118. Pascal's Triangle

1. 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:

2. Example

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]]

3. Constraints

• 1 <= numRows <= 30

4. Solutions

Bit Manipulation

n = numRows
Time complexity: O($n^2$)
Space complexity: O($n^2$)

class Solution {
public:
    vector<vector<int>> generate(int numRows) {
        vector<vector<int>> rows;
        for(int i = 1; i <= numRows; ++i) {
            vector<int> row(i, 1);
            for(int j = 1; j < i - 1; ++j) {
                row[j] = rows[i - 2][j - 1] + rows[i - 2][j];
            }

            rows.emplace_back(move(row));
        }

        return rows;
    }
};