题目描述

blablabla

等差数列求和

设等差数列有$k$项，首项为$a_1$，$a_k=a_1+k-1$，则有$\frac{a_1+a_k}{2}\cdot k=sum$，即$a_1 = \frac{2\cdot sum-k^2+k}{2k}$。
根据题意有$a_1\geq 1, k\geq 2$。根据$k$，寻找$a_1$的整数解。

class Solution(object):
    def findContinuousSequence(self, sum):
        """
        :type sum: int
        :rtype: List[List[int]]
        """
        if sum < 3:
            return []

        def get(k):
            return (2*sum-k*k+k) / (2*k)

        res = []
        k = 2
        while True:
            a = get(k)
            if a < 1:
                break
            if a - int(a) == 0:
                a = int(a)
                res.append(list(range(a, a + k)))
            k += 1
        return res