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:
    def maximumMinimumPath(self, grid: List[List[int]]) -> int:
        def find(x: int) -> int:
            if p[x] != x:
                p[x] = find(p[x])
            return p[x]

        m, n = len(grid), len(grid[0])
        p = list(range(m * n))
        q = [(v, i, j) for i, row in enumerate(grid) for j, v in enumerate(row)]
        q.sort()
        ans = 0
        dirs = (-1, 0, 1, 0, -1)
        vis = set()
        while find(0) != find(m * n - 1):
            v, i, j = q.pop()
            ans = v
            vis.add((i, j))
            for a, b in pairwise(dirs):
                x, y = i + a, j + b
                if (x, y) in vis:
                    p[find(i * n + j)] = find(x * n + y)
        return ans
