First Search; Union Find; Array; Binary Search; Matrix; Heap (Priority Queue)
const DIR: [(i32, i32); 4] = [(-1, 0), (1, 0), (0, -1), (0, 1)];

impl Solution {
    #[allow(dead_code)]
    pub fn swim_in_water(grid: Vec<Vec<i32>>) -> i32 {
        let n = grid.len();
        let m = grid[0].len();
        let mut ret_time = 0;
        let mut disjoint_set: Vec<usize> = vec![0; n * m];

        // Initialize the disjoint set
        for i in 0..n * m {
            disjoint_set[i] = i;
        }

        loop {
            if Self::check_and_union(&grid, &mut disjoint_set, ret_time) {
                break;
            }
            // Otherwise, keep checking
            ret_time += 1;
        }

        ret_time
    }

    #[allow(dead_code)]
    fn check_and_union(grid: &Vec<Vec<i32>>, d_set: &mut Vec<usize>, cur_time: i32) -> bool {
        let n = grid.len();
        let m = grid[0].len();

        for i in 0..n {
            for j in 0..m {
                if grid[i][j] != cur_time {
                    continue;
                }
                // Otherwise, let's union the square with its neighbors
                for (dx, dy) in DIR {
                    let x = dx + (i as i32);
                    let y = dy + (j as i32);
                    if Self::check_bounds(x, y, n as i32, m as i32)
                        && grid[x as usize][y as usize] <= cur_time
                    {
                        Self::union(i * m + j, (x as usize) * m + (y as usize), d_set);
                    }
                }
            }
        }

        Self::find(0, d_set) == Self::find(n * m - 1, d_set)
    }

    #[allow(dead_code)]
    fn find(x: usize, d_set: &mut Vec<usize>) -> usize {
        if d_set[x] != x {
            d_set[x] = Self::find(d_set[x], d_set);
        }
        d_set[x]
    }

    #[allow(dead_code)]
    fn union(x: usize, y: usize, d_set: &mut Vec<usize>) {
        let p_x = Self::find(x, d_set);
        let p_y = Self::find(y, d_set);
        d_set[p_x] = p_y;
    }

    #[allow(dead_code)]
    fn check_bounds(i: i32, j: i32, n: i32, m: i32) -> bool {
        i >= 0 && i < n && j >= 0 && j < m
    }
}
