Maximum Product Of Two Elements In An Array · Interview Problem

Back to problems

Leetcode

Easy

Arrays

Sorting

Greedy

Maximum Product Of Two Elements In An Array

Find the maximum value of $(x-1)(y-1)$ over all pairs of distinct elements in an array.

Acceptance 0%

Start Practice

Problem Statement

Problem

Given an array of positive integers, choose two different elements $x$ and $y$ . Your task is to maximize the value of

$(x - 1) \times (y - 1)$

Return the largest possible product.

Intuition

Since subtracting 1 from each number preserves ordering, the best pair will come from the two largest values in the array.

Input Format

An integer array nums of length at least 2.
Each element is a positive integer.

Output Format

Return a single integer: the maximum value of $(x - 1)(y - 1)$ over all pairs of distinct elements.

Constraints

$2 \le nums.length$
$1 \le nums[i]$
The answer fits in a 32-bit signed integer.

Examples

Sample cases returned by the problem API.

Example 1

Input

nums = [3,4,5,2]

Output

Explanation

The two largest numbers are 5 and 4. The product is (5 - 1) * (4 - 1) = 12.

Example 2

Input

nums = [1,5,4,5]

Output

Explanation

The two largest numbers are 5 and 5. The product is (5 - 1) * (5 - 1) = 16.

Show 1 more example

Example 3

Input

nums = [3,7]

Output

Explanation

Only one pair exists: (3 - 1) * (7 - 1) = 12.

Premium problem context

Unlock deeper context for this problem

Premium adds guided hints, editorial links, similar variants, discussion resources, and concept maps so you can understand why a problem matters, not just solve it once.

Guided hints

Editorial and discussion links

Concept map and variants

Track your progress