preorder meaning: definition, etymology and quotations

preorder

verb

UK /pɹiːˈɔːdə/ · CA, US /ˈpɹiˌoɹdɚ/

Etymology From pre- + order.

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

To sort or arrange beforehand.

noun

Etymology From pre- + order.

An order for goods or services placed in advance.

Mathematics, Order theory, Sciences, Set theory A binary relation that is reflexive and transitive.

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).2002, Yves Nievergelt, Foundations of Logic and Mathematics, Springer (Birkhäuser), page 152:

2 more examples

Let us first compare S#95;1, S#95;2 and S#95;3 w.r.t. the partial preorder #92;succeq.2010, S. Kaci, “Refined Preference-Based Argumentation Frameworks”, in Pietro Baroni, F. Cerutti, M. Giacomin, G. R. Simari, editors, Computational Models of Argument: Proceedings of COMMA 2010, IOS Press, page 306:
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.

Synonyms: quasiorder
Derived terms: preorder algebra, preorder atom, preorder functor, strict preorder
Related terms: preordered set
Hyponyms: well-order, total order, partial order, equivalence relation

adj

Etymology From pre- + order.

Computing, Computing theory, Engineering, Mathematics, Natural sciences, Physical sciences, Sciences Such that, recursively, the root is visited before the left and right subtrees.

Of a traversal of a tree

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.2002, Gabriel Valiente, Algorithms on Trees and Graphs, Springer, page 115:
In the program given above, tree is constructed and is traversed in inorder, preorder and postorder traversal.2006, ISRD Group, Data Structures Using C, Tata McGraw-Hill Education, page 254:

1 more example

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.

Entry derived from the Wiktionary, under licence CC BY-SA 4.0 — list of authors.