# 25. 最小路径和

java

```java
/**
 * 最小路径和
 *
 * 给定一个包含非负整数的 m x n 网格，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。
 *
 * 说明：每次只能向下或者向右移动一步。
 *
 * 示例:
 *
 * 输入:
 * [
 *   [1,3,1],
 *   [1,5,1],
 *   [4,2,1]
 * ]
 * 输出: 7
 * 解释: 因为路径 1→3→1→1→1 的总和最小。
 */
public class Solution64 {
    public int minPathSum(int[][] grid) {
        if(grid.length<1) return 0;

        int m=grid.length;
        int n=grid[0].length;

        //存储最小的路径和
        int[][] arr=new int[m][n];
        //对第一列、第一行进行初始化
        for(int i=0;i<m;i++){
            if(i==0) arr[i][0]=grid[i][0];
            else arr[i][0]=arr[i-1][0]+grid[i][0];
        }
        for(int i=0;i<n;i++){
            if(i==0) arr[0][i]=grid[0][i];
            else arr[0][i]=arr[0][i-1]+grid[0][i];
        }

        //上侧、左侧取最小值与当前值相加
        for(int i=1;i<m;i++){
            for(int j=1;j<n;j++){
                arr[i][j]=Math.min(arr[i-1][j],arr[i][j-1])+grid[i][j];
            }
        }

        return arr[m-1][n-1];
    }
    public static void main(String[] args){
        int[][] grid={
                {1,3,1},
                {1,5,1},
                {4,2,1}
        };
        int r=new Solution64().minPathSum(grid);
        System.out.println(r);
    }
}
```

python

```
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://im-qianuxn.gitbook.io/pytorch/ji-suan-ji/shua-ti/shu-ju-jie-gou-lei/25-zui-xiao-lu-jin-he.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.