Algorithm for computational problematic sit
- 1. A computer is a very powerful and versatile machine capable of performing a multitude of different tasks Intelligence Quotient (I.Q) of a computer is zero A computer performs many tasks exactly in the same manner as it is told to do Responsibility on the user to instruct the computer in a correct and precise manner, so that the machine is able to perform the required job in a proper way The user must have clear understanding of the problem to be solved Once the problem is well-defined and a method of solving it is developed, then instructing he computer to solve the problem becomes relatively easier task It is necessary to formulate or define the problem in a precise manner
- 2. A computer cannot solve a problem on its own. One has to provide step by step solutions of the problem to the computer. In fact, the task of problem solving is not that of the computer. It is the programmer who has to write down the solution to the problem in terms of simple operations which the computer can understand and execute. In order to solve a problem by the computer, one has to pass though certain stages or steps. They are 1. Understanding the problem 2. Analyzing the problem 3. Developing the solution 4. Coding and implementation.
- 3. 1. Understanding the problem: Here we try to understand the problem to be solved in totally. Before with the next stage or step, we should be absolutely sure about the objectives of the given problem. 2. Analyzing the problem: After understanding thoroughly the problem to be solved, we look different ways of solving the problem and evaluate each of these methods. The idea here is to search an appropriate solution to the problem under consideration. The end result of this stage is a broad overview of the sequence of operations that are to be carries out to solve the given problem. 3. Developing the solution: Here the overview of the sequence of operations that was the result of analysis stage is expanded to form a detailed step by step solution to the problem under consideration. 4. Coding and implementation: The last stage of the problem solving is the conversion of the detailed sequence of operations in to a language that the computer can understand. Here each step is converted to its equivalent instruction or instructions in the computer language that has been chosen for the implantation
- 4. Algorithm A set of sequential steps usually written in Ordinary Language to solve a given problem is called Algorithm. The most important factor in the choice of algorithm is the time requirement to execute it, after writing code in High-level language with the help of a computer. The algorithm which will need the least time when executed is considered the best. An algorithm can be defined as “a complete, unambiguous, finite number of logical steps for solving a specific problem “
- 5. Step1. Identification of input: For an algorithm, there are quantities to be supplied called input and these are fed externally. The input is to be indentified first for any specified problem. Step2: Identification of output: From an algorithm, at least one quantity is produced, called for any specified problem. Step3 : Identification the processing operations : All the calculations to be performed in order to lead to output from the input are to be identified in an orderly manner. Step4 : Processing Definiteness : The instructions composing the algorithm must be clear and there should not be any ambiguity in them. Step5 : Processing Finiteness : If we go through the algorithm, then for all cases, the algorithm should terminate after a finite number of steps. Step6 : Possessing Effectiveness : The instructions in the algorithm must be sufficiently basic and in practice they can be carries out easily
- 6. An algorithm must possess the following properties 1. Finiteness: An algorithm must terminate in a finite number of steps 2. Definiteness: Each step of the algorithm must be precisely and unambiguously stated 3. Effectiveness: Each step must be effective, in the sense that it should be primitive easily convert able into program statement) can be performed exactly in a finite amount of time. 4. Generality: The algorithm must be complete in itself so that it can be used to solve problems of a specific type for any input data. 5. Input/output: Each algorithm must take zero, one or more quantities as input data produce one or more output values. An algorithm can be written in English like sentences or in any standard representation sometimes, algorithm written in English like languages are called Pseudo Code.
- 7. Example 1: Suppose we want to find the average of three numbers, the algorithm is as follows Step 1 Read the numbers a, b, c Step 2 Compute the sum of a, b and c Step 3 Divide the sum by 3 Step 4 Store the result in variable d Step 5 Print the value of d Step 6 End of the program
- 8. Example 2: Write an algorithm to calculate the simple interest using the formula. Simple interest = P*N* R/100. Where P is principle Amount, N is the number of years and R is the rate of interest. the algorithm is as follows Step 1: Read the three input quantities’ P, N and R. Step 2 : Calculate simple interest as Simple interest = P* N* R/100 Step 3: Print simple interest. Step 4: Stop.
- 9. Example 3: Write an algorithm to find the area of the triangle. Let b, c be the sides of the triangle ABC and A the included angle between the given sides. the algorithm is as follows Step 1: Input the given elements of the triangle namely sides b, c and angle between the sides A. Step 2: Area = (1/2) *b*C* sin A Step 3: Output the Area Step 4: Stop.
- 10. Write an algorithm to find the largest of three numbers X, Y,Z. Step 1: Read the numbers X,Y,Z. Step 2: if (X > Y) Big = X else BIG = Y Step 3 : if (BIG < Z) Step 4: Big = Z Step 5: Print the largest number i.e. Big Step 6: Stop.
