When talking about data structures, heaps never get the credit they deserve.
Most of the attention is on arrays, linked lists, and hash tables.
But many critical algorithms use heaps. Here are some examples:
1. Finding the K Largest Elements.
Let's say you have a massive dataset with millions of elements, and you only need the top 100. You could sort the entire dataset and pick out the last k items. But this requires O(n log n) comparisons. Using a heap structure, you can solve the problem with only O(n + k*log k) comparisons and swaps. This is a significant improvement if k is much smaller than n, which is typically the case.
2. Dijkstra is a popular algorithm that finds the fastest path between two vertices in a weighted graph. The algorithm must repeatedly find the vertex with the shortest distance and also keep track of new distances for other vertices. A heap is efficient at both tasks: it finds the minimum in O(log V) time and updates the distances in O(log V) time as well, where V is the number of vertices. Prim's algorithm that finds a graph's minimum spanning tree uses heaps in a similar way.
3. Huffman coding is a greedy algorithm that encodes a text by assigning shorter bit sequences to characters that appear more often. The algorithm does multiple iterations where it needs to quickly find the two elements with the smallest frequencies and add a new combined element back to the collection. This is a perfect job for a min-heap.
You can read more about the heap data structure and its real-world use cases in the latest issue of the Polymathic Engineer.
The 146th issue of the Polymathic Engineer is out.
This week, we talk about some important practical applications of the heap data structure:
- Priority Queues
- Finding the K Largest Elements
- Graph Algorithms
- Huffman Coding
Read it here:
newsletter.francofernando.co…