> 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/lian-xi/pascals-triangle.md).

# Pascal's Triangle

GivennumRows, generate the firstnumRowsof Pascal's triangle.

For example, givennumRows= 5,\
Return

```
[
     [1],
    [1,1],
   [1,2,1],
  [1,3,3,1],
 [1,4,6,4,1]
]
```

分析

recursive。每次从前面结果的最后一层计算出新层加入。 A\[i] = A\[i-1]+A\[i],如果i-1或者i出界就用0。

用数组来初始化一个arraylist

```
new ArrayList<Integer>(Arrays.asList(1,2,3,5,8,13,21));
```

```
class Solution {
    public List<List<Integer>> generate(int numRows) {
        List<List<Integer>> ret = new ArrayList<>();
        if(numRows < 1)
            return ret;

        if(numRows == 1){
            ret.add(new ArrayList<Integer>(Arrays.asList(1)));
            return ret;
        }

        List<List<Integer>> last = generate(numRows - 1);
        List<Integer> level = last.get(last.size() - 1);
        List<Integer> path = new ArrayList<Integer>(); 
        for(int i = 0; i <= level.size(); i ++){
            int prev = i - 1 < 0 ? 0 : level.get(i - 1);
            int cur = i == level.size() ? 0 : level.get(i);
            path.add(prev + cur);            
        }

        ret.addAll(last);
        ret.add(path);
        return ret;
    }
}
```