[LeetCode]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.
思路1：这是一个简单的动态规划问题，dp[i][j] = grid[i-1][j-1] + min(dp[i-1][j],dp[i][j-1])
代码1：

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

思路2：看到网上说可以把空间复杂度优化到O(N)