The document discusses data structures and algorithms. It provides an overview of binary trees, binary search trees, and their traversals. It then discusses graphs and poses questions related to binary trees, binary search tree traversals, and graphs.

1. Data Structure & Algorithms

2. Agenda
• Data Structure Overview
• Binary Trees
• Binary Search Trees
• Binary Search Tree Traversal
• Binary Tree, BST Questions
• Graph Overview
• Problems & Questions

3. What Is Data Structure?
Program Contains Data
Where the data to be stored?(Capacity)
How the data efficiently handle & used? (Efficiently)
Data structure just a plain container

4. Analogy

5. Algorithm Analysis

6. Algorithm & Datastructure
A Program is a combination of Algorithm and
Data Structure
Simple Example:
Addition of two Numbers
Int A,B,C
C= A + B
Program Algorithm Data Structure
Addition Logic is an Algorithm
A & B are Data Structure ‘ elements.

7. Types Of Data Structure
Data Structure
Linear DS Non Linear DS

8. Binary Trees

9. Binary Trees

10. Binary Trees Jargons

11. Binary Trees Jargons

12. Binary Tree Vs Tree

13. Binary Tree Terminology

14. Binary Tree Terminology

15. Binary Tree Terminology

16. Binary Tree Terminology

17. Binary Tree Terminology

18. Binary Tree Terminology

19. Binary Tree Terminology

20. Binary Tree Terminology

21. Binary Search Tree

22. Binary Search Tree Examples

23. Binary Search Tree Examples

24. Binary Search Tree Examples

25. Binary Search Tree Examples

26. Binary Search Tree Examples

27. Building a Binary Search Tree

28. Removal Binary Search Tree

29. Removal Binary Search Tree

30. Removal Binary Search Tree

31. Binary Search Tree Traversal
BST
Traversal
BFS DFS

32. Binary Search Tree Traversal

33. Questions
1) Consider the following tree:
If the post order traversal gives a b – c d * + then
the label of the nodes 1,2,3,4,5,6,7 respectively are
a) +, -, *, a, b, c, d (b) a, b, c, d, -, *, +
(c) a, -, b, +, c, *, d (d) -, a, b, +, *, c, d

34. Questions
2) The number of possible ordered trees with 3
nodes A,B,C is
a) 16 (b)12 c)6
(d)10

35. Questions
3) The depth of a complete binary tree with n
nodes is (log is to the base two)
a) Log (n+1) -1 (b) Log (n)
(c)Log (n-1) +1 (d) Log (n) +1

36. Questions
(a)
Explanation: If the depth of a complete binary tree is d, the number of nodes
n= 2d+1-1
n+1=2d+1 Applying logarithm to base 2 on both sides we have
log 2 (n+1) = d+1(log 2 2)
Therefore d= log 2 (n+1) -1
Total no. of nodes n = (2^(d+1))-1
log (n+1) = d+1
d = log(n+1)-1

37. Questions
Which of the following traversal technique lists
the nodes of a binary search tree in ascending
order?
(a)Post-order b) In-order
© Pre-order (d) None of the
above

38. Questions
(b) Inorder traversal visits the nodes in
ascending order as it is left root right in which
left<=root<=right

39. Questions
The number of binary trees with 3 nodes which
when traversed in post order gives the sequence
A,B,C is
(a)3 (b) 9 (c) 7 d) 5

40. Questions

41. Questions
A binary search tree contains the values 1,2,3,4,5,6,7 and 8. The tree is
traversed in preorder and the values are printed out. Which of the following
sequences is a valid output
(a)5 3 1 2 4 7 8 6 (b) 5 3 1 2 6 4 9 7
(c)5 3 2 4 1 6 7 8 d) 5 3 1 2 4 7 6 8

42. Questions
The post order traversal of a binary tree is DEBFCA. Find out the preorder
traversal.
(a) ABFCDE (b) ADBFEC (c) ABDECF
d) ABDCEF

43. Questions

44. Questions
If a node having two children is deleted from a binary tree, it is replaced by its
(A)Inorder predecessor B) Inorder successor
(C)Preorder predecessor (D) None of the above

45. Questions

46. Questions
.The number of leaf nodes in a complete binary tree of depth d is
A) 2d (B) 2d–1+1 (C) 2d+1+1 (D)
2d+1

47. Questions
. The pre-order and post order traversal of a Binary Tree generates the same
output. The tree can have maximum
(A)Three nodes (B) Two nodes
C) One node (D) Any number of nodes

48. Questions
How many nodes in a tree have no ancestors.
(A)0 B) 1 (C) 2 (D) n

49. Questions
In order to get the information stored in a Binary Search Tree in the
descending order, one should traverse it in which of the following order?
(A) left, root, right (B) root, left, right
C) right, root, left (D) right, left, root

50. Questions

51. Introduction to Graph

52. Introduction to Graph

53. Introduction to Graph

54. Introduction to Graph

55. Introduction to Graph

56. Introduction to Graph

57. Introduction to Graph
• Bob has three friends not friends with Rama
that can be suggested to Rama

58. Introduction to Graph
• Lee has one friend(Swati) not friends with Rama
so totally 4 friends can be suggested to Rama

59. Introduction to Graph
• Lee has one friend(Swati) not friends with Rama
so totally 4 friends can be suggested to Rama

60. Introduction to Graph
• Directed Graph

61. Introduction to Graph