Preorder

The relation of logical implication over sentences is an example of a preorder.

Example 436 For each set A, the relation #92;subseteq is a preorder on #92;mathcal#123;P#125;(A).

Let us first compare S#95;1, S#95;2 and S#95;3 w.r.t. the partial preorder #92;succeq.

2000, Jean-Charles Pomerol, Sergio Barba-Romero, Multicriterion Decision in Management: Principles and Practice, Springer, Softcover, page 58, It can easily be verified that the above relation is a preorder, i.e. that it is reflexive and transitive.

Now, the preorder traversal of a tree can be constructed from the preorder traversals of the subtrees rooted at the children of the root of the tree.

In the program given above, tree is constructed and is traversed in inorder, preorder and postorder traversal.

2011, Ananda Rao Akepogu, Radhika Raju Palagiri, Data Structures and Algorithms Using C++, Pearson Education India, page 9.16, The preorder traversal visits a node first after which it traverses its left subtree and then traverses its right subtree.