Leetcode 414: Third Maximum Number | Step-by-Step Solution

In this video, we’ll solve **Leetcode Problem 414: Third Maximum Number**. The task is to find the third distinct maximum number in an array. If the third maximum does not exist, return the maximum number. This problem tests your understanding of **array manipulation**, **sorting**, and **edge case handling**.

🔑 **Problem Breakdown**:
- Given an integer array `nums`, you need to find the third largest distinct number.
- If there is no third distinct number, return the largest number.

📌 **Approach**:
We will solve this problem efficiently using the following steps:
1. **Set**: Use a set to store the unique numbers in the array.
2. **Sorting**: Sort the set in descending order.
3. **Edge Cases**: If there are fewer than three distinct numbers, return the maximum number from the array.

This approach runs in **O(n log n)** time complexity due to sorting, making it efficient for smaller arrays. For larger arrays, you can use an optimized solution with **O(n)** time complexity using a few variables to track the top three maximum numbers.

This problem is great for practicing **array manipulation**, handling **duplicates**, and preparing for **coding interviews**.

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