<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>



#Binary Search Using BFS.
# Our aim to find the minimum effort.
# We know from the given constraints that the maximum height could be 10^6.
# So we know that our required absolute difference values would be 0 and 10^6.
# We could use Binary Search and reduce our search space by half.
# TC=O(log(10^6) * m*n) = O(m*n).
# SC=O(mn).
class Solution:
    def minimumEffortPath(self, heights: List[List[int]]) -> int:
        def helper(mid: int):
            visited = [[0] * C for _ in range(R)]
            queue = [(0, 0)]
            while queue:
                row, col = queue.pop()
                if row == R-1 and col == C-1:
                    return True
                visited[row][col] = True
                for r2, c2 in zip([row+1,row-1,row,row], [col,col,col+1,col-1]):
                    if not (0<=r2<R) or not(0<=c2<C) or visited[r2][c2] == True:
                        continue
                    val = abs(heights[r2][c2] - heights[row][col])
                    if val <= mid:
                        visited[r2][c2] = True
                        queue.append(
                            (r2, c2)
                        )
        R = len(heights)
        C = len(heights[0])
        left = 0
        right = 10**6
        while left < right:
            mid = (right + left) // 2
            if helper(mid):
                right = mid
            else:
                left = mid + 1
        return left
        
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