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]
]

思路

该题比较简单，杨辉三角形，从第三行开始，除了首尾，中间元素的值可通过如下公式计算：cur[i] = prev[i] + prev[i-1]

计算当前行实现要点如下：

• 拷贝上一行，并在末尾添加元素1
• 倒着开始计算，i 不包括首尾，cur[i] += cur[i-1]

C++11

class Solution {
public:
    vector<vector<int>> generate(int numRows) {
        vector<vector<int>> res;
        for (auto i = 0; i < numRows; ++i) {
            vector<int> row;
            if (!res.empty()) 
                row.assign(res.at(i-1).begin(), res.at(i-1).end());
            row.emplace_back(1);
            for (auto j = i - 1; j > 0; --j)
                row[j] += row[j-1];
            res.emplace_back(row);
        }
        return res;
    }
};

update 2019.03.07

class Solution {
public:
    vector<vector<int>> generate(int numRows) {
        vector<vector<int>> res;
        if (!numRows) return res;
        res = {{1}};
        for (int i = 1; i < numRows; i++) {
            vector<int> row;
            row.assign(res.at(i-1).begin(), res.at(i-1).end());
            row.emplace_back(1);
            for (int j = row.size() - 2; j > 0; j--) {
                row[j] += row[j-1];
            }
            res.emplace_back(row);
        }
        return res;
    }
};

ac结果：

Runtime: 4 ms, faster than 100.00% of C++ online submissions for Pascal's Triangle.
Memory Usage: 8.9 MB, less than 24.64% of C++ online submissions for Pascal's Triangle.

内存使用有点高，后面再来想办法改进一下。