The Tree Data Structure: Concepts, Terminology, and Applications, Summaries of Data Structures and Algorithms

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Trees

COL 106

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Acknowledgement :Many slides are courtesy

Douglas Harder, UWaterloo

Amit Kumar Shweta Agrawal

3 Trees A rooted tree data structure stores information in nodes

• Similar to linked lists:
  • There is a first node, or root
  • Each node has variable number of references to successors (children)
  • Each node, other than the root, has exactly one node as its predecessor (or parent)

5 To store hierarchy of people

6 To store organization of departments 6

8 To organize file-systems Unix file system

9 Markup elements in a webpage 9

11 Terminology All nodes will have zero or more child nodes or children

• I has three children: J, K and L For all nodes other than the root node, there is one parent node
• H is the parent of I

12 Terminology The degree of a node is defined as the number of its children: deg(I) = 3 Nodes with the same parent are siblings

• J, K, and L are siblings

14 Terminology Nodes with degree zero are also called leaf nodes All other nodes are said to be internal nodes , that is, they are internal to the tree

15 Terminology Leaf nodes:

17 Terminology These trees are equal if the order of the children is ignored ( Unordered tree s ) They are different if order is relevant ( ordered trees )

• We will usually examine ordered trees (linear orders)
• In a hierarchical ordering, order is not relevant

18 Terminology The shape of a rooted tree gives a natural flow from the root node , or just root

20 Terminology Paths of length 10 (11 nodes) and 4 (5 nodes) Start of these paths End of these paths

21 Terminology For each node in a tree, there exists a unique path from the root node to that node The length of this path is the depth of the node, e. g .,

• E has depth 2
• L has depth 3