# Understanding Top K Elements

Top 'K' Elements is a common problem where the goal is to find the top 'K' elements from a given dataset based on some criteria, such as frequency, value, or priority. This problem can be solved using various techniques, including heap-based solutions, quickselect, and sorting.

### Process

**Initialization**: Define the problem space and initialise the necessary data structures. For heap-based solutions, this might involve creating a min-heap or max-heap, depending on the problem requirements.**Heap Construction**: Insert elements into the heap based on the criteria (e.g., frequency, value). For example, if you use a min-heap to find the top 'K' largest elements, you would insert elements into the heap until it contains 'K' elements.**Heap Maintenance**: For each subsequent element in the dataset, compare it with the root of the heap (the smallest element in the case of a min-heap). If the new element is larger than the root, replace the root with the new element and adjust the heap to maintain the heap property.**Termination**: The process terminates when all elements have been processed, and the heap contains the top 'K' elements based on the specified criteria.

### When to Use

**Priority Queues**: To find the top 'K' elements with the highest or lowest priority.**Frequency Counting**: To find the top 'K' most frequent elements in a dataset.**Sorting and Selection**: To find the top 'K' largest or smallest elements in a dataset without sorting the entire dataset.

### How Does It Reduce Time Complexity?

**Heap-Based Solutions**: Using a heap allows for efficient insertion and extraction of elements, with a time complexity of O(log K) for each operation. This results in an overall time complexity of O(N log K) for processing N elements, which is more efficient than sorting the entire dataset (O(N log N)).**Quickselect**: This algorithm can find the top 'K' elements in an average time complexity of O(N), making it very efficient for large datasets.

### Example problem for better understanding

**Kth Largest Element in an Array**

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