1. Advanced Data Structure using C++

LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110)
(Van Wyk, Christopher J. Data Structures and C Programs, Addison‐Wesley,
1988, p. 175. ISBN 978‐0‐201‐16116‐8.)
A threaded binary tree makes it possible to traverse the values in the binary
tree via a linear traversal that is more rapid than a recursive in‐order traversal.
It is also possible to discover the parent of a node from a threaded binary tree,
without explicit use of parent pointers or a stack, albeit slowly. This can be
useful where stack space is limited, or where a stack of parent pointers is
unavailable (for finding the parent pointer via DFS).
This is possible, because if a node (k) has a right child (m) then m's left pointer
must be either a child, or a thread back to k. In the case of a left child, that left
child must also have a left child or a thread back to k, and so we can follow m's
left children until we find a thread, pointing back to k. The situation is similar for
when m is the left child of k
Multiway Search Trees
A multiway search tree is one with nodes that have two or more children.
Within each node is stored a given key, which is associated to an item we wish
to access through the structure.
Given this definition, a binary search tree is a multiway search tree.
More Formal Definition
Let T be a multiway search tree, then T has the following properties:
• T is ordered, meaning that the all the elements in subtrees to the left of
an item are less than the item itself, and all the elements in subtrees to
the right of an item are greater.
• Each internal node of T has at least 2 children.
• Each d‐node (node with d children) v of T, with children v1,...,vd stores d‐1
items (k1, x1),...,(kd‐1, xd‐1). Where the ki's are keys and xi is the element
associated with key number i.
Prepared By :­
Er. Harvinder Singh
Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 207 ‐