A heap data structure is a complete binary tree that satisfies the heap property. In a heap, the value stored in each node is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the values stored in its children.
A heap supports two main operations: insertion and deletion. These operations maintain the heap property.
To insert an element into a heap, it is placed at the next available position in the tree, typically as the leftmost node in the bottom-most level. Then, it is compared with its parent node. If it violates the heap property, it swaps places with its parent until the property is satisfied again.
In a max-heap, deleting an element removes the root node, which contains the maximum value. The last node of the tree replaces the root and then moves down until it finds its correct position based on its value. This process is called “down-heap” or “percolate-down”.
When to Use Heap Data Structure?
The heap data structure has various applications due to its efficient implementation of priority queues and sorting algorithms.
- Priority Queues: A priority queue is a type of queue where each element has an associated priority. Heaps can efficiently implement priority queues by keeping elements organized based on their priorities.
- Heap Sort: Heap sort is an efficient sorting algorithm that uses heaps to sort elements in ascending or descending order.
It has a time complexity of O(n log n).
- Dijkstra’s Algorithm: Dijkstra’s algorithm uses heaps to find shortest paths in a weighted graph efficiently. It maintains a priority queue of vertices and selects the one with the minimum distance.
- Event-driven Simulations: Heaps are commonly used in event-driven simulations to handle events that occur at different times. The event with the smallest time can be quickly retrieved from the heap.
In summary, a heap data structure is a complete binary tree that satisfies the heap property. It is used for efficient implementation of priority queues, sorting algorithms, graph algorithms, and event-driven simulations. By understanding its operations and applications, you can leverage heaps to improve the efficiency of various algorithms and data structures.