118. Pascal's Triangle

Problem:

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]
]

思路：
每一行由上一行产生，第一个和最后一个数为1，然后中间的数由上一行对应的数与它左边的数相加得到。也称为杨辉三角，在中国南宋数学家杨辉1261年所著的《详解九章算法》一书中出现，比欧洲的帕斯卡早了393年。

Solution:

vector<vector<int>> generate(int numRows) {
    if (numRows == 0)   return vector<vector<int>>{};
    vector<vector<int>> res(1, {1});
    
    for (int i = 1 ; i < numRows; i++) {
        vector<int> ans(i+1);
        ans[0] = ans[i] = 1;
        for (int j = 1; j <= i-1; j++) {
            ans[j] = res.back()[j-1] + res.back()[j];
        }
        res.push_back(ans);
    }
    return res;
}

性能：
Runtime: 0 ms  Memory Usage: 8.8 MB