题目描述

自己解法

运用动态规划思想，当前层下标0、-1的元素值为1，下标从1到len(res)-1的元素中，若下标为i，其值等于上一层下标[i]、[i-1]的元素之和，Python实现：

class Solution:
    def generate(self, numRows: int) -> List[List[int]]:
        if not numRows:
            return []
        else:
            ans = []
            for i in range(numRows):
                res = [1] * (i+1)
                if i > 1:
                    for j in range(1,len(res)-1):
                        res[j] = ans[i-1][j-1] + ans[i-1][j]
                ans.append(res)
            return ans

官方解法

官方解法的思路跟我一样，也差不多：

class Solution:
    def generate(self, num_rows):
        triangle = []

        for row_num in range(num_rows):
            # The first and last row elements are always 1.
            row = [None for _ in range(row_num+1)]
            row[0], row[-1] = 1, 1

            # Each triangle element is equal to the sum of the elements
            # above-and-to-the-left and above-and-to-the-right.
            for j in range(1, len(row)-1):
                row[j] = triangle[row_num-1][j-1] + triangle[row_num-1][j]

            triangle.append(row)

        return triangle

题解区

题解区大佬发现发现当前一行只比上一行多了一个元素，最最关键的一点：本行元素等于上一行元素往后错一位再逐个相加，具体参考：
取巧解法

class Solution:
    def generate(self, numRows: int) -> List[List[int]]:
        if numRows == 0: return []
        res = [[1]]
        while len(res) < numRows:
            newRow = [a+b for a, b in zip([0]+res[-1], res[-1]+[0])]
            res.append(newRow)      
        return res