- 11. Write down an algorithm to find the largest data value of a set of given data values Algorithm largest of all data values: Step 1: LARGE <- 0 Step 2: read NUM Step 3: While NUM > = 0 do 3.1 if NUM > LARGE 3.1.1 then 3.1.1.1 LARGE <- NUM 3.2. read NUM Step 4: Write “largest data value is”, LARGE Step 5: end.
- 12. Write an algorithm which will test whether a given integer value is prime or not. Algorithm prime testing: Step 1: M <- 2 Step 2: read N Step 3: MAX <- SQRT (N) Step 4: While M < = MAX do 4.1 if (M* (N/M) = N 4.1.1 then 4.1.1.1 go to step 7 4.2. M <- M + 1 Step 5: Write “number is prime” Step 6: go to step 8 Step 7: Write “number is not a prime” Step 8: end.
- 13. Write algorithm to find the factorial of a given number N Step 1: PROD <- 1 Step 2: I <- 0 Step 3: read N Step 4: While I < N do 4.1 I <- I + 1 4.2. PROD <- PROD* I Step 5: Write “Factorial of”, N, “is”, PROD Step 6: end.
- 14. Write an algorithm to find sum of given data values until negative value is entered. Algorithm Find – Sum Step 1: SUM <- 0 Step 2: I <- 0 Step 3: read NEW VALUE Step 4: While NEW VALUE <= 0 do 4.1 SUM <- SUM + NEW VALUE 4.2 I <- I + 1 4.3 read NEW VALUE Step 5: Write “Sum of”, I, “data value is, “SUM Step 6: END
- 15. FlowChart A flow chart is a step by step diagrammatic representation of the logic paths to solve a given problem. Or A flowchart is visual or graphical representation of an algorithm. The flowcharts are pictorial representation of the methods to be used to solve a given problem and help a great deal to analyze the problem and plan its solution in a systematic and orderly manner. A flowchart when translated in to a proper computer language, results in a complete program.
- 16. FlowChart Advantages of Flowcharts 1. The flowchart shows the logic of a problem displayed in pictorial fashion which felicitates easier checking of an algorithm. 2. The Flowchart is good means of communication to other users. It is also a compact means of recording an algorithm solution to a problem. 3. The flowchart allows the problem solver to break the problem into parts. These parts can be connected to make master chart. 4. The flowchart is a permanent record of the solution which can be consulted at a later time.
- 17. FlowChart Differences Between Algorithm & FlowChart
- 18. FlowChart Symbols used in Flow-Charts Oval: Rectangle with rounded sides is used to indicate either START/ STOP of the program Input and output indicators: Parallelograms are used to represent input and output operations. Statements like INPUT, READ and PRINT are represented in these Parallelograms. Process Indicators: - Rectangle is used to indicate any set of processing operation such as for storing arithmetic operations. Decision Makers: The diamond is used for indicating the step of decision making and therefore known as decision box. Decision boxes are used to test the conditions or ask questions and depending upon the answers, the appropriate actions are taken by the computer. The decision box symbol is
- 19. FlowChart Symbols used in Flow-Charts Flow Lines: Flow lines indicate the direction being followed in the flowchart. In a Flowchart, every line must have an arrow on it to indicate the direction. The arrows may be in any direction On- Page connectors: Circles are used to join the different parts of a flowchart and these circles are called on-page connectors. The uses of these connectors give a neat shape to the flowcharts. In a complicated problems, a flowchart may run in to several pages. The parts of the flowchart on different pages are to be joined with each other. The parts to be joined are indicated by the circle.
- 20. FlowChart Symbols used in Flow-Charts Off-page connectors: This connector represents a break in the path of flowchart which is too large to fit on a single page. It is similar to on-page connector. The connector symbol marks where the algorithm ends on the first page and where it continues on the second.
- 21. FlowChart Examples: Draw the Flowchart to find Roots of Quadratic equation ax2+ bx + c = 0. The coefficients a, b, c are the input data
- 22. FlowChart Examples: Draw a flowchart to find out the biggest of the three unequal positive numbers.
- 23. FlowChart Examples: Draw a flowchart for adding the integers from 1 to 100 and to print the sum.
- 24. FlowChart Examples: Draw a flowchart to find the factorial of given positive integer N.
- 25. PsuedoCode The Pseudo code is neither an algorithm nor a program. It is an abstract form of a program. It consists of English like statements which perform the specific operations. It is defined for an algorithm. It does not use any graphical representation. In pseudo code, the program is represented in terms of words and phrases, but the syntax of program is not strictly followed. Advantages: • Easy to read • Easy to understand • Easy to modify.
- 26. PsuedoCode Examples: Example: Write a pseudo code to perform the basic arithmetic operations. Read n1, n2 Sum = n1 + n2 Diff = n1 – n2 Mult = n1 * n2 Quot = n1/n2 Print Sum, Diff, Mult, Quot End.