Summary
Like stacks, queues are fundamental data structures. Queues help us realize the FIFO approach. We looked at how FIFO queues are implemented in the imperative world. We noted that we would end up with too much of copying if we insert new nodes at the end of a list. We could do this in the imperative world but would end up with O(n) copying performance to achieve persistent FIFO queues.
Instead, we looked at an innovative design involving two stacks. We also looked at the Scala implementation and discussed some Scala idioms.
Priority queues are an important variation of queues. We define a priority for each element of the queue and wish to pop the element with the highest priority.
Heap is a famous data structure for implementing the priority queue ADT. Heaps are realized with a full and complete binary tree. This is not a BST though. The heap invariant is this: the value at the root is less than its children.
We looked a beautiful algorithm, based on arrays, to implement heaps. However...
