[leedcode 64] 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.

public class Solution {
    public int minPathSum(int[][] grid) {
        //动态规划思想：构造一个dp[][]二维数组，dp[i][j]代表到达i行j列的最少和，
        //当i>0并且j>0时，dp[i][j]=Math.min(dp[i][j-1],dp[i-1][j])+grid[i][j]
        //注意第一行和第一列的处理
        //有一种做法，不需要额外的空间，直接在原有的数组上进行修改数值
        int row=grid.length;
        int col=grid[0].length;
        int dp[][]=new int[row][col];
        for(int i=0;i<row;i++){
            if(i==0) dp[i][0]=grid[i][0];
            else dp[i][0]=grid[i][0]+dp[i-1][0];
            for(int j=1;j<col;j++){
                if(i==0){
                    dp[i][j]=dp[i][j-1]+grid[i][j];
                }else{
                    dp[i][j]=Math.min(dp[i][j-1],dp[i-1][j])+grid[i][j];
                }
                
            }
        }
        return dp[row-1][col-1];
    }
}