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.

解析：

转换方程为：

dp[i][j]=Math.min(dp[i-1][j]+grid[i][j],dp[i][j]+grid[i][j]);

public class Solution {
    public int minPathSum(int[][] grid) {
        int m=grid.length;
        int n=grid[0].length;
        int[][] dp=new int[m][n];
        
        dp[0][0]=grid[0][0];
        
        for(int i=1;i<m;i++)
        {
            dp[i][0]=dp[i-1][0]+grid[i][0];
        }
         for(int j=1;j<n;j++)
        {
            dp[0][j]=dp[0][j-1]+grid[0][j];
        }
       
        for(int i=1;i<m;i++)
        {
            for(int j=1;j<n;j++)
            dp[i][j]=Math.min(dp[i-1][j]+grid[i][j],dp[i][j-1]+grid[i][j]);
        }
        return dp[m-1][n-1];
    }
}