<p>You are a hiker preparing for an upcoming hike. You are given <code>heights</code>, a 2D array of size <code>rows x columns</code>, where <code>heights[row][col]</code> represents the height of cell <code>(row, col)</code>. You are situated in the top-left cell, <code>(0, 0)</code>, and you hope to travel to the bottom-right cell, <code>(rows-1, columns-1)</code> (i.e.,&nbsp;<strong>0-indexed</strong>). You can move <strong>up</strong>, <strong>down</strong>, <strong>left</strong>, or <strong>right</strong>, and you wish to find a route that requires the minimum <strong>effort</strong>.</p>

<p>A route&#39;s <strong>effort</strong> is the <strong>maximum absolute difference</strong><strong> </strong>in heights between two consecutive cells of the route.</p>

<p>Return <em>the minimum <strong>effort</strong> required to travel from the top-left cell to the bottom-right cell.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2020/10/04/ex1.png" style="width: 300px; height: 300px;" /></p>

<pre>
<strong>Input:</strong> heights = [[1,2,2],[3,8,2],[5,3,5]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The route of [1,3,5,3,5] has a maximum absolute difference of 2 in consecutive cells.
This is better than the route of [1,2,2,2,5], where the maximum absolute difference is 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2020/10/04/ex2.png" style="width: 300px; height: 300px;" /></p>

<pre>
<strong>Input:</strong> heights = [[1,2,3],[3,8,4],[5,3,5]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The route of [1,2,3,4,5] has a maximum absolute difference of 1 in consecutive cells, which is better than route [1,3,5,3,5].
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/10/04/ex3.png" style="width: 300px; height: 300px;" />
<pre>
<strong>Input:</strong> heights = [[1,2,1,1,1],[1,2,1,2,1],[1,2,1,2,1],[1,2,1,2,1],[1,1,1,2,1]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> This route does not require any effort.
</pre>

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

<ul>
	<li><code>rows == heights.length</code></li>
	<li><code>columns == heights[i].length</code></li>
	<li><code>1 &lt;= rows, columns &lt;= 100</code></li>
	<li><code>1 &lt;= heights[i][j] &lt;= 10<sup>6</sup></code></li>
</ul>

class UnionFind:
    def __init__(self, size):
        self.parent = [x for x in range(size)]
        self.rank = [0] * size
    
    def find(self, i):
        if self.parent[i] != i:
            self.parent[i] = self.find(self.parent[i])
        
        return self.parent[i]
    
    def union(self, x, y):
        parent_x = self.find(x)
        parent_y = self.find(y)

        if parent_x != parent_y:
            if self.rank[parent_x] > self.rank[parent_y]:
                self.parent[parent_y] = parent_x
            elif self.rank[parent_y] > self.rank[parent_x]:
                self.parent[parent_x] = parent_y
            else:
                self.parent[parent_y] = parent_x
                self.rank[parent_x] += 1
 
class Solution:
    def minimumEffortPath(self, heights: List[List[int]]) -> int:
        row, col = len(heights), len(heights[0])

        if row == 1 and col == 1:
            return 0
        
        edge_list = []

        for current_row in range(row):
            for current_col in range(col):
                if current_row > 0:
                    difference = abs(heights[current_row][current_col] - heights[current_row - 1][current_col])
                    edge_list.append((difference, current_row * col + current_col, (current_row - 1) * col + current_col))
                
                if current_col > 0:
                    difference = abs(heights[current_row][current_col] - heights[current_row][current_col - 1])
                    edge_list.append((difference, current_row * col + current_col, current_row * col + current_col - 1))

        edge_list.sort()
        union_find = UnionFind(row * col)

        for difference, x, y in edge_list:
            union_find.union(x, y)
            if union_find.find(0) == union_find.find(row * col - 1):
                return difference

        return -1

20600