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Bayer and McCreight (1972), [3] Comer (1979), [2] and others define the order of B-tree as the minimum number of keys in a non-root node. Folk and Zoellick [9] points out that terminology is ambiguous because the maximum number of keys is not clear. An order 3 B-tree might hold a maximum of 6 keys or a maximum of 7 keys.
To turn a regular search tree into an order statistic tree, the nodes of the tree need to store one additional value, which is the size of the subtree rooted at that node (i.e., the number of nodes below it). All operations that modify the tree must adjust this information to preserve the invariant that size[x] = size[left[x]] + size[right[x]] + 1
The order or branching factor b of a B+ tree measures the capacity of interior nodes, i.e. their maximum allowed number of direct child nodes. This value is constant over the entire tree. For a b-order B+ tree with h levels of index: [citation needed] The maximum number of records stored is =
Binary search Visualization of the binary search algorithm where 7 is the target value Class Search algorithm Data structure Array Worst-case performance O (log n) Best-case performance O (1) Average performance O (log n) Worst-case space complexity O (1) Optimal Yes In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search ...
Such a tree has exactly + leaf nodes, which can be identified (in the order given by the binary tree) with the + input weights. The goal of the problem is to find a tree, among all of the possible trees with internal nodes, that minimizes the weighted sum of the external path lengths. These path lengths are the numbers of steps from the root to ...
The length of a branch is the ordinal that is order isomorphic to the branch. For each ordinal α, the α-th level of T is the set of all elements of T of height α. A tree is a κ-tree, for an ordinal number κ, if and only if it has height κ and every level has cardinality less than the cardinality of κ.
This graph is a tree in the graph-theoretic sense. The root of the tree is the empty sequence. In order theory, a different notion of a tree is used: an order-theoretic tree is a partially ordered set with one minimal element in which each element has a well-ordered set of predecessors.
Depth - Length of the path from the root to the node. The set of all nodes at a given depth is sometimes called a level of the tree. The root node is at depth zero. Height - Length of the path from the root to the deepest node in the tree. A (rooted) tree with only one node (the root) has a height of zero. In the example diagram, the tree has ...