notesCHAPTER_5_tree_data_structure_ds.pppt
- 1. Topic 5 TREE DFC 30233 DATA STRUCTURE
- 2. 1.0 Define tree,binary tree and binary search tree BINARY TREE A type of data structure where each parent node can have at most two child nodes These two child nodes are known as the left child and right child.
- 3. 1.0 Define tree,binary tree and binary search tree BINARY SEARCH TREE A binary search tree is a binary tree in which the nodes are assigned values, with the following restrictions ; • No duplicate values • Left child node is smaller than its parent Node • Right child node is greater than its parent Node
- 5. ― Irene M. Pepperberg
- 6. 1.2 Terminology in relation to trees: 1. Root, 2. Parent, 3. Children, 4. Leaves, 5. Sibling, 6. Node, 7. Path, 8. Degree, 9. Level
- 7. Root ROOT NODE - the first node root node is the origin of tree data structure must be only one root node Terminology: 1. Root
- 8. Parent Node PARENT NODE - the node which is predecessor of any node the node which has branch from it to any other node Terminology: 2. Parent
- 9. Child Child Node - the node which is descendant of any node the node which has a link from its parent node any parent node can have any number of child nodes all the nodes except root are child nodes Terminology: 3. Children
- 10. Leaf LEAF Node - the node which does not have a child leaf node is also called as Terminal node Terminology: 4. Leaf
- 11. Siblings SIBLINGS - nodes which belong to same Parent Terminology: 5. Siblings
- 12. Internal Nodes INTERNAL Node - the node which has at least one child Internal nodes are also called as 'Non-Terminal' nodes Terminology: 6. Internal Nodes
- 13. Path PATH - the sequence of Nodes and Edges from one node to another node Length of a Path is total number of nodes in that path. Example: the path A - B - E - J has length 4 Terminology: 7. Path
- 14. Degree PATH - the sequence of Nodes and Edges from one node to another node Length of a Path is total number of nodes in that path. Example: the path A - B - E - J has length 4 Terminology: 8. Degree
- 15. Edge EDGE - the connecting link between any two nodes In a tree with 'N' number of nodes there will be a maximum of ● 'N-1' number of edges. Terminology: 9. Edge
- 16. Level LEVEL - each step from top to bottom the root node - Level 0 the children of root node - Level 1 Terminology: 10. Level
- 17. Height height of all leaf nodes is '0' Terminology: 11. Height
- 18. Depth height of all leaf nodes is '0' Terminology: 12. Depth
- 19. Terminology: 13. Sub Tree
- 21. 2.0 Binary Tree. Binary Tree is a tree in which every node can have a maximum of two children. Every node can have either 0 children or 1 child or 2 children but not more than 2 children.
- 22. Full Binary Tree Binary Tree
- 23. Perfect Binary Tree Complete Binary Tree obtained from a perfect binary tree by deleting consecutive leaves of the tree from right to left
- 25. Example: arithmetic expression tree for the expression (2 × (a - 1)) + (3 × b) :
- 26. Infix, Prefix and Postfix traversal An infix expression, the operator appears between its operands. In a prefix expression, places a binary operator before its operands. In a postfix expression, the binary operators comes after its operands.
- 28. Example 1 State the order of nodes visited using prefix, infix and postfix traversal. Prefix: - 8 / 4 2 Infix: 8 – ( 4 / 2 ) Postfix: 8 4 2 / -
- 29. Example 2 State the order of nodes visited using prefix, infix and postfix traversal. Infix form: Prefix form: Postfix form:
- 30. a) (x+xy) + (x/y) b) x+ ((xy+x)/y) 1. Represent the expressions using binary trees. 2. Write these expressions in prefix notation. 3. Write these expressions in postfix notation. 4. Write these expressions in infix notation.
- 31. Binary Tree Representations A binary tree data structure is represented using two methods. Those methods are as follows. Array Representation Linked List Representation Consider the following binary tree.
- 32. 1. Array Representation 2. Linked List Representation