<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 Solution:
    def minimumEffortPath(self, heights: List[List[int]]) -> int:
        
        m = len(heights)
        n = len(heights[0])         

        def max_listlists(heights):
            return max([max(lst) for lst in heights])

        def valid(i,j):
            return 0<= i < m and 0 <= j < n
        
        
        def dfs(cur_i,cur_j, dist):
            if cur_i == m-1 and cur_j == n-1:
                return True
            neighbours = [(cur_i+1, cur_j), (cur_i, cur_j + 1), (cur_i-1, cur_j), (cur_i, cur_j-1)]
            
            for i,j in neighbours:
                if valid(i,j) and abs(heights[i][j] - heights[cur_i][cur_j]) <= dist and not visited[i][j]:
                    visited[i][j] = 1
                    return dfs(i,j, dist)
            return False

        def check(effort):
            directions = [(0, 1), (1, 0), (0, -1), (-1, 0)]
            seen = {(0, 0)}
            stack = [(0, 0)]
            
            while stack:
                row, col = stack.pop()
                if (row, col) == (m - 1, n - 1):
                    return True
                
                for dx, dy in directions:
                    next_row, next_col = row + dy, col + dx
                    if valid(next_row, next_col) and (next_row, next_col) not in seen:
                        if abs(heights[next_row][next_col] - heights[row][col]) <= effort:
                            seen.add((next_row, next_col))
                            stack.append((next_row, next_col))
            
            return False
        
        left = 0
        right = max_listlists(heights)

        while left <= right:
            mid = (left + right)//2
            visited = [[0]*n for _ in range(m)]
            visited[0][0] = 1
            if check(mid):
                right = mid -1
            else:
                left = mid + 1
        return left





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