Unit I Data structure and algorithms notes
- 1. Data Structures and Algorithm INSTRUCTOR: ELLEN GRACE PORRAS FIRST SEMESTER 2022-2023
- 2. Introduction Data Structure • Data Structure is a way of collecting and organizing data in such a way that we can perform operations on these data in an effective way. Data Structures is about rendering data elements in terms of some relationship, for better organization and storage. • Data Structures are structures programmed to store ordered data, so that various operations can be performed on it easily. It represents the knowledge of data to be organized in memory. • It should be designed and implemented in such a way that it reduces the complexity and increases the efficiency.
- 3. Characteristics of a Data Structure 3 • Correctness − Data structure implementation should implement its interface correctly. • Time Complexity − Running time or the execution time of operations of data structure must be as small as possible. • Space Complexity − Memory usage of a data structure operation should be as little as possible.
- 4. Need for Data Structure 4 As applications are getting complex and data rich, there are three common problems that applications face now-a-days. • Data Search − Consider an inventory of 1 million (106) items of a store. If the application is to search an item, it has to search an item in 1 million (106) items every time slowing down the search. As data grows, search will become slower. • Processor Speed − Processor speed although being very high, falls limited if the data grows to billion records. • Multiple Requests − as thousands of users can search data simultaneously on a web server, even the fast server fails while searching the data. To solve the above-mentioned problems, data structures come to rescue. Data can be organized in a data structure in such a way that all items may not be required to be searched, and the required data can be searched almost instantly
- 5. What is an Algorithm? 5 • Algorithm is a step-by-step procedure, which defines a set of instructions to be executed in a certain order to get the desired output. Algorithms are generally created independent of underlying languages, i.e. an algorithm can be implemented in more than one programming language. • In computer programming terms, an algorithm is a set of well-defined instructions to solve a particular problem. It takes a set of input(s) and produces the desired output. For example: An algorithm to add two numbers: • Take two number inputs • Add numbers using the + operator • Display the result
- 6. 6 Let us consider the problem of preparing an omelette. To prepare an omelette, we follow the steps given below: 1) Get the frying pan. 2) Get the oil. a. Do we have oil? • If yes, put it in the pan. • If no, do we want to buy oil? If yes, then go out and buy. If no, we can terminate. 3)Turn on the stove, etc... What we are doing is, for a given problem (preparing an omelette), we are providing a step-by step procedure for solving it. The formal definition of an algorithm can be stated as: An algorithm is the step-by-step unambiguous instructions to solve a given problem.
- 7. Qualities of a Good Algorithm 7 • Input and output should be defined precisely. • Each step in the algorithm should be clear and unambiguous. • Algorithms should be most effective among many ways to solve a problem. • An algorithm shouldn't include computer code. Instead, the algorithm should be written in such a way that it can be used in different programming languages.
- 8. 8 From the data structure point of view, following are some important categories of algorithms − • Search − Algorithm to search an item in a data structure. • Sort − Algorithm to sort items in a certain order. • Insert − Algorithm to insert item in a data structure. • Update − Algorithm to update an existing item in a data structure. • Delete − Algorithm to delete an existing item from a data structure.
- 9. Characteristics of an Algorithm 9 Not all procedures can be called an algorithm. An algorithm should have the following characteristics − • Unambiguous − Algorithm should be clear and unambiguous. Each of its steps (or phases), and their inputs/outputs should be clear and must lead to only one meaning. • Input − an algorithm should have 0 or more well-defined inputs. • Output − an algorithm should have 1 or more well-defined outputs, and should match the desired output. • Finiteness − Algorithms must terminate after a finite number of steps. • Feasibility − should be feasible with the available resources. • Independent − an algorithm should have step-by-step directions, which should be independent of any programming code.
