leetcode-64. Minimum Path Sum/最小路径和

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.

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给出一个包含非负元素的二维数组，只能往右边和下边走，让求出从左上到右下的最小路径和，跟leetcode63很相似。还是动态规划。

代码：

class Solution {
    public int minPathSum(int[][] grid) {
        int [][]dp=new int [grid.length][grid[0].length];
        dp[0][0]=grid[0][0];
        for(int i=1;i<grid.length;i++){
            dp[i][0]=dp[i-1][0]+grid[i][0];
        }
        for(int j=1;j<grid[0].length;j++){
            dp[0][j]=dp[0][j-1]+grid[0][j];
        }
        for(int i=1;i<grid.length;i++){
            for(int j=1;j<grid[0].length;j++){
                dp[i][j]=(dp[i-1][j]<dp[i][j-1]?dp[i-1][j]:dp[i][j-1])+grid[i][j];
            }
        }
        return dp[grid.length-1][grid[0].length-1];
    }
}