Path With Maximum Minimum Value
<p>Given an <code>m x n</code> integer matrix <code>grid</code>, return <em>the maximum <strong>score</strong> of a path starting at </em><code>(0, 0)</code><em> and ending at </em><code>(m - 1, n - 1)</code> moving in the 4 cardinal directions.</p>

<p>The <strong>score</strong> of a path is the minimum value in that path.</p>

<ul>
	<li>For example, the score of the path <code>8 &rarr; 4 &rarr; 5 &rarr; 9</code> is <code>4</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1100-1199/1102.Path%20With%20Maximum%20Minimum%20Value/images/maxgrid1.jpg" style="width: 244px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [[5,4,5],[1,2,6],[7,4,6]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The path with the maximum score is highlighted in yellow. 
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1100-1199/1102.Path%20With%20Maximum%20Minimum%20Value/images/maxgrid2.jpg" style="width: 484px; height: 165px;" />
<pre>
<strong>Input:</strong> grid = [[2,2,1,2,2,2],[1,2,2,2,1,2]]
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1100-1199/1102.Path%20With%20Maximum%20Minimum%20Value/images/maxgrid3.jpg" style="width: 404px; height: 485px;" />
<pre>
<strong>Input:</strong> grid = [[3,4,6,3,4],[0,2,1,1,7],[8,8,3,2,7],[3,2,4,9,8],[4,1,2,0,0],[4,6,5,4,3]]
<strong>Output:</strong> 3
</pre>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 100</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 10<sup>9</sup></code></li>
</ul>
Depth-First Search; Breadth-First Search; Union Find; Array; Binary Search; Matrix; Heap (Priority Queue)
class Solution {
    private int[] p;

    public int maximumMinimumPath(int[][] grid) {
        int m = grid.length, n = grid[0].length;
        p = new int[m * n];
        List<int[]> q = new ArrayList<>();
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                q.add(new int[] {grid[i][j], i, j});
                p[i * n + j] = i * n + j;
            }
        }
        q.sort((a, b) -> b[0] - a[0]);
        boolean[][] vis = new boolean[m][n];
        int[] dirs = {-1, 0, 1, 0, -1};
        int ans = 0;
        for (int i = 0; find(0) != find(m * n - 1); ++i) {
            int[] t = q.get(i);
            vis[t[1]][t[2]] = true;
            ans = t[0];
            for (int k = 0; k < 4; ++k) {
                int x = t[1] + dirs[k], y = t[2] + dirs[k + 1];
                if (x >= 0 && x < m && y >= 0 && y < n && vis[x][y]) {
                    p[find(x * n + y)] = find(t[1] * n + t[2]);
                }
            }
        }
        return ans;
    }

    private int find(int x) {
        if (p[x] != x) {
            p[x] = find(p[x]);
        }
        return p[x];
    }
}