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In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited.
A full binary tree An ancestry chart which can be mapped to a perfect 4-level binary tree. A full binary tree (sometimes referred to as a proper, [15] plane, or strict binary tree) [16] [17] is a tree in which every node has either 0 or 2 children.
Fig. 1: A binary search tree of size 9 and depth 3, with 8 at the root. In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree.
That increases root-to-leaf traversal time. On the other hand, less work has to be expended at each visited node to check its children for overlap. The opposite holds for a high-degree tree: although the tree will be of smaller height, more work is spent at each node. In practice, binary trees (degree = 2) are by far the most common.
Henzinger and King [2] suggest to represent a given tree by keeping its Euler tour in a balanced binary search tree, keyed by the index in the tour. So for example, the unbalanced tree in the example above, having 7 nodes, will be represented by a balanced binary tree with 14 nodes, one for each time each node appears on the tour.
Patricia trees are a particular implementation of the compressed binary trie that uses the binary encoding of the string keys in its representation. [23] [15]: 140 Every node in a Patricia tree contains an index, known as a "skip number", that stores the node's branching index to avoid empty subtrees during traversal.
In computer science, graph traversal (also known as graph search) refers to the process of visiting (checking and/or updating) each vertex in a graph. Such traversals are classified by the order in which the vertices are visited. Tree traversal is a special case of graph traversal.
The tree rotation renders the inorder traversal of the binary tree invariant. This implies the order of the elements is not affected when a rotation is performed in any part of the tree. Here are the inorder traversals of the trees shown above: Left tree: ((A, P, B), Q, C) Right tree: (A, P, (B, Q, C))