Consecutive Numbers Sum — LeetCode 829 Python Solution

The problem

Given an integer n, return the number of ways you can write n as the sum of consecutive positive integers.

Example

Input

n = 5

Output

2

Explanation

5 = 2 + 3

Python solution

class Solution:
    def consecutiveNumbersSum(self, n: int) -> int:
        n <<= 1
        ans, k = 0, 1
        while k * (k + 1) <= n:
            if n % k == 0 and (n // k - k + 1) % 2 == 0:
                ans += 1
            k += 1
        return ans

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 829. Consecutive Numbers Sum is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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