###### tags: `Leetcode` `easy` `math` `sort` `python` `c++`

# 628. Maximum Product of Three Numbers

## [題目連結:] https://leetcode.com/problems/maximum-product-of-three-numbers/

## 題目:
Given an integer array ```nums```, find three numbers whose product is maximum and return the maximum product.

**Example 1:**

Input: nums = [1,2,3]
Output: 6

**Example 2:**

Input: nums = [1,2,3,4]
Output: 24

**Example 3:**

Input: nums = [-1,-2,-3]
Output: -6

## 解題想法:
* 題目要求數組中任意三個數的最大乘積
* 先將數組排序:
* case1:數組可能有正有負
* 最大可以是， **左邊兩個最負的相乘，搭配最右邊的**
* case2: 若數組全正or全負
* 最大的乘積為， **最右邊三個相乘**

## Python:

class Solution(object):
    def maximumProduct(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        nums.sort()
        max1=nums[0]*nums[1]*nums[-1]
        max2=nums[-1]*nums[-2]*nums[-3]
        return max(max1,max2)
    
if __name__ == '__main__':
    result=Solution()
    ans=result.maximumProduct(nums = [1,2,3])
    print(ans) #6

## C++:

#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;

class Solution {
public:
    int maximumProduct(vector<int>& nums) {
        //<algorithm> for sort()
        int n=nums.size();
        sort(nums.begin(),nums.end());
        int max1=nums[0]*nums[1]*nums[n-1];
        int max2=nums[n-1]*nums[n-2]*nums[n-3];
        return max(max1,max2);
    }
};

int main(){
          Solution res;
          vector<int> nums={1,2,3,4};
          int ans=res.maximumProduct(nums);
          cout<<ans<<endl;
          return 0;
}