A heap data structure is a binary tree-based data structure that is commonly used in computer science and programming. It is a complete binary tree, meaning that all levels of the tree are completely filled except for the last level, which is filled from left to right.
A heap has two important properties:
- Complete Binary Tree: As mentioned earlier, a heap is a complete binary tree where all levels are completely filled except for the last level.
- Heap Order Property: A heap can be of two types: max heap or min heap. In a max heap, for any given node, the value of that node is greater than or equal to the values of its children. Similarly, in a min heap, the value of any given node is less than or equal to the values of its children.
A heap supports several operations:
- Insertion: To insert an element into a heap, we first place it at the bottom-most rightmost position maintaining the complete binary tree property. Then we compare it with its parent and swap it if necessary to maintain the heap order property.
- Deletion: The deletion operation involves removing an element from the root of the heap.
Once removed, we replace it with the last element present in the last level and then compare it with its children to restore the heap order property.
- Peek/Get Minimum or Maximum: This operation retrieves (without removing) either the minimum or maximum value depending on whether it is a min or max heap respectively. In a max heap, peek operation returns the maximum value, while in a min heap, it returns the minimum value.
Applications of Heap Data Structure
The heap data structure is widely used in various algorithms and applications:
- Priority Queue: A priority queue is an abstract data type that is similar to a queue but with some additional properties. It is commonly implemented using a heap to efficiently retrieve the element with the highest or lowest priority.
- Heap Sort: Heap sort is a comparison-based sorting algorithm that uses a heap data structure to sort elements in ascending or descending order.
- Dijkstra’s Algorithm: Dijkstra’s algorithm, used for finding the shortest path between nodes in a graph, relies on the efficient extraction of the minimum value from a priority queue, often implemented using a heap.
A heap data structure is an essential tool in computer science and programming. Its ability to efficiently retrieve the minimum or maximum value and its applications in various algorithms make it a valuable asset. By understanding its properties and operations, you can leverage heaps to solve complex problems effectively.