Path With Minimum Effort

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

A route’s effort is the maximum absolute difference in heights between two consecutive cells of the route.

Return the minimum effort required to travel from the top-left cell to the bottom-right cell.

Input format

First Parameter - matrix height of size rows x columns

Output Format

Return the number.

Example 1:

Input: 
3 3
1 2 2
3 8 2
5 3 5
Output:
2
Explanation: 
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.

Example 2:

Input: 
3 3
1 2 3
3 8 4
5 3 5
Output:
1
Explanation: 3 3 represents the size of the matrix.
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].

Example 3:

Input: 
5 5
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
Output:
0
Explanation: 5 5 represents the size of the matrix.
This route does not require any cost.

Constraints:

• rows == height.length
• columns == height[i].length
• 1 <= rows, columns <= 100
• 1 <= height[i][j] <= 10⁶
• Expected Time Complexity: O(rows * cols* log(MAX_HEIGHT))
• Expected Auxiliary Space: O(m*n)