Algorithms and Flowcharts Week 2

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1 Algorithms and Flowcharts Week 2 1

2 Principles of Programming The program or set of programs in a computer that helps in processing the information is called SOFTWARE. Software is a detailed writing of stepwise instructions for the computer to carry out the particular task efficiently and properly. The art of writing software is called programming. Software is an essential part of a computer. Without the software the computer will neither accept information nor give the desired result. 2

3 What is an Algorithm? An algorithm is a finite set of instructions for accomplishing some specific task. (The word is derived from the name of the Persian mathematician Al Khwarizmi). The instructions need not be computer-based instructions, and an algorithm need not be implemented as a computer program. Rather, it is a formal way of specifying a solution to a specific problem one wishes to solve 3

4 What is an Algorithm? A typical programming task can be divided into two phases: Problem solving phase produce an ordered sequence of steps that describe solution of problem this sequence of steps is called an algorithm Implementation phase implement the program in some programming language 4

5 Steps in Problem Solving First produce a general algorithm (one can use pseudocode) Refine the algorithm successively to get step by step detailed algorithm that is very close to a computer language. Pseudocode is an artificial and informal language that helps programmers develop algorithms. Pseudocode is very similar to everyday English.

6 Algorithm? A step-by-step procedure to solve the given problem is known as Algorithm. The essential properties of Algorithm are: It should be simple It should be clear with no ambiguity It should lead to a unique solution of the problem. It should involve a finite number of steps to arrive at a solution. It should have the capability to handle some-unexpected situations. For example if a student wants to purchase a pen, what is the steps that he has to follow??? 6

7 Pseudocode 1. He has to get money from parents. 2. Come out of the House to cross the road 3. Check the vehicle movement for safe crossing. 4. When it is safe to cross the road, he crosses the road. 5. He gets into the shop. 6. Asks for a pen. 7. Selects a pen from the lot shown to him by the shopkeeper. 8. Pays money to the shopkeeper. 7

8 Flow Chart The graphical or visual representation of algorithm is called as flow chart. The flow charts are easier to understand the flow of the solution. Flow charts are drawn with the standard symbols accepted worldwide. Each standard flow chart symbol represents on action to be performed such as Start or Stop, input operations Read or Write, decision making et 8

9 Flow Chart Symbols Terminal (Start or Stop Symbol) Input / Output Processing 9

10 Flow Chart Symbols Flow Lines: These are arrow mark symbols used to connect two boxes and to indicate the direction of data or processing flow. Decision Box: This is a diamond shaped box, which is used to indicate logical checking and gives decision after comparing between two or more objects (Eg. Yes or No; True or False, =, >, <, etc.) Is a<b? Connector: This is a Circular-shaped symbol used to connect different parts of flowchart. When the flow chart is lengthy, it is split into different pages. Then these connectors are used to connect between these pages at the beginning and at the end of each page. 10

11 Example 1 Algorithm and flow chart to read the name and print the name Algorithm Flow Chart Step 1 : Start Step 2 : Read input name Step 3 : Print name Step 4 : Stop 11

12 Example 2 Algorithm and flow chart to add two numbers. Algorithm Step 1 : Start Step 2 : Input first number A Step 3 : Input second number B Step 4 : Add the two numbers and store it in total Step 5 : Print Total Step 6 : Stop Flow Chart 12

13 Example 3 Algorithm and a flow chart to calculate area of square Algorithm Step 1 : Start Step 2 : Read value for a (side) Step 3 : [Compute] Area = A * A Step 4 : Output Area Step 5 : Stop Flow Chart 13

14 Example 4 Algorithm and flow chart to find the average of three numbers. Algorithm Step1 : Start Step 2 : Enter Three Numbers A, Band C Step 3 : Compute Average = (A+B+C)/3 Step 4 : Print Average Step 5 : Stop Flow Chart 14

15 Example 5 Algorithm and flow chart to find the largest of two numbers. Algorithm Step1: Start Step 2: Enter two numbers A and B Step 3: Check if A is greater than B if yes go to Step 4 else go to Step 5 Step 4: Print A is greater than B Step 5: Check if B is greater than A if yes go to Step 6 else go to Step 7 Step 6: Print B is greater than A Step 7: Print A is equal to B Step 8: Stop 15

16 Example 6 Write a pseudocode to determine a student s final grade and indicate whether it is passing or failing. The final grade is calculated as the average of four marks. Input a set of 4 marks Calculate their average by summing and dividing by 4 if average is below 50 Print FAIL else Print PASS 16

17 Example 6 Cont. Write an algorithm to determine a student s final grade and indicate whether it is passing or failing. The final grade is calculated as the average of four marks. Step 1: Input M1,M2,M3,M4 Step 2: Step 3: GRADE (M1+M2+M3+M4)/4 if (GRADE < 50) then else Print FAIL Print PASS 17

18 Example 6 Cont. Draw a flowchart for the same example 18

19 Example 7 Write an algorithm and draw a flowchart to convert the length in feet to centimeter. Algorithm Step 1: Input ft Step 2: cm ft x 30 Step 3: Print cm

20 Example 8 Write an algorithm and draw a flowchart that will calculate the roots of a quadratic equation 2 ax bx c 0 Hint: d = sqrt ( b x1 = ( b + d)/2a and x2 = ( b d)/2a 2 4ac ), and the roots are:

21 Example 8 Algorithm: Step 1: Input a, b, c Step 2: d sqrt ( b b 4 a c ) Step 3: x1 ( b + d) / (2 x a) Step 4: x2 ( b d) / (2 x a) Step 5: Print x1, x2

22 Example 9 Algorithm and a flow chart to find the factorial of a number. Algorithm Step 1: Start Step 2: Read N Step 3: [Initialize all counters] Set FACT= 1, i = 1 Step 4: Compute Fact = Fact * I Increment i Step 5: Check if i < = N if true repeat step 4 if false go to step 6 Step 6: Print fact Step 7: Stop 22

23 Example 10 Start Draw a flowchart to sum up the integers 1 to N. 1, 2, 3,..., N For example, if the N = 6, then the result will be: Stop

24 Example 11 The algorithm sums all the even numbers between 1 and 20 inclusive and then displays the sum ALGORITHM sum = 0 count = 1 REPEAT IF count is even THEN sum = sum + count count = count + 1 UNTIL count > 20 DISPLAY sum 24

25 HOMEWORK 1 Write an algorithm and draw a flowchart that reads three numbers and prints the value of the largest number.

26 HOMEWORK 2 Write an algorithm and draw a flowchart to a) read an employee name (NAME), overtime hours worked (OVERTIME), hours absent (ABSENT) and b) determine the bonus payment (PAYMENT).

27 Using this table Bonus Schedule OVERTIME (2/3)*ABSENT Bonus Paid >40 hours >30 but 40 hours >20 but 30 hours >10 but 20 hours 10 hours $50 $40 $30 $20 $10

28 HOMEWORK 3 Design an algorithm with a natural number, n, as its input which calculates the following formula and writes the result in the standard output: 28

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