Path With Minimum Effort

Hard

0/120

Average time to solve is 20m

Contributed by

34 upvotes

Asked in companies

Problem statement

You are given heights, a 2D array of size 'rows' x 'columns', where heights[row][col] represents the height of a cell (which would contain a row and column).

You are a Ninja training for an upcoming battle. 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 time. A route's time is the maximum absolute difference in heights between two consecutive cells of the route.

You must return the minimum time required to travel from the top-left cell to the bottom-right cell.

For Example:

Input: 'heights' = [[1, 8, 8],[3, 8, 9],[5,3,5]]
Output: 2

Explanation: The route of [1,3,5,3,5] has a maximum absolute difference of 2 in consecutive cells.

Detailed explanation ( Input/output format, Notes, Images )

Input Format:

The first line contains two space-separated integers, 'rows' and 'columns'.

Next 'rows' lines contain 'columns' space-separated integers.

Output Format:

The only line contains the minimum time you require to travel from the top-left cell to the bottom-right cell.

Sample Input 1:

Sample output 1:

Explanation:

The figure above describes the following heights list (array). 

Here, The route of [1,2,3,4,5] has a maximum absolute difference of 1 in consecutive cells, which is better than the route [1,3,5,3,5].

Sample Input 2:

Sample output 2:

Constraint :

rows == heights.length
columns == heights[i].length
1 <= rows, columns <= 100
1 <= heights[i][j] <= 10^6

Where ‘rows’ is the number of rows and ‘columns’ is the number of columns. 

Time Limit: 1 sec

Console