What is the time complexity of Maximum Product of Two Elements in an Array?

The optimal solution has a time complexity of O(n log n).

What data structures are used to solve Maximum Product of Two Elements in an Array?

This problem uses Array, Sorting, Heap (Priority Queue). Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Maximum Product of Two Elements in an Array?

Insight 1: The maximum product will always be obtained by multiplying the two largest numbers in the array (after subtracting 1 from each). Insight 2: Sorting the array allows us to efficiently find the two largest elements.

Which companies ask LeetCode 1464. Maximum Product of Two Elements in an Array in interviews?

This problem is frequently asked at Cisco, J.P. Morgan, Samsung.

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Maximum Product of Two Elements in an Array - LeetCode 1464 Solution

Maximum Product of Two Elements in an Array - Complete Solution Guide

Maximum Product of Two Elements in an Array is LeetCode problem 1464, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in java.

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

Detailed Explanation

The problem asks you to find the maximum product that can be obtained by multiplying two distinct elements from an array, after subtracting 1 from each element. The input is an array of integers (`nums`), and the output is a single integer representing the maximum product. The constraints specify that the array will always have at least two elements, and the elements themselves will be positive integers within a specific range.

Solution Approach

The provided Java solution utilizes a simple and efficient approach. It first sorts the input array `nums` in ascending order. Then, it directly accesses the two largest elements (located at indices `nums.length - 1` and `nums.length - 2`) and calculates their product after subtracting 1 from each. This product is then returned as the maximum product.

Step-by-Step Algorithm

Step 1: Sort the input array `nums` using `Arrays.sort(nums)`. This arranges the elements in ascending order.
Step 2: Access the second-to-last element (`nums[nums.length - 2]`) and the last element (`nums[nums.length - 1]`).
Step 3: Subtract 1 from each of these elements.
Step 4: Multiply the results from Step 3 together.
Step 5: Return the product calculated in Step 4.

Key Insights

Insight 1: The maximum product will always be obtained by multiplying the two largest numbers in the array (after subtracting 1 from each).
Insight 2: Sorting the array allows us to efficiently find the two largest elements.
Insight 3: No special handling is needed for negative numbers because all numbers are positive; this simplifies the problem significantly.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(1)

Topics

This problem involves: Array, Sorting, Heap (Priority Queue).

Companies

Asked at: Cisco, J.P. Morgan, Samsung.

Maximum Product of Two Elements in an Array | LeetCode 1464

Easy

Array Sorting Heap (Priority Queue)

Time: O(n log n)Space: O(1)

Solution Code

Available in:

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

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Problem Info

Description

Problem 1464: Maximum Product of Two Elements in an Array - Detailed explanation and solution approaches.

Topics

Array Sorting Heap (Priority Queue)

Companies

CiscoJ.P. MorganSamsung

Stats

Difficulty:Easy

Languages:1

Companies:3

Problem #:1464

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

5 steps

1
Step 1: Sort the input array `nums` using `Arrays.sort(nums)`. This arranges the elements in ascending order.
2
Step 2: Access the second-to-last element (`nums[nums.length - 2]`) and the last element (`nums[nums.length - 1]`).
3
Step 3: Subtract 1 from each of these elements.
4
Step 4: Multiply the results from Step 3 together.
5
Step 5: Return the product calculated in Step 4.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n log n)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The dominant operation is the sorting of the array, which has a time complexity of O(n log n) for efficient algorithms like merge sort or quicksort. The remaining steps (accessing elements, subtraction, multiplication) take constant time O(1) relative to the input size. The solution uses a constant amount of extra space, independent of the input size, hence O(1) space complexity.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Linear Scan

Iterate through the array twice, maintaining the two largest elements seen so far.

Time: O(n)Space: O(1)

Trade-offs: This approach avoids sorting, resulting in a linear time complexity. It's preferable if memory usage is strictly constrained or the input size is extremely large, but the sorting approach can be more concise and arguably easier to understand.

✨

Key Insights

1Insight 1: The maximum product will always be obtained by multiplying the two largest numbers in the array (after subtracting 1 from each).
2Insight 2: Sorting the array allows us to efficiently find the two largest elements.
3Insight 3: No special handling is needed for negative numbers because all numbers are positive; this simplifies the problem significantly.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: The array contains only two elements. The solution correctly handles this by selecting these two elements.
Edge case 2: The array contains duplicate elements. The solution correctly finds the two largest elements, even if they are identical, and computes the product correctly.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to subtract 1 from each element before multiplying. This would lead to an incorrect result.

✗Common mistake 2: Incorrectly handling edge cases, such as arrays with only two elements or arrays containing duplicate values.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: In optimization problems, finding the combination of two items yielding the maximum profit (after considering costs). This could be applied in resource allocation or supply chain management.

🏦Real-world scenario 2: In data analysis, identifying the pair of features that have the highest combined influence (after accounting for baseline effects). This could be useful in machine learning feature selection.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Even for easy problems, discuss time and space complexity. Interviewers want to see you think analytically.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: June 25, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 13

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 6

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Maximum Product of Two Elements in an Array"?

For this easy-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether sorting techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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