[LeetCode] Pascal's Triangle 楊輝三角

 

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]
]

楊輝三角是二項式系數的一種寫法，如果熟悉楊輝三角的五個性質，那么很好生成，可參見我的上一篇博文Pascal's Triangle II。具體生成算是：每一行的首個和結尾一個數字都是1，從第三行開始，中間的每個數字都是上一行的左右兩個數字之和。代碼如下：

 

class Solution {
public:
    vector<vector<int>> generate(int numRows) {
        vector<vector<int>> res(numRows, vector<int>());
        for (int i = 0; i < numRows; ++i) {
            res[i].resize(i + 1, 1);
            for (int j = 1; j < i; ++j) {
                res[i][j] = res[i - 1][j - 1] + res[i - 1][j];
            }
        }
        return res;
    }
};

 

類似題目：

Pascal's Triangle II

 

參考資料：

https://leetcode.com/problems/pascals-triangle/

https://leetcode.com/problems/pascals-triangle/discuss/38150/My-C%2B%2B-code-0ms

 

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