Minimum Path Sum

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Solution: 这道题跟Unique Path系列是思路一样的。2维DP

public class Solution {
    public int minPathSum(int[][] grid) {
        if(grid == null)
            return 0;
        
        int row = grid.length;
        int col = grid[0].length;
        
        int[][] sum = new int[row][col];
        sum[0][0] = grid[0][0];
        
        //for column
        for(int i = 1; i < row; i++) {
            sum[i][0] = sum[i - 1][0] + grid[i][0];
        }
        
        //for row
        for(int i = 1; i < col; i++) {
            sum[0][i] = sum[0][i - 1] + grid[0][i];
        }
        
        for(int i = 1; i < row; i++) {
            for(int j = 1; j < col; j++) {
                sum[i][j] = grid[i][j] + Math.min(sum[i - 1][j], sum[i][j - 1]);
            }
        }
        
        return sum[row - 1][col - 1];
    }
}