829.md

Consecutive Numbers Sum

Description

link

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Solution

• See Code

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Code

class Solution:
    '''
    思路：
        1. 数学证明：
            x + (x+1) + (x+2)+...+ k terms = N
            kx + k*(k-1)/2 = N
            kx = N - k*(k-1)/2
        2. 存在这种x即可，x就是起始位置
    '''
    def consecutiveNumbersSum(self, N: int) -> int:
        res = 1
        for k in range(2, int(sqrt(2*N)) + 1):
            if (N - k*(k - 1)//2) % k == 0:
                res += 1
        return res