829. Consecutive Numbers Sum
阿新 • • 發佈:2018-11-12
Description
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.
Problem URL
Solution
給一個數字N,找到它可以有多少種方式,由一串連續的數字加和而成。
If it is a consecutive sequence, we have
So, for each I, we could judge wether it could be a mutilpe of a constant equal to it. Since I = 1, it is always valid(it is itself), we start iteration from 2.
Code
class Solution {
public int consecutiveNumbersSum(int N) {
int count = 1;
for (int i = 2; i * (i + 1) / 2 <= N; i++){
if ((N - i * (i + 1) / 2) % i == 0){
count++;
}
}
return count;
}
}
Time Complexity: O(N ^ 0.5)
Space Complexity: O(1)