Min heap

What does Min heap mean?

Min heap, short for minimum heap, is a complete binary tree data structure that satisfies the heap property: the value of each node is greater than or equal to the value of its children. In a min heap, the root node (the topmost node) contains the minimum value among all nodes in the heap. It is a specialized variant of a binary heap data structure.

Min heaps are often used in Priority queues, where the smallest Element is retrieved First. They are also used in algorithms like Dijkstra’s algorithm for finding the shortest path in a weighted graph.

Internally, a min heap is represented as an array. The root node is stored at index 0, its left child at index 1, its right child at index 2, and so on. Each node’s index can be calculated as (i-1)/2, where i is the node’s index.

Applications

Min heaps have numerous applications in computer science, particularly in priority queues. Priority queues are data structures that Store elements with associated priorities. When an element is retrieved from a Priority queue, the element with the highest priority is returned first.

Min heaps are ideal for implementing priority queues because they allow for efficient retrieval of the minimum element in O(1) time. This makes them suitable for applications where it is important to prioritize elements based on their values.

Other applications of min heaps include:

• Dijkstra’s algorithm: Min heaps are used in Dijkstra’s algorithm to find the shortest path in a weighted graph.
• Huffman coding: Min heaps are used in Huffman coding to create optimal prefix codes for data compression.
• Selection algorithm: Min heaps can be used to find the k-th smallest element in an array in O(n log k) time.

History

The concept of min heaps was first introduced by Robert W. Floyd in 1964. Floyd’s original paper described a data structure called a “heap” that could be used to implement priority queues and other applications.

Since then, min heaps have become an essential data structure in computer science. They are widely used in various programming languages and applications, including:

• Java: The PriorityQueue class in Java uses a min heap to implement priority queues.
• Python: The heapq module in Python provides functions for creating and manipulating min heaps.
• C++: The priority_queue class in the C++ Standard Library can be used to implement min heaps.

The development of min heaps has played a significant role in the efficiency of priority queues and other algorithms that rely on efficient retrieval of minimum elements. They remain an important data structure in modern computer science.