LeetCode每日一题(829. Consecutive Numbers Sum)

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最新推荐文章于 2025-08-18 07:15:00 发布 · 195 阅读

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#leetcode #算法

给定一个整数n，返回将其写为连续正整数之和的方式数。例如，当n=5时，有2种方式：5=2+3；当n=9时，有3种方式：9=4+5，9=2+3+4。对于每个数x，可以有2到x个连续数的组合，需要找到所有可能的n值，使得n有整数解。

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

Example 1:

Input: n = 5
Output: 2

Explanation: 5 = 2 + 3

Example 2:

Input: n = 9
Output: 3

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

Example 3:

Input: n = 15
Output: 4

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

Constraints:

1 <= n <= 109

对于任何一个数 x 进行拆解:

2 个连续数: x = n + (n + 1) = 2n + 1
3 个连续数: x = n + (n + 1) + (n + 2) = 3n + 3
4 个连续数: x = n + (n + 1) + (n + 2) + (n + 3) = 4n + 6
5 个连续数: x = n + (n + 1) + (n + 2) + (n + 3) + (n + 4)= 5n + 10
…

只要其中的 n 有整数解就可以, 当 n<1 的时候，就没必要再继续检测了

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