How do I approach finding consecutive integers that sum to a number?

Start by recognizing that three consecutive integers can be expressed as x-1, x, x+1. If the sum is valid, x can be calculated directly.

What is the time complexity of this problem?

The time complexity is O(1) as the solution involves only basic mathematical calculations without loops.

What happens if no three consecutive integers sum to the number?

If no solution exists, return an empty array, indicating that it's not possible to express the number as the sum of three consecutive integers.

Can the GhostInterview platform help with similar mathematical problems?

Yes, GhostInterview can help by breaking down similar problems and applying mathematical patterns to find solutions.

What if the number is too large for consecutive integers to sum?

If the number is too large or cannot be split into three consecutive integers, the solution will return an empty array.

#2177

Medium

auto_awesome数学·结合·模拟

LeetCode 题解工作台

找到和为给定整数的三个连续整数

给你一个整数 num ，请你返回三个连续的整数，它们的和为 num 。如果 num 无法被表示成三个连续整数的和，请你返回一个空数组。示例 1：输入： num = 33 输出： [10,11,12] 解释： 33 可以表示为 10 + 11 + 12 = 33 。 10, 11, 12 …

数学模拟

题目描述

给你一个整数 num ，请你返回三个连续的整数，它们的和为 num 。如果 num 无法被表示成三个连续整数的和，请你返回一个空数组。

示例 1：

输入：num = 33
输出：[10,11,12]
解释：33 可以表示为 10 + 11 + 12 = 33 。
10, 11, 12 是 3 个连续整数，所以返回 [10, 11, 12] 。

示例 2：

输入：num = 4
输出：[]
解释：没有办法将 4 表示成 3 个连续整数的和。

提示：

0 <= num <= 10¹⁵

lightbulb

解题思路

方法一：数学

我们假设三个连续的整数分别为 $x-1$ , $x$ , $x+1$ ，则它们的和为 $3x$ ，因此 $\textit{num}$ 必须是 $3$ 的倍数。如果 $\textit{num}$ 不是 $3$ 的倍数，则无法表示成三个连续整数的和，返回空数组。否则，令 $x = \frac{\textit{num}}{3}$ ，则 $x-1$ , $x$ , $x+1$ 就是三个连续整数，它们的和为 $\textit{num}$ 。

时间复杂度 $O(1)$ ，空间复杂度 $O(1)$ 。

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class Solution:
    def sumOfThree(self, num: int) -> List[int]:
        x, mod = divmod(num, 3)
        return [] if mod else [x - 1, x, x + 1]

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Understand if the candidate can recognize and leverage patterns in number theory.
question_mark
Evaluate the candidate's ability to quickly derive a mathematical approach and apply it in simulation.
question_mark
Check if the candidate can handle edge cases, such as small or large values of num.

warning

常见陷阱

外企场景

error
Failing to recognize the mathematical relationship between three consecutive numbers and their sum.
error
Overcomplicating the solution by trying unnecessary loops or searches.
error
Not correctly handling edge cases, like when num is too small or large for a valid solution.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Generalizing the problem to find n consecutive integers that sum to a given number.
arrow_right_alt
Changing the number of integers to sum (e.g., four or five consecutive integers).
arrow_right_alt
Adding constraints such as finding consecutive prime numbers that sum to a given number.

help

常见问题

外企场景

继续练习

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