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tree Data Structures in python Traversals.pptx
- 1. TREE DATA STRUCTURE EXAMPLE:COMPUTERFILE SYSTEM
- 2. A HYPOTHETICAL FAMILY TREE
- 3. A tree consists of a finite set of elements, called nodes, and a finite set of directed lines, called branches, that connect the nodes. TREE ADT ⦿Tree is a non-linear data structure which organizes data in recursive hierarchical structure. ⦿In tree data structure, every individual element is called as Node. ⦿Node in a tree data structure stores the actual data of that particular element and link to next element in hierarchical structure.
- 4. STRUCTURE OF A TREE ⦿There is one and only one path between every pair of nodes in a tree.
- 6. ROOT NODE ⦿In a tree data structure, the first node is called as Root Node. ⦿Every tree must have a root node. ⦿In any tree, there must be only one root node.
- 7. EDGE ⦿The connecting link between any two nodes is called as EDGE. ⦿In a tree with 'N' number of nodes there will be a maximum of 'N-1' number of edges.
- 8. PARENT NODES
- 9. CHILD NODES
- 10. ANCESTOR AND DESCENDANT ⦿Ancestors: Any node in the path from the current node to the root node. ⦿Descendant: Any node in the path from the current node to the leaf nodes.. ⦿Ancestor(J)=E,B,A ⦿ Descendant(C)=G,K,H
- 11. SIBLINGS
- 12. LEAF NODES ⦿The leaf nodes are also called as External Nodes or Terminal Nodes
- 13. INTERNAL NODES
- 14. DEGREE ⦿The Degree of a node is total number of children it has. ⦿The highest degree of a node among all the nodes in a tree is called as 'Degree of Tree'
- 15. LEVEL ⦿ In a tree each step from top to bottom is called as a Level and the Level count starts with '0' and incremented by one at each step. ⦿Level- distance from the root node.
- 16. HEIGHT ⦿Height of all leaf nodes is 0.
- 17. DEPTH ⦿Depth of the root node is '0'
- 18. PATH • Length of a Path is total number of edges in that path.
- 19. SUBTREE ⦿Each child node with a parent node forms a subtree recursively. ⦿Any connected structure below root is a subtree. ⦿Collection of subtrees makes a tree.
- 20. FOREST ⦿A forest is a set of disjoint trees.
- 21. COMPARISON
- 24. CLASSIFY THE TWO TRAVERSALS PERFORMED IN TREE ADT. ⦿ A traversal of a tree requires that each node of the tree be visited once ⦿ A typical reason to traverse a tree is to display the data stored at each node of the tree ⦿Traversal Types ⦿ preorder ■ Inorder ■ Postorder ■ level-order
- 26. Traversal ⦿Starts at the root node and explores as deep as possible along each branch and backtrack to sibling branch until all nodes are visited. ⦿It is a recursive approach for all subtrees.
- 27. PREORDER TRAVERSAL ⦿Processing order: Root → Left → Right Algorithm 1. Visit the root 2. Traverse the left sub tree i.e. call Preorder (left sub tree) 3. Traverse the right sub tree i.e. call Preorder (right sub tree)
- 28. EXAMPLE
- 29. Traverse the entire tree starting iron the root rode keeping yourself to theleft. Preorder Traversal : A , B, D, E, C, F, G
- 30. INORDER TRAVERSAL ⦿Processing order: Left → Root → Right Algorithm 1. Traverse the left sub tree i.e. call Inorder (left sub tree) 2. Visit the root 3. Traverse the right sub tree i.e. call Inorder (right sub tree)
- 31. EXAMPLE
- 33. POSTORDER TRAVERSAL ⦿Processing order: Left → Right → Root Algorithm 1. Traverse the left sub tree i.e. call Postorder (left sub tree) 2. Traverse the right sub tree i.e. call Postorder (right sub tree) 3. Visit the root
- 34. EXAMPLE
- 36. EXERCISE
- 37. Q1 1. Visit the following tree in a breadth first manner and print all the nodes.
- 38. ANSWER
- 39. Binary Tree Expression Tree Binary Search Tree Trees AVL Tree B Tree Heap Tree TYPES OF TREES
- 40. BINARY TREE AND ITS RELATED OPERATIONS ⦿ A tree whose elements have at most 2 children is called a binary tree. Since each element in a binary tree can have only 2 children, we typically name them the left and right child. ⦿ A Binary Tree node contains following parts. ■ Data ■ Pointer to left child ■ Pointer to right child
- 41. BINARY TREE ⦿A node can have 0,1, and 2 children in a binary tree
- 42. CONT.. ⦿In a tree each node contains information and may or may not contain links.
- 43. PROPERTIES OF BINARY TREE ⦿At any level ‘i’, maximum number of nodes possible is 2^i
- 44. ⦿ Maximum number of nodes of height h= CONT..
- 45. ⦿ Minimum number of nodes of height h=h+1 CONT..
- 46. CONT.. ⦿Maximum height of the tree if minimum number of nodes is given is (n-1)
- 47. CONT.. ⦿ Minimum height of the tree if maximum number of possible nodes is given by
- 48. TYPES OF BINARY TREE ⦿ Full/Strict/ Proper Binary Tree ⦿Complete Binary Tree ⦿Perfect Binary Tree ⦿Degenerate Binary Tree ⦿ Balanced Binary Tree ⦿ Unbalanced Binary Tree
- 49. FULL BINARY TREE ⦿It is a binary tree where each node will contains exactly two children except leaf node
- 50. Full Binary Tree
- 51. COMPLETE BINARY TREE ⦿It is a binary tree where all levels are completely filled (except possibly the last level) and the last level has nodes as left as possible
- 53. PERFECT BINARY TREE ⦿It is a binary tree where all internal nodes have 2 children and all leaves are at same level ⦿A perfect binary tree is a complete binary tree or full binary tree but vice versa is not true
- 54. DEGENERATE BINARY TREE ⦿It is a binary tree where all internal nodes are having only one child
- 55. BALANCED BINARY TREE ⦿Find Balance Factor, B=HL-HR ⦿HL- height of left subtree; HR-height of right subtree ⦿The height of the left and right subtrees differs by no more than one i.e., its balance factor of every node should be –1, 0, or +1