preorder

present singular third person preorders · participle present preordering · participle past preordered · past preordered · alternative pre-order

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

   Preorder now at website.com!

2. transitiveTo sort or arrange beforehand.

plural preorders · alternative pre-order

1. An order for goods or services placed in advance.

   available for preorder

   1 more example

   Head over to website.com and get your preorder in.

2. mathematicsA binary relation that is reflexive and transitive.

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

   3 more examples

   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

   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.

alternative pre-order

1. not comparablecomputingSuch that, recursively, the root is visited before the left and right subtrees.

   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.

   2 more examples

   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