1464 - Maximum Product of Two Elements in an Array (Easy)

Problem Link

https://leetcode.com/problems/maximum-product-of-two-elements-in-an-array/

Problem Statement

Given the array of integers nums, you will choose two different indices i and j of that array. Return the maximum value of (nums[i]-1)*(nums[j]-1).

Example 1:

Input: nums = [3,4,5,2]
Output: 12 
Explanation: If you choose the indices i=1 and j=2 (indexed from 0), you will get the maximum value, that is, (nums[1]-1)*(nums[2]-1) = (4-1)*(5-1) = 3*4 = 12.

Example 2:

Input: nums = [1,5,4,5]
Output: 16
Explanation: Choosing the indices i=1 and j=3 (indexed from 0), you will get the maximum value of (5-1)*(5-1) = 16.

Example 3:

Input: nums = [3,7]
Output: 12

Constraints:

• $2 <= nums.length <= 500$
• $1 <= nums[i] <= 10^3$

Approach 1: Sorting

We can just choose the two largest values to maximum the product.

Python

Written by @jaffar

class Solution:
    def maxProduct(self, nums: List[int]) -> int:
        sorted_nums = sorted(nums, reverse=True)
        first_max = sorted_nums[0] - 1
        second_max = sorted_nums[1] - 1
        return first_max * second_max

Erlang

Written by @jit

%% Lazy but whatever
max_product(Nums) ->
  [A, B | _] = lists:sort(fun erlang:'>='/2, Nums),
  (A - 1) * (B - 1).

Java

Written by @wingkwong

class Solution {
    public int maxProduct(int[] nums) {
        Arrays.sort(nums);
        int n = nums.length;
        return (nums[n - 1] - 1) * (nums[n - 2] - 1);
    }
}