Why is this binary search tree an example of pre-order?

Question

I'm a bit confused. I'm trying to learn about binary search tree's at the moment, and my understanding is that, in pre-order traversing, the left branch node value should be less than the root value. E.g., root: 7, leftchild: 6, rightchild: 8.

But I've seen this example of pre-order traversal that goes: 1 2 4 5 3. And images re-iterate that 1 is the root, and 2 is the leftchild node. But 2 is obviously more than 1.

Am I misunderstanding something?

Answer 1

Your understanding of binary search trees is correct.

But pre-order traversals (and other types of traversals) are not just a thing for binary search trees. You will find examples of such traversals of other types of trees that are not necessarily binary search trees. Preorder, postorder, breadth-first and depth-first traversals are also relevant for any other kind of tree -- they don't have to be search trees, and not even binary.

Only inorder traversals assume the tree is binary. And if that inorder traversal happens to visit the tree values in their proper order, then we are dealing with a binary search tree.