# preorder

## EnglishEdit

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pre- +‎ order.

### VerbEdit

preorder (third-person singular simple present preorders, present participle preordering, simple past and past participle preordered)

1. (transitive) To order (goods or services) in advance, before they are available.

### NounEdit

preorder (plural preorders)

1. An order for goods or services placed in advance.
2. (set theory, order theory) A binary relation that is reflexive and transitive.
The relation of logical implication over sentences is an example of a preorder.
• 2002, Yves Nievergelt, Foundations of Logic and Mathematics, Springer (Birkhäuser), page 152,
Example 436 For each set ${\displaystyle A}$ , the relation ${\displaystyle \subseteq }$  is a preorder on ${\displaystyle {\mathcal {P}}(A)}$ .
• 2010, S. Kaci, Refined Preference-Based Argumentation Frameworks, Pietro Baroni, F. Cerutti, M. Giacomin, G. R. Simari (editors), Computational Models of Argument: Proceedings of COMMA 2010, IOS Press, page 306,
Let us first compare ${\displaystyle S_{1}}$ , ${\displaystyle S_{2}}$  and ${\displaystyle S_{3}}$  w.r.t. the partial preorder ${\displaystyle \succeq }$ .
• 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.

#### SynonymsEdit

• (binary relation that is reflexive and transitive): quasiorder

#### TranslationsEdit

preorder (not comparable)

1. (computing theory, of a traversal of a tree) Such that, recursively, the root is visited before the left and right subtrees.
• 2002, Gabriel Valiente, Algorithms on Trees and Graphs, Springer, page 115,
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.
• 2006, ISRD Group, Data Structures Using C, Tata McGraw-Hill Education, page 254,
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.