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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.
The degree of a tree is the maximum degree of a node in the tree. Distance The number of edges along the shortest path between two nodes. Level The level of a node is the number of edges along the unique path between it and the root node. [4] This is the same as depth. Width The number of nodes in a level. Breadth The number of leaves. Forest
English: PDF version of the Think Python Wikibook. This file was created with MediaWiki to LaTeX . The LaTeX source code is attached to the PDF file (see imprint).
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
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.
"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 ...
In depth-first order, we always attempt to visit the node farthest from the root node that we can, but with the caveat that it must be a child of a node we have already visited. Unlike a depth-first search on graphs, there is no need to remember all the nodes we have visited, because a tree cannot contain cycles. Pre-order is a special case of ...
For an m-ary tree with height h, the upper bound for the maximum number of leaves is . The height h of an m-ary tree does not include the root node, with a tree containing only a root node having a height of 0. The height of a tree is equal to the maximum depth D of any node in the tree.