Difference between std::set and std::priority_queue

Question

Since both std::priority_queue and std::set (and std::multiset) are data containers that store elements and allow you to access them in an

Answer 1

set/multiset are generally backed by a binary tree. http://en.wikipedia.org/wiki/Binary_tree

priority_queue is generally backed by a heap. http://en.wikipedia.org/wiki/Heap_(data_structure)

So the question is really when should you use a binary tree instead of a heap?

Both structures are laid out in a tree, however the rules about the relationship between anscestors are different.

We will call the positions P for parent, L for left child, and R for right child.

In a binary tree L < P < R.

In a heap P < L and P < R

So binary trees sort "sideways" and heaps sort "upwards".

So if we look at this as a triangle than in the binary tree L,P,R are completely sorted, whereas in the heap the relationship between L and R is unknown (only their relationship to P).

This has the following effects:

• If you have an unsorted array and want to turn it into a binary tree it takes O(nlogn) time. If you want to turn it into a heap it only takes O(n) time, (as it just compares to find the extreme element)

• Heaps are more efficient if you only need the extreme element (lowest or highest by some comparison function). Heaps only do the comparisons (lazily) necessary to determine the extreme element.

• Binary trees perform the comparisons necessary to order the entire collection, and keep the entire collection sorted all-the-time.

• Heaps have constant-time lookup (peek) of lowest element, binary trees have logarithmic time lookup of lowest element.