> For the complete documentation index, see [llms.txt](https://liuyang89116.gitbook.io/my-leetcode-book/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://liuyang89116.gitbook.io/my-leetcode-book/chapter_5_dynamic_programming/matrix-lei-xing/problem_64_minimum_path_sum.md).

# Problem 64: Minimum Path Sum

> <https://leetcode.com/problems/minimum-path-sum/>

## 思路

和前边的题目一样，矩阵型问题，重要的就是想清楚是怎么在这个矩阵中行走的。路线规划好，小心脚标。 ![](/files/-Lpv9zik1DBkb8TntJZE)

```java
public class Solution {
    public int minPathSum(int[][] grid) {
        if (grid == null || grid.length == 0 || grid[0].length == 0) {
            return 0;
        }

        //state
        int m = grid.length;
        int n = grid[0].length;
        int[][] f = new int[m][n];

        //initiate
        f[0][0] = grid[0][0];
        for (int i = 1; i < n; i++) {
            f[0][i] = f[0][i - 1] + grid[0][i];
        }
        for (int i = 1; i < m; i++) {
            f[i][0] = f[i - 1][0] + grid[i][0];
        }

        //function
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                f[i][j] = Math.min(f[i - 1][j], f[i][j - 1]) + grid[i][j];
            }
        }
        //answer
        return f[m - 1][n - 1];
    }
}
```

## 易错点

1. 初始化是从1开始的

   ```java
   //initiate
   f[0][0] = grid[0][0];
   for (int i = 1; i < n; i++) {
      f[0][i] = f[0][i - 1] + grid[0][i];
   }
   ```
2. Min函数

   ```java
   Math.min(f[i - 1][j], f[i][j - 1])
   ```

   这个函数写错好几次。第一是把之间的逗号写成加号;第二是总是把Math这个词忘掉


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