Consecutive Numbers Sum Python Solution

Tested Python solution for LeetCode 829 with 22 pytest cases. Generate a practice environment with lcpy.

LeetCode 829, Hard. Topics: Math, Enumeration. View on LeetCode.

Generate this problem as a practice environment: tested reference solution, 22 parametrized pytest cases, and a playground notebook:

lcpy gen -n 829   # by problem number
lcpy gen -s consecutive_numbers_sum   # by problem name

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Problem

Given an integer <code>n</code>, return <em>the number of ways you can write </em><code>n</code><em> as the sum of consecutive positive integers.</em>

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Examples

Input: n = 5
Output: 2

Explanation: 5 = 2 + 3

Input: n = 9
Output: 3

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

Input: n = 15
Output: 4

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

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Constraints

• 1 <= n <= 10^9

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Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

class Solution:
    # Time: O(sqrt(n))
    # Space: O(1)
    def consecutive_numbers_sum(self, n: int) -> int:
        count = 0
        k = 1
        while k * (k - 1) // 2 < n:
            if (n - k * (k - 1) // 2) % k == 0:
                count += 1
            k += 1
        return count

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Complexity

Time	Space
O(sqrt(n))	O(1)

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