[Java][LeetCode]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.

Example:

Input:

[

  [1,3,1],

  [1,5,1],

  [4,2,1]

]

Output: 7

Explanation: Because the path 1→3→1→1→1 minimizes the sum.

class Solution {
    public int minPathSum(int[][] grid) {
        //到达位置i,j的要么来自于i-1,j(上)，或者i,j-1(左)，考虑构建一个新的paths网格来记录到达当前位置的最小值即加上上或者左
        int m=grid.length;
        int n=grid[0].length;
        int[][] paths=new int[m][n];//记录路径到达某点 的的最小值
        paths[0][0]=grid[0][0];

        for(int i=1;i<m;++i){
            paths[i][0]=paths[i-1][0]+grid[i][0];//获得第一列的paths值
        }

        for(int j=1;j<n;++j){
            paths[0][j]=paths[0][j-1]+grid[0][j];//获得第一行的paths值
        }

        for(int i=1;i<m;++i){
            for(int j=1;j<n;++j){
                paths[i][j]=Math.min(paths[i-1][j],paths[i][j-1])+grid[i][j];//获得当前位置的paths值即路径自小和
            }
        }
        return paths[m-1][n-1];
    }
}