Description:
Given an integer array nums, find three numbers whose product is maximum and return the maximum product.
Examples:
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: -6Solution in Python:
Steps to Solve the Problem:
- Sort the Array:
- By sorting the array, we can easily access the largest and smallest numbers.
- Consider Two Cases:
- The maximum product can be achieved in two ways:
- The product of the three largest numbers.
- The product of the two smallest numbers (which can be negative, resulting in a positive product when multiplied) and the largest number.
- The maximum product can be achieved in two ways:
- Return the Maximum of the Two Cases:
- Compute both potential products and return the maximum of the two.
Python
from typing import List
class Solution:
def maximumProduct(self, nums: List[int]) -> int:
# Step 1: Sort the array
nums.sort()
# Step 2: Compute the product of the three largest numbers
max1 = nums[-1] * nums[-2] * nums[-3]
# Step 3: Compute the product of the two smallest numbers and the largest number
max2 = nums[0] * nums[1] * nums[-1]
# Step 4: Return the maximum of the two computed products
return max(max1, max2)Solution in Javascript:
JavaScript
/**
* @param {number[]} nums
* @return {number}
*/
var maximumProduct = function(nums) {
// Step 1: Sort the array
nums.sort((a, b) => a - b);
// Step 2: Compute the product of the three largest numbers
const max1 = nums[nums.length - 1] * nums[nums.length - 2] * nums[nums.length - 3];
// Step 3: Compute the product of the two smallest numbers and the largest number
const max2 = nums[0] * nums[1] * nums[nums.length - 1];
// Step 4: Return the maximum of the two computed products
return Math.max(max1, max2);
};Solution in Java:
Java
import java.util.Arrays;
class Solution {
public int maximumProduct(int[] nums) {
// Step 1: Sort the array
Arrays.sort(nums);
// Step 2: Compute the product of the three largest numbers
int max1 = nums[nums.length - 1] * nums[nums.length - 2] * nums[nums.length - 3];
// Step 3: Compute the product of the two smallest numbers and the largest number
int max2 = nums[0] * nums[1] * nums[nums.length - 1];
// Step 4: Return the maximum of the two computed products
return Math.max(max1, max2);
}
}Solution in C#:
C#
public class Solution {
public int MaximumProduct(int[] nums) {
// Step 1: Sort the array
Array.Sort(nums);
// Step 2: Compute the product of the three largest numbers
int max1 = nums[nums.Length - 1] * nums[nums.Length - 2] * nums[nums.Length - 3];
// Step 3: Compute the product of the two smallest numbers and the largest number
int max2 = nums[0] * nums[1] * nums[nums.Length - 1];
// Step 4: Return the maximum of the two computed products
return Math.Max(max1, max2);
}
}