829. Consecutive Numbers Sum

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

Example 1:

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

Example 2:

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

Example 3:

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

Note: 1 <= N <= 10 ^ 9.

思路：觀察規律達到如下

舉例子：N = 15

(1) 15 = 15*1  + (0) 

      15%1 = 0

(2) 15 = 7 + 8 = 7*2 + (0 + 1)

      (15-1)%2 = 0

(3) 15 = 4 + 5 + 6 = 4*3 + (0 + 1 + 2)

       (15 -1 -2)%3 = 0

(4) 15 = 1 + 2 +3 + 4 + 5 = 1*5 + (0 + 1 + 2 +3 + 4)

      (15 - 1 -2 -3 -4)%5 = 0

代碼如下：

class Solution {
public:
    int consecutiveNumbersSum(int N) {
        int ans = 0;
        for (int i = 1; N > 0; N-=i, i++)
            ans += (N % i == 0);
        return ans;

    }
};