#2087

Minimum Cost Homecoming of a Robot in a Grid

medium · verified · 51.6% accepted · 745 likes · top 41%

Description

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 startPos = [startrow, startcol] indicates that initially, a robot is at the cell (startrow, startcol). You are also given an integer array homePos where homePos = [homerow, homecol] indicates that its home is at the cell (homerow, homecol).

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 rowCosts[2] = 3.

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

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

-> It goes right to (2, 3). This move costs colCosts[3] = 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.

Solution