Problem Solving Techniques notes for Unit 1
- 1. UNIT - 1 Introduction: The Role of Algorithms in Computing, Algorithms as a technology, Analyzing algorithms, Designing algorithms, Growth of Functions, Asymptotic notation, Standard notations and common functions. Fundamental Algorithms: Exchanging the values of two variables, Counting, Summation of a set of numbers, Factorial Computation, Generating of the Fibonacci sequence, Reversing the digits of an integer, Character to number conversion.
- 2. Problem solving •It is a systematic approach to find and implement the solution to a problem. Program •It is a set of instructions written in computer languages Software •It is a collection of computer program (or) data and instructions. •It is responsible for controlling, integration and managing hardware components and perform specific tasks.
- 3. Classifications of software System software •It is a set of one or more programs that manage and support a computer system hardware and its data processing activities. •Ex: Operating system, Compilers, Assemblers Application software •It is a set of one or more programs, designed to solve a specific problem or a specific task. •Ex: Ms-Word ,Ms-Excel, Ms-Powerpoint
- 4. Steps in Problem Solving 1. Problem Definition 2. Problem Analysis 3. Design 4. Coding 5. Testing 6. Maintenance
- 5. 1. Problem Definition •To solve a problem, the first step is to identify and define the problem. •The problem must be stated clearly, accurately and precisely. •Ex: Find largest of three numbers
- 6. 2. Problem Analysis The problem analysis helps in designing and coding for that particular problem. 1. Input specifications •The number of inputs and what forms the input are available 2.Output specifications •The number of outputs and what forms the output should be displayed. Ex: •input – a,b,c •output – a (or) b (or) c
- 7. 3. Designing a program Algorithms •Algorithm - step by step procedure of solving a problem Flowcharts •Flowcharts – It is the graphical representation of the algorithm.
- 8. 4. Coding • Writing instructions in a particular language to solve a problem. 5. Testing a Program • After writing a program, programmer needs to test the program for completeness, correctness, reliability and maintainability. • Unit testing • Program Testing • Verification Testing • Validation Testing
- 9. 6. Maintaining the program •It means periodic review of the programs and modifications based on user requirements.
- 10. What is an Algorithm? •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: 1. Take two number inputs 2. Add numbers using the + operator 3. Store the result 4. Display the result Hint: Need of the Algorithm: Algorithms are used to solve problems or automate tasks in a systematic and efficient manner. They are a set of instructions or rules that guide the computer or software in performing a particular task or solving a problem.
- 11. Qualities of a 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. Instead, the algorithm should be written in such a way that it can be used in different programming languages.
- 12. Characteristics of an algorithm The characteristics of an algorithm are •(i) Algorithm must have finite number of steps. •(ii) No instructions should be repeated. •(iii) An algorithm should be simple. •(iii) An algorithm must take atleast one or more input values. •(iv) An algorithm must provide atleast one or more output values.
- 13. Characteristics of an algorithm
- 14. Advantages •Algorithms are very easy to understand. •Algorithm is programming language independent. •Algorithm makes the problem simple, clear, correct.
- 15. The Role of Algorithms • Algorithms play a crucial role in computing by providing a set of instructions for a computer to perform a specific task. • They are used to solve problems and carry out tasks in computer systems, such as sorting data, searching for information, image processing, and much more. • An algorithm defines the steps necessary to produce the desired outcome, and the computer follows the instructions to complete the task efficiently and accurately.
- 16. Role of Algorithm in Applications
- 17. Role of Algorithm in Computing
- 18. Role of Algorithm in Networking
- 19. Algorithm to Add two numbers entered by the user • 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
- 20. Algorithm for Swapping two numbers using third variable: Step 1: Declare a variable a,b and c as integer; Step 2: Read two numbers a and b; Step 3: c=a; Step 4: a=b; Step 5: b=c; Step 6: Print a and b STEP 1: START STEP 2: ENTER A, B STEP 3: PRINT A, B STEP 4: A = A + B STEP 5: B= A - B STEP 6: A =A - B STEP 7: PRINT A, B STEP 8: END Algorithm for Swapping two numbers without using third variable:
- 21. Algorithm to find Summation of a set of numbers Step 1: Start Step 2: Read the number n Step 3: Calculate the sum of n natural number, sum = n * (n + 1) / 2 Step 4: Display sum Step 5: End
- 22. Algorithm to find count of numbers of digits in a number • Step 1: Declare variable a and n; //n variable is used for counting • Step 2: Read number a; • Step 3: while(a not equal 0) • a=a/10; • n=n+1; • end • Step 4: Print n; • Step 5: End
- 23. Algorithm to 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
- 24. Algorithm to Find the factorial of a number Step 1: Start Step 2: Declare variables n, fact and i. Step 3: Initialize variables fact← 1 i ← 1 Step 4: Read value of n Step 5: Repeat the steps until i = n 5.1: fact ← fact*i 5.2: i ← i+1 Step 6: Display fact Step 7: Stop
- 25. Algorithm 6: Find the Fibonacci series • Step 1: Start • Step 2: Declare variable a, b, c, n, i • Step 3: Initialize variable a=0, b=1 and i=2 • Step 4: Read n from user • Step 5: Print a and b • Step 6: Repeat until i<=n : Step 6.1: c=a+b Step 6.2: print c Step 6.3: a=b, b=c Step 6.4: i=i+1 • Step 7: Stop
- 26. Algorithm to Reversing the digits of an integer • Step 1: Declare variable n, rev and rem as integer; • Step 2: Read the number n; • Step 3: while n not equal 0 { rem=n%10; rev=rev * 10 + rem; n=n/10; } • Step 4: Print rev
- 35. FIBONACCI SERIES
- 38. Algorithms as a technology