---
comments: true
difficulty: 简单
edit_url: https://github.com/doocs/leetcode/edit/main/solution/0100-0199/0118.Pascal%27s%20Triangle/README.md
tags:
- 数组
- 动态规划
---
# [118. 杨辉三角](https://leetcode.cn/problems/pascals-triangle)
[English Version](/solution/0100-0199/0118.Pascal%27s%20Triangle/README_EN.md)
## 题目描述
给定一个非负整数 numRows
,生成「杨辉三角」的前 numRows
行。
在「杨辉三角」中,每个数是它左上方和右上方的数的和。
示例 1:
输入: numRows = 5
输出: [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]
示例 2:
输入: numRows = 1
输出: [[1]]
提示:
## 解法
### 方法一:模拟
我们先创建一个答案数组 $f$,然后将 $f$ 的第一行元素设为 $[1]$。接下来,我们从第二行开始,每一行的开头和结尾元素都是 $1$,其它 $f[i][j] = f[i - 1][j - 1] + f[i - 1][j]$。
时间复杂度 $O(n^2)$,空间复杂度 $O(n^2)$。其中 $n$ 是行数。
#### Python3
```python
class Solution:
def generate(self, numRows: int) -> List[List[int]]:
f = [[1]]
for i in range(numRows - 1):
g = [1] + [a + b for a, b in pairwise(f[-1])] + [1]
f.append(g)
return f
```
#### Java
```java
class Solution {
public List> generate(int numRows) {
List> f = new ArrayList<>();
f.add(List.of(1));
for (int i = 0; i < numRows - 1; ++i) {
List g = new ArrayList<>();
g.add(1);
for (int j = 0; j < f.get(i).size() - 1; ++j) {
g.add(f.get(i).get(j) + f.get(i).get(j + 1));
}
g.add(1);
f.add(g);
}
return f;
}
}
```
#### C++
```cpp
class Solution {
public:
vector> generate(int numRows) {
vector> f;
f.push_back(vector(1, 1));
for (int i = 0; i < numRows - 1; ++i) {
vector g;
g.push_back(1);
for (int j = 0; j < f[i].size() - 1; ++j) {
g.push_back(f[i][j] + f[i][j + 1]);
}
g.push_back(1);
f.push_back(g);
}
return f;
}
};
```
#### Go
```go
func generate(numRows int) [][]int {
f := [][]int{[]int{1}}
for i := 0; i < numRows-1; i++ {
g := []int{1}
for j := 0; j < len(f[i])-1; j++ {
g = append(g, f[i][j]+f[i][j+1])
}
g = append(g, 1)
f = append(f, g)
}
return f
}
```
#### TypeScript
```ts
function generate(numRows: number): number[][] {
const f: number[][] = [[1]];
for (let i = 0; i < numRows - 1; ++i) {
const g: number[] = [1];
for (let j = 0; j < f[i].length - 1; ++j) {
g.push(f[i][j] + f[i][j + 1]);
}
g.push(1);
f.push(g);
}
return f;
}
```
#### Rust
```rust
impl Solution {
#[allow(dead_code)]
pub fn generate(num_rows: i32) -> Vec> {
let mut ret_vec: Vec> = Vec::new();
let mut cur_vec: Vec = Vec::new();
for i in 0..num_rows as usize {
let mut new_vec: Vec = vec![1; i + 1];
for j in 1..i {
new_vec[j] = cur_vec[j - 1] + cur_vec[j];
}
cur_vec = new_vec.clone();
ret_vec.push(new_vec);
}
ret_vec
}
}
```
#### JavaScript
```js
/**
* @param {number} numRows
* @return {number[][]}
*/
var generate = function (numRows) {
const f = [[1]];
for (let i = 0; i < numRows - 1; ++i) {
const g = [1];
for (let j = 0; j < f[i].length - 1; ++j) {
g.push(f[i][j] + f[i][j + 1]);
}
g.push(1);
f.push(g);
}
return f;
};
```