## Problem Description

In the "Top K Frequent Elements - LeetCode Problem" question, we are given an array of integers and an integer k. Our task is to find the k most frequent elements in the array. If there are multiple elements with the same frequency, we must return all of them.

## Solution

To solve this problem, we can make use of a dictionary to store the frequency of each element in the input array. We can then sort the dictionary based on the frequency of the elements and return the k most frequent elements.

Here are the steps we can follow to implement this solution in Python:

Create an empty dictionary to store the frequency of each element in the input array.

Loop through each element in the input array and update the frequency in the dictionary.

Sort the dictionary based on the frequency of the elements in descending order.

Return the first k keys of the sorted dictionary.

Here's the Python code to implement the above steps:

```
class Solution:
def topKFrequent(self, nums: List[int], k: int) -> List[int]:
freq = {}
for num in nums:
freq[num] = freq.get(num, 0) + 1
sorted_freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)
return [x[0] for x in sorted_freq[:k]]
```

## Complexity Analysis

The time complexity of this solution is O(n log n), where n is the length of the input array. This is because we use the sorted function to sort the dictionary, which has a worst-case time complexity of O(n log n).

The space complexity of this solution is O(n), where n is the length of the input array. This is because we use a dictionary to store the frequency of each element in the input array.

## Conclusion

In this post, we have learned how to solve the Top K Frequent Elements problem using Python. We have broken down the problem into simple steps and come up with a working solution. hope this post has been helpful in your journey to mastering algorithms and data structures in Python. Happy coding! 😎