# 118. Pascal’s Triangle

## Description

Given an integer numRows, return the first numRows of Pascal's triangle.

In Pascal's triangle, each number is the sum of the two numbers directly above it as shown:

Example 1:

Input: numRows = 5
Output: [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]


Example 2:

Input: numRows = 1
Output: [[1]]


Constraints:

• 1 <= numRows <= 30

## Solutions

Solution 1: Simulation

First, we create an answer array $f$, and then set the first row of $f$ to $[1]$. Next, starting from the second row, the first and last elements of each row are $1$, and the other elements are calculated by $f[i][j] = f[i - 1][j - 1] + f[i - 1][j]$.

The time complexity is $O(n^2)$, and the space complexity is $O(n^2)$. Here, $n$ is the number of rows.

• class Solution {
public List<List<Integer>> generate(int numRows) {
List<List<Integer>> f = new ArrayList<>();
for (int i = 0; i < numRows - 1; ++i) {
List<Integer> g = new ArrayList<>();
for (int j = 0; j < f.get(i).size() - 1; ++j) {
g.add(f.get(i).get(j) + f.get(i).get(j + 1));
}
}
return f;
}
}

• class Solution {
public:
vector<vector<int>> generate(int numRows) {
vector<vector<int>> f;
f.push_back(vector<int>(1, 1));
for (int i = 0; i < numRows - 1; ++i) {
vector<int> 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;
}
};

• 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


• 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
}

• 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;
}


• /**
* @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;
};


• impl Solution {
pub fn generate(num_rows: i32) -> Vec<Vec<i32>> {
let mut ret_vec: Vec<Vec<i32>> = Vec::new();
let mut cur_vec: Vec<i32> = Vec::new();

for i in 0..num_rows as usize {
let mut new_vec: Vec<i32> = 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
}
}