## Pascal's Triangle

### 描述

Given numRows, generate the first numRows of Pascal's triangle.

For example, given numRows = 5,

Return

[
[1],
[1,1],
[1,2,1],
[1,3,3,1],
[1,4,6,4,1]
]


### 从左到右

// LeetCode, Pascal's Triangle
// 时间复杂度O(n^2)，空间复杂度O(n)
class Solution {
public:
vector<vector<int> > generate(int numRows) {
vector<vector<int> > result;
if(numRows == 0) return result;

result.push_back(vector<int>(1,1)); //first row

for(int i = 2; i <= numRows; ++i) {
vector<int> current(i,1);  // 本行
const vector<int> &prev = result[i-2];  // 上一行

for(int j = 1; j < i - 1; ++j) {
current[j] = prev[j-1] + prev[j]; // 左上角和右上角之和
}
result.push_back(current);
}
return result;
}
};


### 从右到左

// LeetCode, Pascal's Triangle
// 时间复杂度O(n^2)，空间复杂度O(n)
class Solution {
public:
vector<vector<int> > generate(int numRows) {
vector<vector<int> > result;
vector<int> array;
for (int i = 1; i <= numRows; i++) {
for (int j = i - 2; j > 0; j--) {
array[j] = array[j - 1] + array[j];
}
array.push_back(1);
result.push_back(array);
}
return result;
}
};