Practice/Meta/Leetcode 829. Consecutive Numbers Sum

Leetcode 829. Consecutive Numbers Sum

CodingOptional

Problem

Given a positive integer n, determine how many distinct ways you can express it as the sum of consecutive positive integers.

For example, the number 9 can be expressed in three ways:

• 9 (single number)
• 4 + 5 (two consecutive numbers)
• 2 + 3 + 4 (three consecutive numbers)

Your task is to count all such possible representations.

Requirements

1. Return the total count of ways to express n as a sum of consecutive positive integers
2. A single number counts as one way (sequence of length 1)
3. All numbers in the sequence must be positive integers
4. The solution must handle large values of n efficiently

Constraints

• 1 ≤ n ≤ 10^9
• Time complexity should be O(√n) or better
• Space complexity should be O(1)

Examples

Example 1:

` Input: n = 5 Output: 2 Explanation:

• 5 (one number)
• 2 + 3 (two consecutive numbers) `

Example 2:

` Input: n = 9 Output: 3 Explanation:

• 9 (one number)
• 4 + 5 (two consecutive numbers)
• 2 + 3 + 4 (three consecutive numbers) `

Example 3:

` Input: n = 15 Output: 4 Explanation:

• 15 (one number)
• 7 + 8 (two consecutive numbers)
• 4 + 5 + 6 (three consecutive numbers)
• 1 + 2 + 3 + 4 + 5 (five consecutive numbers) `