In computer science, a Cartesian tree is a binary tree derived from a sequence of numbers; it can be uniquely defined from the properties that it is heap-ordered and that a symmetric (in-order) traversal of the tree returns the original sequence. Introduced by Vuillemin (1980) in the context of geometric range searching data structures, Cartesian trees have also been used in the definition of the treap and randomized binary search tree data structures for binary search problems. The Cartesian tree for a sequence may be constructed in linear time using a stack-based algorithm for finding all nearest smaller values in a sequence.
Read more about Cartesian Tree: Definition, Range Searching and Lowest Common Ancestors, Treaps, Efficient Construction, Application in Sorting, History
Famous quotes containing the word tree:
“I have come to the conclusion that the closer people are to what may be called the front lines of government ... the easier it is to see the immediate underbrush, the individual tree trunks of the moment, and to forget the nobility the usefulness and the wide extent of the forest itself.... They forget that politics after all is only an instrument through which to achieve Government.”
—Franklin D. Roosevelt (1882–1945)