AOA Week 01.ppt
- 1. Design and Analysis of Algorithm Week 01
- 2. Problem Solving Solving problems is the core of computer science. Programmers must first understand how a human solves a problem, then understand how to translate this "algorithm" into something a computer can do, and finally how to "write" the specific syntax (required by a computer) to get the job done. It is sometimes the case that a machine will solve a problem in a completely different way than a human.
- 3. Problem Solving Computer Programmers are problem solvers. In order to solve a problem on a computer you must: Know how to represent the information (data) describing the problem. Determine the steps to transform the information from one representation into another.
- 5. Algorithm An algorithm is a clearly defined set of instructions to be followed to solve a problem. Algorithms are generally created independent of underlying programming languages. Informally, an algorithm is any well-defined computational procedure that takes some value, or set of values, as input and produces some value, or set of values, as output. An algorithm is thus a sequence of computational steps that transform the input into the output. 5
- 6. Characteristics of an Algorithm 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. 6
- 7. Characteristics of an Algorithm – 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.
- 8. Example Problem − Design an algorithm to add two numbers and display the result. – Step 1 – START – Step 2 – declare three integers a, b & c – Step 3 – define values of a & b – Step 4 – add values of a & b – Step 5 – store output of Step 4 to c – Step 6 – print c – Step 7 – STOP 8
- 9. Example Problem − Design an algorithm to add two numbers and display the result. – Step 1 – START ADD – Step 2 – get values of a & b – Step 3 – c a + b – Step 4 – display c – Step 5 – STOP Second method is preferable in Data Structure and Algorithms 9
- 10. Algorithm Analysis Efficiency of an algorithm can be analyzed at two different stages, before implementation and after implementation. They are the following − – A Priori Analysis − This is a theoretical analysis of an algorithm. Efficiency of an algorithm is measured by assuming that all other factors, for example, processor speed, are constant and have no effect on the implementation. – A Posterior Analysis − This is an empirical analysis of an algorithm. The selected algorithm is implemented using programming language. This is then executed on target computer machine. In this analysis, actual statistics like running time and space required, are collected 10
- 11. Pseudo Code and Algorithm An algorithm is a systematic logical approach used to solve problems in a computer. Pseudocode is the statement in plain English which may be translated later into a programming language (program). Pseudo code is an intermediary between an algorithm and implemented program
- 12. Example Pseudo code to add two numbers: Take two number inputs Add numbers using the + operator Display the result
- 13. Pseudo Code Example If Ali’s height is greater then 6 feet Then Ali can become a member of the Basket Ball team
- 14. Conversion from Pseudo code to Source code Pseudo Code If amir’s age is greater than Ammara’s age then show message that amir is elder than amara, otherwise show message that amir is younger than ammara.
- 15. Conversion from Pseudo code to Source code Source Code if (AmirAge > AmaraAge) { cout<< “Amir is older than Amara” ; } else { cout<<“Amir is younger than or of the same age as Amara” ; }
- 16. Algorithm : Find the largest number among three numbers 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
- 17. Algorithm: Find the factorial of a number Step 1: Start Step 2: Declare variables n, factorial and i. Step 3: Initialize variables factorial ← 1 i ← 1 Step 4: Read value of n Step 5: Repeat the steps until i = n 5.1: factorial ← factorial*i 5.2: i ← i+1 Step 6: Display factorial Step 7: Stop
- 18. Sorting Problem we might need to sort a sequence of numbers into non decreasing order. This problem arises frequently in practice and provides fertile ground for introducing many standard design techniques and analysis tools. Here is how we formally define the sorting problem: Input: A sequence of n numbers (a1, a2,……an).
- 19. Sorting Problem For example, given the input sequence (31; 41; 59; 26; 41; 58) a sorting algorithm returns as output the sequence (26; 31; 41; 41; 58; 59). Such an input sequence is called an instance of the sorting problem. In general, an instance of a problem consists of the input (satisfying whatever constraints are imposed in the problem statement) needed to compute a solution to the problem. Because many programs use it as an intermediate step, sorting is a fundamental operation in computer science. As a result, we have a large number of good sorting algorithms at our disposal. Which algorithm is best for a given application depends on—among other factors—the number of items to be sorted, the extent to which the items are already somewhat sorted, possible restrictions on the item values, the architecture of the computer, and the kind of storage devices to be used: main memory, disks, or even tapes.
- 20. What kinds of problems are solved by algorithms? The Human Genome Project has made great progress toward the goals of identifying all the 100,000 genes in human DNA, determining the sequences of the 3 billion chemical base pairs that make up human DNA, storing this information in databases, and developing tools for data analysis. Each of these steps requires sophisticated algorithms. The Internet enables people all around the world to quickly access and retrieve large amounts of information. With the aid of clever algorithms, sites on the internet are able to manage and manipulate this large volume of data. Examples of problems that make essential use of algorithms include finding good routes. Electronic commerce enables goods and services to be negotiated and exchanged electronically, and it depends on the privacy of personal information such as credit card numbers, passwords, and bank statements. The core technologies used in electronic commerce include public-key cryptography and digital signatures which are based on numerical algorithms and number theory.
- 21. What kinds of problems are solved by algorithms? Manufacturing and other commercial enterprises often need to allocate scarce resources in the most beneficial way. An oil company may wish to know where to place its wells in order to maximize its expected profit. A political candidate may want to determine where to spend money buying campaign advertising in order to maximize the chances of winning an election. An airline may wish to assign crews to flights in the least expensive way possible, making sure that each flight is covered and that government regulations regarding crew scheduling are met. An Internet service provider may wish to determine where to place additional resources in order to serve its customers more effectively. All of these are examples of problems that can be solved using linear programming algos.