What is the main approach for solving the 'Find Greatest Common Divisor of Array' problem?

The main approach is to find the minimum and maximum values in the array in a single iteration, then calculate their greatest common divisor using an efficient method like the Euclidean algorithm.

How does the Euclidean algorithm work for GCD?

The Euclidean algorithm works by repeatedly subtracting the smaller number from the larger one until one number becomes zero. The non-zero number is the GCD.

Can the problem be solved with a more efficient approach for large arrays?

Yes, by finding the min and max values in one pass and using an efficient GCD algorithm, the solution can handle large arrays efficiently.

What is the time complexity of the solution?

The time complexity is O(n) for finding the min and max values, and O(log(min, max)) for computing the GCD.

Are there any edge cases to consider in the 'Find Greatest Common Divisor of Array' problem?

Yes, edge cases include arrays with identical elements, where the GCD is the element itself, and arrays with very large or small numbers.

#1979

Easy

auto_awesome数组·数学

LeetCode 题解工作台

找出数组的最大公约数

给你一个整数数组 nums ，返回数组中最大数和最小数的最大公约数。两个数的最大公约数是能够被两个数整除的最大正整数。示例 1：输入： nums = [2,5,6,9,10] 输出： 2 解释： nums 中最小的数是 2 nums 中最大的数是 10 2 和 10 的最大公约数是 2…

数组数学数论

题目描述

给你一个整数数组 nums ，返回数组中最大数和最小数的 最大公约数 。

两个数的 最大公约数 是能够被两个数整除的最大正整数。

示例 1：

输入：nums = [2,5,6,9,10]
输出：2
解释：
nums 中最小的数是 2
nums 中最大的数是 10
2 和 10 的最大公约数是 2

示例 2：

输入：nums = [7,5,6,8,3]
输出：1
解释：
nums 中最小的数是 3
nums 中最大的数是 8
3 和 8 的最大公约数是 1

示例 3：

输入：nums = [3,3]
输出：3
解释：
nums 中最小的数是 3
nums 中最大的数是 3
3 和 3 的最大公约数是 3

提示：

2 <= nums.length <= 1000
1 <= nums[i] <= 1000

lightbulb

解题思路

方法一：模拟

我们根据题意模拟即可，即先找出数组 $\textit{nums}$ 中的最大值和最小值，然后求最大值和最小值的最大公约数。

时间复杂度 $O(n)$ ，其中 $n$ 为数组 $\textit{nums}$ 的长度。空间复杂度 $O(1)$ 。

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class Solution:
    def findGCD(self, nums: List[int]) -> int:
        return gcd(max(nums), min(nums))

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
Look for an efficient approach to find the min and max values in one iteration.
question_mark
Ensure that the candidate uses an efficient method like the Euclidean algorithm for GCD.
question_mark
Watch for edge cases such as arrays with identical elements, where GCD is the element itself.

warning

常见陷阱

外企场景

error
Misunderstanding that the problem only asks for the GCD of the smallest and largest numbers, not all pairs.
error
Not handling arrays with identical elements correctly, where the GCD should be the element itself.
error
Using an inefficient method to find the minimum and maximum values, causing unnecessary time complexity.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Find the GCD of the largest two elements instead of min and max.
arrow_right_alt
Calculate the GCD for multiple pairs within the array and return the smallest GCD.
arrow_right_alt
Allow larger arrays, potentially introducing more optimization techniques for finding the min and max.

help

常见问题

外企场景

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