LeetCode [1463] Cherry Pickup II

 1463. Cherry Pickup II

Hard

Given a rows x cols matrix grid representing a field of cherries. Each cell in grid represents the number of cherries that you can collect.

You have two robots that can collect cherries for you, Robot #1 is located at the top-left corner (0,0) , and Robot #2 is located at the top-right corner (0, cols-1) of the grid.

Return the maximum number of cherries collection using both robots  by following the rules below:

• From a cell (i,j), robots can move to cell (i+1, j-1) , (i+1, j) or (i+1, j+1).
• When any robot is passing through a cell, It picks it up all cherries, and the cell becomes an empty cell (0).
• When both robots stay on the same cell, only one of them takes the cherries.
• Both robots cannot move outside of the grid at any moment.
• Both robots should reach the bottom row in the grid.

 

Example 1:

Input: grid = [[3,1,1],[2,5,1],[1,5,5],[2,1,1]]
Output: 24
Explanation: Path of robot #1 and #2 are described in color green and blue respectively.
Cherries taken by Robot #1, (3 + 2 + 5 + 2) = 12.
Cherries taken by Robot #2, (1 + 5 + 5 + 1) = 12.
Total of cherries: 12 + 12 = 24.

Example 2:

Input: grid = [[1,0,0,0,0,0,1],[2,0,0,0,0,3,0],[2,0,9,0,0,0,0],[0,3,0,5,4,0,0],[1,0,2,3,0,0,6]]
Output: 28
Explanation: Path of robot #1 and #2 are described in color green and blue respectively.
Cherries taken by Robot #1, (1 + 9 + 5 + 2) = 17.
Cherries taken by Robot #2, (1 + 3 + 4 + 3) = 11.
Total of cherries: 17 + 11 = 28.

Example 3:

Input: grid = [[1,0,0,3],[0,0,0,3],[0,0,3,3],[9,0,3,3]]
Output: 22

Example 4:

Input: grid = [[1,1],[1,1]]
Output: 4

 

Constraints:

• rows == grid.length
• cols == grid[i].length
• 2 <= rows, cols <= 70
• 0 <= grid[i][j] <= 100 

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/* - 3D-DP question - m: rows. n: columns - Must move down at every step, hence there are m-1 steps - dp is n*n matrix. - Update dp at every step k=1..m-1 - At step k, dp[i][j] maintains the max cherries when robot1 is at [k,i] and robot2 is at [k,j] */ class Solution { int[] shift = new int[]{-1,0,1}; public int cherryPickup(int[][] grid) { int m = grid.length, n = grid[0].length; int[][] dp = new int[n][n]; for(int t=0; t<n; ++t) Arrays.fill(dp[t], -1); dp[0][n-1] = grid[0][0] + grid[0][n-1]; int ret = 0; for(int k=1; k<=m-1; ++k){ int[][] tmp = new int[n][n]; for(int t=0; t<n; ++t) Arrays.fill(tmp[t], -1); for(int i=0; i<n; ++i){ for(int j=0; j<n; ++j){ int cherries = -1; for(int di : shift){ for(int dj : shift){ if(i+di>=0 && i+di<n && j+dj>=0 && j+dj<n){ cherries = Math.max(cherries, dp[i+di][j+dj]); } } } if(cherries<0) continue; tmp[i][j] = cherries + grid[k][i] + (j==i?0:grid[k][j]); ret = Math.max(ret, tmp[i][j]); } } dp = tmp; } return ret; } }