CSE 443 (1).pptx
- 1. CSE-443 SUMMER INTERNSHIP ON DATA STRUCTURE AND ALGORITHMS (GFG) Presented by :- Name: I.Jayakrishna Reddy Reg. No.: 11913860
- 2. Topics Covered INTRODUCTION DATA STRUCTURES i. Asymptotic Notations ii. Time Complexity iii. Arrays, Trees, Linked List, etc. ALGORITHMS CONCLUSION
- 3. INTRODUCTION A computer program is a collection of instructions to perform a specific task. For this, a computer program may need to store data, retrieve data, and perform computations on the data. A data structure is a named location that can be used to store and organize data. And, an algorithm is a collection of steps to solve a particular problem. Learning data structures and algorithms allow us to write efficient and optimized computer programs. An algorithm is a set of well-defined instructions in sequence to solve a problem.
- 4. Asymptotic Notation Asymptotic notations are mathematical tools to represent the time complexity of algorithms for asymptotic analysis. Types of Asymptotic notation: Big Oh notation: It represents the upper bound of the running time of an algorithm. Thus, it gives the worst case complexity of an algorithm. Big Theta notation: It encloses the function from above and below. Since it represents the upper and the lower bound of the running time of an algorithm, it is used for analyzing the average case complexity of an algorithm. Big Omega notation: It represents the lower bound of the running time of an algorithm. Thus, it provides best case complexity of an algorithm.
- 5. (i)Big O (ii)Big Theta (iii)Big Omega
- 6. Time Complexity Time complexity of an algorithm signifies the total time required by the program to run till its completion. Types of Time complexity: Worst Case: In the worst case analysis, we calculate upper bound on running time of an algorithm. Average case: In average case analysis, we take all possible inputs and calculate computing time for all of the inputs. Best case: In the best case analysis, we calculate lower bound on running time of an algorithm
- 7. ARRAYS An array is a collection of items of same data type stored at contiguous memory locations. Location of the next element depends on the datatype of the element. Arrays allows to access elements randomly. Elements in an array can be accessed using indexes. It gives a better performance as access time become faster because we can randomly access the elements and its an advantage of array. Operations like searching, insertion, deletion, reversing we can with array.
- 8. TREE A Tree is a non-linear data structure where each node is connected to a number of nodes with the help of pointers or references. Basic terminologies in tree: root node, leaf node, edge, siblings, height of tree, etc. Special case of tree: Binary tree A Tree is said to be a Binary Tree if all of its nodes have at most 2 children i.e. all of its node can have either no child, 1 child or 2 child nodes. Types of binary tree: Full binary tree, Complete binary tree, Perfect binary tree. Operations on tree are Traversal, Insertion, Deletion, etc.
- 9. LINKED LIST Linked Lists are linear or sequential data structures in which elements are stored at non-contiguous memory location and are linked to each other using pointers. Each linked list has two parts : Data Next pointer Types of linked list: Singly linked list Doubly linked list Circular linked list Operations are like searching, insertion and deletion, etc.
- 10. STRINGS Strings are defined as a stream of characters. Strings are used to represent text and are generally represented by enclosing text within quotes. In java, objects of string are immutable which means a constant and cannot be changed once created. Some methods in strings: Finding the length and substring Index of string, Concatenating two strings Comparing two strings, Uppercase, Lowercase, Trim and Replace. Searching algorithms: Naïve pattern searching: O(m*(n-m+1))
- 11. STACK Stack is a linear data structure which follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out). The LIFO order says that the element which is inserted at the last in the Stack will be the first one to be removed. In LIFO order insertion takes place at the rear end of the stack and deletion occurs at the front of the stack. Operations such as push, pop, etc. are performed. It can be implemented in two ways using arrays and linked list. Pros: Easy to implement. Memory is saved as pointers are not involved. Cons: It is not dynamic. It doesn’t grow and shrink depending on needs at runtime.
- 12. QUEUE Queue is also a linear data structure which follows a particular order in which the operations are performed. The order is First In First Out (FIFO) which means that the element which is inserted first in the queue will be the first one to be removed from the queue. Operations: Enqueue: Adds an item to the queue. If the queue is full, then it is said to be an Overflow Condition. Dequeue: Removes an item from the queue. The items are popped in the same order in which they are pushed. If the queue is empty, then it is said to be an Underflow Condition. Front: Get the front item from queue. Rear: Get the last item from queue.
- 13. GRAPH A graph is a data structure that consists of the following two components: A finite set of vertices also called nodes. A finite set of ordered pair of the form (u, v) called as edge. Two types of graph: Directed graph : The Directed graphs are such graphs in which edges are directed in a single direction. Undirected graph: Undirected graphs are such graphs in which the edges are directionless or in other words bi-directional. Operations such as Traversal(two types) Breadth first traversal Depth first traversal
- 14. ALGORITHMS Qualities of Good Algorithm Searching Recursion Sorting Insertion Deletion , etc.
- 15. QUALITIES OF GOOD ALGORITHM Input and output should be defined precisely. Each step in the algorithm should be clear and unambiguous. Algorithms should be most effective among many different ways to solve a problem. An algorithm shouldn't include computer code. The algorithm should be written in such a way that it can be used in different programming languages.
- 16. SEARCHING Searching means searching a particular element in any data structure. Two types: 1. Linear search: i. It is also known as sequential search. ii. Time complexity: O(n) 2. Binary search: i. It performs the search operation by repeatedly dividing the search interval in half. ii. It performed only on sorted arrays and it is also more efficient than the linear search algorithm. iii. Time complexity: O(Log n)
- 17. RECURSION The process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called as recursive function. Recursion algorithm must have base condition in recursive program, the solution to base case is provided and solution of bigger problem is expressed in terms of smaller problems. Pros: Recursion provides a simple and clean way to write codes. Cons: It takes greater space and also greater time for processing.
- 18. SORTING Sorting any sequence means to arrange the elements of that sequence according to some specific criterion. Types: ► Insertion sort: O(n^2) ► Selection sort: O(n^2) ► Bubble sort: O(n^2) ► Quick sort: O(n^2) ► Merge sort: O(log n)