introduction to data structure & algorithms - sethuonline.com | sathyabama university chennai

Data Structure & Algorithms

Agenda

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

What Is Data Structure?

Program Contains DataWhere the data to be stored?(Capacity)How the data efficiently handle & used? (Efficiently)Data structure just a plain container

Analogy

Algorithm Analysis

Algorithm & Datastructure

A Program is a combination of Algorithm and Data Structure

Simple Example:Addition of two Numbers Int A,B,CC= A + B

Program Algorithm Data Structure

Addition Logic is an AlgorithmA & B are Data Structure ‘ elements.

Types Of Data Structure

Data Structure

Linear DS Non Linear DS

Binary Trees

Binary Trees Jargons

Binary Tree Vs Tree

Binary Tree Terminology

Binary Search Tree

Binary Search Tree Examples

Building a Binary Search Tree

Removal Binary Search Tree

Binary Search Tree Traversal

BST Traversal

BFS DFS

Binary Search Tree Traversal

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

Questions

2) The number of possible ordered trees with 3 nodes A,B,C is

a) 16 (b)12 c)6 (d)10

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

Questions (a)Explanation: If the depth of a complete binary tree is d, the number of nodes n= 2d+1-1n+1=2d+1 Applying logarithm to base 2 on both sides we havelog 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

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

Questions

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

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

Questions

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

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

d) ABDCEF

Questions

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

Questions

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

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 nodesC) One node (D) Any number of nodes

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

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, rightC) right, root, left (D) right, left, root

Questions

Introduction to Graph


• Bob has three friends not friends with Rama that can be suggested to Rama


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


• Directed Graph

introduction to data structure & algorithms - sethuonline.com | sathyabama university chennai

Software