118. Pascal's Triangle

Given a non-negative integer numRows, generate the first numRows of Pascal's triangle.

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

Example:

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

vector<vector<int>> generate(int numRows) { // time: O(n^2); space: O(n^2)
    vector<vector<int> > res(numRows);
    for (int i = 0; i < numRows; ++i) {
        res[i].resize(i + 1);
        res[i][0] = res[i][i] = 1;
        for (int j = 1; j < i; ++j) {
            res[i][j] = res[i - 1][j - 1] + res[i - 1][j];
        }
    }
    return res;
}