Maximum Product Of Two Elements In An Array · Interview Problem

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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 100%

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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.

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Example 3

Input

nums = [3,7]

Output

Explanation

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

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