829. Consecutive Numbers Sum

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829. Consecutive Numbers Sum

题目描述

Given a positive integer N, how many ways can we write it as a sum of consecutive positive integers?

Example 1:

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Input: 5
Output: 2
Explanation: 5 = 5 = 2 + 3

Example 2:

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Input: 9
Output: 3
Explanation: 9 = 9 = 4 + 5 = 2 + 3 + 4

Example 3:

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Input: 15
Output: 4
Explanation: 15 = 15 = 8 + 7 = 4 + 5 + 6 = 1 + 2 + 3 + 4 + 5

Note: 1 <= N <= 10 ^ 9.

题目大意

求正整数 N，有多少种方法可以把它写成连续正整数的和？

解题思路

由题目规律可得：
N / c 为 第c / 2 + c % 2个数，所以 N / c >= c / 2 + c % 2
符合下列情况时，存在连续正整数的和为 N。
若 c 为奇数，N 可以整除 c
若 c 为偶数，并且 (N / c) * c + c / 2 == N

代码

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class Solution {
    func consecutiveNumbersSum(_ N: Int) -> Int {
        var ans = 0
        var c = 0
        while true {
            c += 1
            if N / c < c / 2 + c % 2 {
                break
            }
            if c % 2 == 1 && N % c == 0 {
                ans += 1
            }else if c % 2 == 0 && (N / c) * c + c / 2 == N {
                ans += 1
            }
        }
        return ans
    }
}
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