Chapter 11. Solving real problems with advanced trees

 

This chapter covers

  • Avoiding stack overflow with self-balancing trees
  • Implementing the red-black tree
  • Creating functional maps
  • Designing a functional priority queue

In the previous chapter, you learned about the binary tree structure and basic tree operations. But you saw that to fully benefit from trees, you must either have very specific use cases, such as handling randomly ordered data, or a limited data set, in order to avoid any risk of stack overflows. Making trees stack-safe is much more difficult than it is for lists, because each computing step involves two recursive calls, which makes it impossible to create tail-recursive versions.

In this chapter, we’ll study two specific trees:

  • The red-black tree is a self-balancing, general-purpose tree with high performance. It’s suitable for general use and data sets of any size.
  • The leftist heap is a very specific tree suitable for implementing priority queues.

11.1. Better performance and stack safety with self-balancing trees

11.2. A use case for the red-black tree: maps

11.3. Implementing a functional priority queue

11.4. A priority queue for noncomparable elements

11.5. Summary