Maximum Product of Three Numbers | LeetCode 628 | C++ Solution with Explanation

In this video, we solve LeetCode Problem 628: Maximum Product of Three Numbers using a clear and structured approach that is easy to understand for beginners.

We start by understanding the problem statement and why simply picking the three largest numbers does not always give the correct answer. Then, we go through detailed examples to see how negative numbers can affect the final result. This helps build intuition for choosing the correct combination of numbers.

After that, we explore different approaches:

A basic sorting-based solution
An optimized single-pass approach

We also explain why the answer can come from either:

The product of the three largest numbers
Or the product of the two smallest (most negative) numbers and the largest number
🧠 What You Will Learn in This Video:
How to analyze the problem effectively
Importance of handling negative numbers
Step-by-step dry run with examples
Sorting-based approach
Optimized approach using one pass
Clean and readable C++ implementation
Time and Space Complexity analysis
🧩 Problem Summary:

Given an integer array nums, your task is to find the maximum product that can be obtained by multiplying any three numbers from the array.

The array may contain both positive and negative numbers, so careful consideration is required while selecting the three numbers.

💡 Key Insight:

The maximum product can be formed in two ways:

Product of the three largest numbers
Product of the two smallest numbers (which can be negative) and the largest number

You need to compare both and return the maximum.

💻 Approach Explained:
🔹 Approach 1: Sorting
Sort the array
Calculate:
Product of last three elements
Product of first two elements and last element
Return the maximum
🔹 Approach 2: Optimized (Single Pass)
Track:
Three largest numbers
Two smallest numbers
Compute both possible products
Return the maximum result

⏱️ Complexity Analysis:

Sorting Approach:
Time Complexity: O(n log n)
Space Complexity: O(1)
Optimized Approach:
Time Complexity: O(n)
Space Complexity: O(1)

💻 Topics Covered:
Arrays
Greedy thinking
Handling negative numbers
Optimization techniques

🚀 Why Watch This Video?

This problem is a great example of how edge cases (like negative numbers) can change the solution. It helps you think beyond the obvious approach and improve your problem-solving skills for coding interviews.

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Видео Maximum Product of Three Numbers | LeetCode 628 | C++ Solution with Explanation канала PATEL MANN