2087 - Minimum Cost Homecoming of a Robot in a Grid.

Medium

There is an m x n grid, where (0, 0) is the top-left cell and (m - 1, n - 1) is the bottom-right cell. You are given an integer array startPos where <code>startPos = start_row, start_col</code> indicates that initially , a robot is at the cell <code>(start_row, start_col)</code>. You are also given an integer array homePos where <code>homePos = home_row, home_col</code> indicates that its home is at the cell <code>(home_row, home_col)</code>.

The robot needs to go to its home. It can move one cell in four directions: left , right , up , or down , and it can not move outside the boundary. Every move incurs some cost. You are further given two 0-indexed integer arrays: rowCosts of length m and colCosts of length n.

• If the robot moves up or down into a cell whose row is r, then this move costs rowCosts[r].

• If the robot moves left or right into a cell whose column is c, then this move costs colCosts[c].

Return the minimum total cost for this robot to return home.

Example 1:

Input: startPos = 1, 0, homePos = 2, 3, rowCosts = 5, 4, 3, colCosts = 8, 2, 6, 7

Output: 18

Explanation: One optimal path is that:

Starting from (1, 0)

-> It goes down to ( 2 , 0). This move costs rowCosts2 = 3.

-> It goes right to (2, 1 ). This move costs colCosts1 = 2.

-> It goes right to (2, 2 ). This move costs colCosts2 = 6.

-> It goes right to (2, 3 ). This move costs colCosts3 = 7.

The total cost is 3 + 2 + 6 + 7 = 18

Example 2:

Input: startPos = 0, 0, homePos = 0, 0, rowCosts = 5, colCosts = 26

Output: 0

Explanation: The robot is already at its home. Since no moves occur, the total cost is 0.

Constraints:

• m == rowCosts.length

• n == colCosts.length

• <code>1 <= m, n <= 10⁵</code>

• <code>0 <= rowCostsr, colCostsc<= 10⁴</code>

• startPos.length == 2

• homePos.length == 2

• <code>0 <= start_row, home_row< m</code>

• <code>0 <= start_col, home_col< n</code>