- 10. Algorithm 1: Add two numbers entered by the user 10 Step 1: Start Step 2: Declare variables num1, num2 and sum. Step 3: Read values num1 and num2. Step 4: Add num1 and num2 and assign the result to sum. sum←num1+num2 Step 5: Display sum Step 6: Stop
- 11. Algorithm 2: Find the largest number among three numbers 11 Step 1: Start Step 2: Declare variables a,b and c. Step 3: Read variables a,b and c. Step 4: If a > b If a > c Display a is the largest number. Else Display c is the largest number. Else If b > c Display b is the largest number. Else Display c is the greatest number. Step 5: Stop
- 12. A good algorithm maintains a level of correctness while being efficient. Meaning, there is little error, and it doesn’t take much time to complete. Another important component is comprehensibility. We wouldn’t be able to use algorithms so frequently if they couldn’t be understood. Algorithmic and computational thinking is so pervasive that it governs the simplest things in our daily lives. Here are some examples of algorithms you interact with everyday. 12
- 13. Recipes Just like sorting papers and even tying your shoes, following a recipe is a type of algorithm. The goal of course being to create a duplicated outcome. In order to complete a recipe, you must follow a given set of steps. Say you are making bread. You need flour, yeast and water. After you have your ingredients, you need to combine them in a certain way that will create a predictable outcome, in this case a loaf of bread. 13
- 14. A simple task and yet it uses algorithmic thinking. When you are sorting office files or your personal documents you are implementing an algorithm. In its most basic sense, you are following a set of tasks to achieve an outcome. The reason why sorting papers is a great example, is because it shows the variety of tasks and specifications algorithms can use. For instance, you can sort your files alphabetically, by word count, by date, and countless others. The goal is to simplify the organizational process by using small tasks. 14 Sorting Papers
- 16. Write down at least 3 algorithms you interact with everyday and present it in front of the class. 16
- 17. Types of Data Structure 17 Basically, data structures are divided into two categories: • Linear data structure • Non-linear data structure Linear data structures • In linear data structures, the elements are arranged in sequence one after the other. Since elements are arranged order, they are easy to implement. • However, when the complexity of the program increases, the linear data structures might not be the best choice because of operational complexities
- 18. 18 Popular linear data structures are: 1. Array Data Structure In an array, elements in memory are arranged in continuous memory. All the elements of an array are of the same type. And the type of elements that can be stored in the form of arrays is determined by the programming language. An array with each element represented by an index
- 19. 19 2. Stack Data Structure In stack data structure, elements are stored in the LIFO principle. That is, the last element stored in a stack will be removed first. It works just like a pile of plates where the last plate kept on the pile will be removed first. In a stack, operations can be performed only from one end (top here).
- 20. 20 3. Queue Data Structure Unlike stack, the queue data structure works in the FIFO principle where first element stored in the queue will be removed first. It works just like a queue of people in the ticket counter where first person on the queue will get the ticket first. In a queue, addition and removal are performed from separate ends.
- 21. 21 4. Linked List Data Structure In linked list data structure, data elements are connected through a series of nodes. And each node contains the data items and address to the next node. A linked list
- 22. 22 Unlike linear data structures, elements in non-linear data structures are not in any sequence. Instead they are arranged in a hierarchical manner where one element will be connected to one or more elements. Non-linear data structures are further divided into graph and tree-based data structures. 1. Graph Data Structure In graph data structure, each node is called vertex and each vertex is connected to other vertices through edges. Graph data structure example Non-linear data structures
- 23. 23 2. Trees Data Structure Like a graph, a tree is also a collection of vertices and edges. However, in tree data structure, here can only be one edge between two vertices. Tree data structure example Non-linear data structures
- 24. 24 Now that we know about linear and non-linear data structures, let's see the major differences between them. Linear Vs Non-linear Data Structures Linear Data Structures Non-Linear Data Structures The data items are arranged in sequential order, one after the other. The data items are arranged in non- sequential order (hierarchical manner). All the items are present on the single layer. The data items are present at different layers. It can be traversed on a single run. That is, if we start from the first element, we can traverse all the elements sequentially in a single pass. It requires multiple runs. That is, if we start from the first element it might not be possible to traverse all the elements in a single pass. The memory utilization is not efficient. Different structures utilize memory in different efficient ways depending on the need. The time complexity increases with the data size. Time complexity remains the same. Example: Arrays, Stack, Queue Example: Tree, Graph, Map
- 25. Thank you Presenter name: Ellen Grace D. Porras Email address: [email protected]