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In computer science, a red–black tree is a self-balancing binary search tree data structure noted for fast storage and retrieval of ordered information. The nodes in a red-black tree hold an extra "color" bit, often drawn as red and black, which help ensure that the tree is always approximately balanced.
An example of simplicial complex, and the corresponding simplex tree data structure. Notice the two lowest nodes have a path of 4 to the node, indicating the 2 3-dimensional simplexes composed of 4 vertices each. In topological data analysis, a simplex tree is a type of trie used to represent efficiently any general simplicial complex.
A red–black tree with branching factor 2. In computing, tree data structures, and game theory, the branching factor is the number of children at each node, the outdegree.If this value is not uniform, an average branching factor can be calculated.
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The left figure below shows a binary decision tree (the reduction rules are not applied), and a truth table, each representing the function (,,).In the tree on the left, the value of the function can be determined for a given variable assignment by following a path down the graph to a terminal.
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As with any binary search tree, the inorder traversal order of the nodes is the same as the sorted order of the keys. The structure of the tree is determined by the requirement that it be heap-ordered: that is, the priority number for any non-leaf node must be greater than or equal to the priority of its children.
This OCaml example which defines a red–black tree and a function to re-balance it after element insertion shows how to match on a more complex structure generated by a recursive data type. The compiler verifies at compile-time that the list of cases is exhaustive and none are redundant.