You will find that using data structures is a very common occurrence as a programmer, so being proficient in basic data structures such as binary trees, stacks, and queues is vital to your success. But if you want to improve your skills and stand out from the crowd, you need to be familiar with advanced data structures as well.

Advanced data structures are an essential component of data science, and they help clarify inefficient management and provide storage for large sets of data. Software engineers and data scientists constantly use advanced data structures to design algorithms and software.

1. Fibonacci Heap

If you’ve already invested some time in learning data structures, you should be familiar with binary heaps. Fibonacci heaps are quite similar, and they follow either the min-heap or max-heap properties. You can think of a Fibonacci heap as a collection of trees where the minimum or maximum value node is always at the root.

The heap also satisfies the Fibonacci property such that a node n will have at least F(n+2) nodes. Within a Fibonacci heap, the roots of each node are linked together, usually via a circular doubly-linked list. This makes it possible to delete a node and append two lists in only O(1) time.

Fibonacci heaps are more flexible than binary and binomial heaps, making them useful in a wide range of applications. They are commonly used as priority queues in Dijkstra’s algorithm to significantly improve the running time of the algorithm.

2. AVL Tree

AVL (Adelson–Velsky and Landis) trees are one of many different types of trees in computer science. They are essentially a self-balancing binary search tree.

Standard binary search trees can skew in some edge cases and have a worst-case time complexity of O(n), making them inefficient for real-world applications. Self-balancing trees automatically change their structure when this balancing property is violated.

In an AVL tree, each node has an additional attribute containing its balance factor. The balance factor is the value obtained by subtracting the height of the left subtree from the right subtree at that node. The self-balancing property of an AVL tree requires that the balancing factor always be -1, 0, or 1.

If the self-balancing property (balancing factor) is violated, the AVL tree rotates its nodes to maintain the balancing factor. An AVL tree uses four main rotations – rotate right, rotate left, rotate left-right and rotate right-left.

The self-balancing property of an AVL tree improves its worst-case time complexity to only O(log n), which is significantly more efficient than the performance of a binary search tree.

Since AVL trees maintain themselves through the balancing factor, you can calculate the minimum number of nodes given the height. The recurrence relation comes down to N(h) = N(h-1) + N(h-2) + 1 and there must be at least three nodes in an AVL tree (n > 2). The base cases of the recurrence relation are N(0) = 1 and N(1) = 2, respectively.

3. Red-black tree

A red–black tree is another self-balancing binary search tree that uses an extra bit as its self-balancing property. The bit is usually called red or black, hence the name red-black tree.

In Red-Black each node is either red or black, but the root node must always be black. There cannot be two adjacent red nodes, and all leaf nodes must be black. These rules preserve the self-balancing property of the tree.

Unlike binary search trees, red–black trees have approximately O(log n) efficiency, making them far more efficient. However, AVL trees tend to be more balanced due to the fixed self-balancing property.