Algorithm design and problem solving
- 1. ALGORITHM DESIGN AND PROBLEM SOLVING -In practice, in order to solve any complex real life problems, first we have to define the problem and then, design algorithm to solve it. Def Algorithm is a step-by-step process of solving a well-defined computational problem Algorithm: a sequence of steps that can be carried out to perform a task We use algorithms in everyday life. If you need to change a wheel on a car, you mightneed to follow instructions (the algorithm) from a manual: 1 Take a spanner and loosen the wheel nuts. 2 Position a jack in an appropriate place. 3 Raise the car. 4 Take off the wheel nuts and the wheel. 5 Lift replacement wheel into position . 6 Replace wheel nuts and tighten by hand. 7 Lower the car. 8 Fully tighten wheel nuts. -This mightsound all very straightforward. -However, if the instructions are notfollowed in the correct logical sequence,the process mightbecome much more difficult or even impossible. -For example,if you tried to do Step 1 after Step 3, the wheel may spin and you can't loosen the wheel nuts. - You can't do Step 4 before Step 3. Many problems we try to solve with a computer involve data. The solution involves inputting data to the computer,processing the data and outputting results. Input Process Output Algorithm Tools Structured English: a subset of the English language that consists of command statements used to describe an algorithm Pseudocode: a way of using keywords and identifiers to describe an algorithm without following the syntax of a particular programming language Flowchart: shapes linked together to represent the sequential steps of an algorithm However, before writing a program, we need to write the steps to solve the problem in simple English language. Example Let us take one simple day-to-day example by writing algorithm for making “SADZA” Step 1: Start Step 2: Take pan with water Step 3: Put pan on the burner Step 4: Switch on the gas/burner Step 6: Give two minutes to boil Step 7: Put mealie meal Step 8: Take out the stir stick and stir it Step 9 Allow it to simmer Step 10 Stir again and adding mealie meal Step 11: Put the sadza on the plate and serve it
- 2. Step 12: Stop. Purposes of designing an Algorithm in problem-solving 1. Expresses a function starting from an initial state and initial input. 2. algorithms are used to simplify the program implementation CONTROL STRUCTURE In computer science, when writing algorithms, we use basic types of construct: Sequence: -a number of steps are performed, one after the other. • Selection: -under certain conditions some steps are performed, otherwise different (or no) steps are performed. Repetition: -a sequence of steps is performed a number of times. This is also known as iteration or looping. 1. Sequence statements: In this program, all the instructions are executed one after another. Example 1 Write an algorithm to print, “ Good Morning.” Step 1: Start Step 2: Print “Good Morning” Step 3: Stop Example 2 Write an algorithm to find area of a rectangle. Step 1: Start Step 2: Take length and breadth and store them as L and B? Step 3: Multiply by L and B and store it in area Step 4: Print area Step 5: Stop
- 3. NB In the above mentioned two examples (Example II and III), all the instructions are executed one after another. These examples are executed under sequential statement. 2.Selective Statements: -In this program, some portion of the program is executed based upon the conditional test. -If the conditional test is true, compiler will execute some part of the program, otherwise it will execute the other part of the program. Example 3 Write an algorithm to check whether he is eligible to vote? (more than or equal to 18 years old). Step 1: Start Step 2: Take age and store it in age Step 3: Check age value, if age >= 18 then go to step 4 else step 5 Step 4: Print “Eligible to vote” and go to step 6 Step 5: Print “Not eligible to vote” Step 6: Stop Example 4
- 4. Write an algorithm to check whether given number is +ve, -ve or zero. Step 1: Start Step 2: Take any number and store it in n. Step 3: Check n value, if n > 0 then go to step 5 else go to step 4 Step 4: Check n value, if n < 0 then go to step 6 else go to step 7 Step 5: Print “Given number is +ve” and go to step 8 Step 6: Print “Given number is -ve” and go to step 8 Step 7: Print “Given number is zero” Step 8: Stop Example. What would be output if the numbers 7 and 18 were input? -In the above mentioned examples IV and V, all the statements are not executed, but based upon the input, some portions of the algorithm are executed, because we have “true” or „false‟ situation in the program.
- 5. //+99999999999999 3. Iterative/Repetition statements: -In some programs, certain set of statements are executed again and again based upon conditional test. i.e. executed more than one time. -This type of execution is called “looping or iteration.” Example 5 Write an algorithm to print all natural numbers up to „n‟.+9 Step 1: Start Step 2: Take any number and store it in n. Step 3: Store 1 in I Step 4: Check I value, if I<=n then go to step 5 else go to step 8 Step 5: Print I Step 6: Increment I value by 1 Step 5: Go to step 4 Step 8: Stop In the above example, steps 4, 5, 6 and 7 are executed more than one time. -Fin-ite and Infinite loop
- 6. -In looping statements, if some set of statements are executed „n‟ times (fixed number of times), then it is called “finite loop”. -At the same time, if some set of statements are executed again and again without any end (infinite times), then it is called “infinite loop”. + Note: Set of statements is executed again and again without any end is called infinite loop. Flowchart -we have learnt to write algorithms, i.e. step-by step process of solving a problem. -We can also show these steps in graphical form by using some symbols. NB: Flowchart is the graphical representation of an algorithm -This is called flowcharting Problem solving • Step 1: – Clearly specify the problem to be solved. • Step 2: – Draw flowchart or write algorithm.
- 7. • Step 3: Dept. of CSE, IIT KGP – Convert flowchart (algorithm) into program code. • Step 4: – Compile the program into object code. • Step 5: – Execute the program Flowchart Symbols: