> For the complete documentation index, see [llms.txt](https://nataliekung.gitbook.io/ladder_code/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://nataliekung.gitbook.io/ladder_code/l4dong-tai-gui-hua/triangle.md).

# Triangle

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle

```
[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]
```

The minimum path sum from top to bottom is`11`(i.e.,2+3+5+1= 11).

分析

这里没判断triangle的null和大小也行？

从底部向上，选更小那个加

类似minimal path sum, 要求最小的，row0 col0都设为最大防止干扰。dp还是m\*n ： f = \[\[float('inf')] \* (m + 1) for \_ in range(n+1)]

```
f[i][j] = Math.min(f[i + 1][j], f[i + 1][j + 1]) + triangle.get(i).get(j);
```

```
class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {

        int n = triangle.size();
        int[][] f = new int[n][triangle.get(n-1).size()];
        for(int i = 0; i < triangle.get(n - 1).size(); i ++){
            f[n-1][i] = triangle.get(n - 1).get(i);
        }
        for(int i = n - 2; i >= 0; i --){
            for(int j = 0; j < i + 1; j ++){
                f[i][j] = Math.min(f[i + 1][j], f[i + 1][j + 1]) + triangle.get(i).get(j);
            }
        }

        return f[0][0];
    }
}
```


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