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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.
A BST can be traversed through three basic algorithms: inorder, preorder, and postorder tree walks. [10]: 287 Inorder tree walk: Nodes from the left subtree get visited first, followed by the root node and right subtree. Such a traversal visits all the nodes in the order of non-decreasing key sequence.
In pre-order, we always visit the current node; next, we recursively traverse the current node's left subtree, and then we recursively traverse the current node's right subtree. The pre-order traversal is a topologically sorted one, because a parent node is processed before any of its child nodes is done.
A level-order walk effectively performs a breadth-first search over the entirety of a tree; nodes are traversed level by level, where the root node is visited first, followed by its direct child nodes and their siblings, followed by its grandchild nodes and their siblings, etc., until all nodes in the tree have been traversed.
"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 later simplification by Garsia and Wachs, the Garsia–Wachs algorithm, performs the same comparisons in the same order. The algorithm works by using a greedy algorithm to build a tree that has the optimal height for each leaf, but is out of order, and then constructing another binary search tree with the same heights. [7]
The pre-order traversal goes to parent, left subtree and the right subtree, and for traversing post-order it goes by left subtree, right subtree, and parent node. For traversing in-order, since there are more than two children per node for m > 2, one must define the notion of left and right subtrees. One common method to establish left/right ...
In a binary search tree the internal nodes are labeled by numbers or other ordered values, called keys, arranged so that an inorder traversal of the tree lists the keys in sorted order. The external nodes remain unlabeled. [3] Binary trees may also be studied with all nodes unlabeled, or with labels that are not given in sorted order.