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Depending on the problem at hand, pre-order, post-order, and especially one of the number of subtrees − 1 in-order operations may be optional. Also, in practice more than one of pre-order, post-order, and in-order operations may be required. For example, when inserting into a ternary tree, a pre-order operation is performed by comparing items.
This unsorted tree has non-unique values (e.g., the value 2 existing in different nodes, not in a single node only) and is non-binary (only up to two children nodes per parent node in a binary tree). The root node at the top (with the value 2 here), has no parent as it is the highest in the tree hierarchy.
Remove the root of a tree and process each of its children, or; Join two trees together by making one tree a child of the other. Operation (1) it is very efficient. In LCRS representation, it organizes the tree to have a right child because it does not have a sibling, so it is easy to remove the root. Operation (2) it is also efficient.
"A binary tree is threaded by making all right child pointers that would normally be null point to the in-order successor of the node (if it exists), and all left child pointers that would normally be null point to the in-order predecessor of the node." [1] This assumes the traversal order is the same as in-order traversal of the tree. However ...
A tree whose root node has two subtrees, both of which are full binary trees. A perfect binary tree is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level (the level of a node defined as the number of edges or links from the root node to a node). [18] A perfect binary tree is a full ...
The Nested Set model is appropriate where the tree element and one or two attributes are the only data, but is a poor choice when more complex relational data exists for the elements in the tree. Given an arbitrary starting depth for a category of 'Vehicles' and a child of 'Cars' with a child of 'Mercedes', a foreign key table relationship must ...
Split is a left rotation and level increase to replace a subtree containing two or more consecutive right horizontal links with one containing two fewer consecutive right horizontal links. Implementation of balance-preserving insertion and deletion is simplified by relying on the skew and split operations to modify the tree only if needed ...
According to Knuth's definition, a B-tree of order m is a tree which satisfies the following properties: [7] Every node has at most m children. Every node, except for the root and the leaves, has at least ⌈m/2⌉ children. The root node has at least two children unless it is a leaf. All leaves appear on the same level.