1.4.2a CONCEPT OF ALGORITHM AND FLOWCHART

 ALGORITHM

The fundamental knowledge necessary to solve problems using a computer is the notion of an algorithm. An algorithm is a precise specification of a sequence of instructions to be carried out in order to solve a given problem. Each instruction tells us what task is to be performed.

The fundamental knowledge necessary to solve problems using a computer is the notion of  an algorithm. An algorithm is precise specification of a sequence of instructions to be carried out to solve a given problem.

Def:

            An algorithm can be defined as a step-by step procedure to solve a particular problem.

Criteria for algorithm

An algorithm is a finite set of instructions which, if followed, accomplish a particular task. In addition every algorithm must satisfy the following criteria:

1.      Input: there are zero or more quantities which are externally supplied.

2.      Output: at least one quantity is produced.

3.      Definiteness: each instruction must be clear and unambiguous.

4.      Finiteness: if we trace out the instructions of an algorithm, then for cases the algorithm must terminate after a finite number of steps.

5.      Effectiveness: every instruction must be sufficiently basic that it can in principle be carried out by a person using only pencil and paper. It is not enough that each operation be definite, but it must also be feasible.

 

Algorithmic Notations

ü  Name of the algorithm: it specifies the problem to be solved.

ü  Initialization of algorithm: it specifies the start of the algorithm.

ü  Step number: identification tag of an instruction and it is unsigned positive integer.

ü  Explanatory comment: describes the operations, should be written in square brackets [ ] is optional.

ü  Termination: it specifies the end of the algorithm.

Few examples of algorithm

1.      To find the sum and average of 3 numbers.

Algorithm: To find sum and average of three numbers

Step 1: START

Step 2: PRINT “Enter any three numbers”

Step 3: INPUT a, b, c

Step 4: COMPUTE d = a + b + c

Step 5: COMPUTE e = d / 3

Step 6: PRINT d, e

Step 7: STOP

2.      To find simple interest.

Algorithm: To calculate simple interest

Step 1: START

Step 2: PRINT “Enter principal, rate of interest and time period”

Step 3: INPUT p, r, t

Step 4: COMPUTE si = p * r * t / 100

Step 5: PRINT si

Step 6: STOP
 

3.      To convert Fahrenheit temperature to centigrade

Algorithm: To convert temperature given in ^oF to ^oC

Step 1: START

Step 2: PRINT “Enter temperature in ^oF

Step 3: INPUT f

Step 4: COMPUTE c = ( ( f – 32 ) * 100 ) / 180

Step 5: PRINT “Temperature in ^oC=”, c

Step 6: STOP

4.      To swap two numbers using a third variable.

Algorithm: To swap two numbers using a third variable

Step 1: START

Step 2: PRINT “Enter any two numbers”

Step 3: INPUT a, b

Step 4: LET c = a

Step 5: LET a = b

Step 6: LET b = c

Step 7: PRINT a, b

Step 8: STOP

5.      To swap two numbers without using a third variable.

Algorithm: To swap two numbers without using a third variable

Step 1: START

Step 2: PRINT “Enter any two numbers”

Step 3: INPUT a, b

Step 4: COMPUTE a = a + b

Step 5: COMPUTE b = a - b

Step 6: COMPUTE a = a - b

Step 7: PRINT a, b

Step 8: STOP

6.      To find whether the number is odd or even.

Algorithm: To check whether the entered number is even or odd

Step 1: START

Step 2: PRINT “Enter any number”

Step 3: INPUT a

Step 4: IF (a % 2 = = 0) GOTO Step 5 ELSE GOTO Step 6

Step 5: PRINT “Given number is even” GOTO Step 7

Step 6: PRINT “Given number is odd”

Step 7: STOP

7.      To check whether the roots of quadratic equation are real or imaginary.

Algorithm: To check whether the roots of quadratic equation are real or imaginary

Step 1: START

Step 2: PRINT “Enter the values of a, b and c”

Step 3: INPUT a, b, c

Step 4: COMPUTE d = b * b – 4 * a * c

Step 5: IF (d > 0) GOTO Step 6 ELSE GOTO Step 7

Step 6: PRINT “Roots are real” GOTO Step 8

Step 7: PRINT “Roots are imaginary”

Step 8: STOP

8.      To find the largest among given two numbers.

Algorithm: To find the largest among given two numbers

Step 1: START

Step 2: PRINT “Enter any two numbers”

Step 3: INPUT a, b

Step 4: IF (a > b) GOTO Step 5 ELSE GOTO Step 6

Step 5: PRINT “First number is greater than second” GOTO Step 7

Step 6: PRINT “Second number is greater than first”

Step 7: STOP

9.      To find the largest among given three numbers.

Algorithm: To find the largest among given three numbers

Step 1: START

Step 2: PRINT “Enter any three numbers”

Step 3: INPUT a, b, c

Step 4: IF (a > b) GOTO Step 5 ELSE GOTO Step 6

Step 5: IF (a > c) PRINT a ELSE Print c GOTO Step 7

Step 6: IF (b > c) PRINT b ELSE PRINT c

Step 7: STOP

10.  To find the sum of the digits of n-digit number.

Algorithm: To find the sum of the digits of a number

Step 1: START

Step 2: PRINT “Enter any number”

Step 3: INPUT n

Step 4: LET sum = 0

Step 5: WHILE (n > 0)

            {

                        r = n % 10

                        sum = sum + r

                        n = n / 10

            }

Step 6: PRINT sum

Step 7: STOP

11.  To reverse the digits of given n-digit number.

Algorithm: To reverse the digits of a number

Step 1: START

Step 2: PRINT “Enter any number”

Step 3: INPUT n

Step 4: LET rev = 0

Step 5: WHILE (n > 0)

            {

                        r = n % 10

                        rev = rev * 10  + r

                        n = n / 10

            }

Step 6: PRINT rev

Step 7: STOP

12.  To print numbers divisible by 7 from 1 to N numbers.

Algorithm: To find the numbers divisible by 7 in range 1 to N

Step 1: START

Step 2: PRINT “Enter the range”

Step 3: INPUT n

Step 4: LET count = 1

Step 5: WHILE (count < = n)

            {

                        IF (count % 7 = = 0)

                        {

                                    PRINT count

                                    count = count + 1

                        }

                        ELSE

                                    count = count + 1

            }

Step 6: STOP

13.  To calculate the factorial of a number.

Algorithm: To calculate the factorial of a number

Step 1: START

Step 2: PRINT “Enter any number”

Step 3: INPUT n

Step 4: LET fact = 1, i = 1

Step 5: WHILE (i < = n)

            {

                        fact = fact * i

i = i + 1

            }

Step 6: PRINT fact

Step 7: STOP

14.  To find whether a given number is prime or not.

Algorithm: To check whether the given number is prime or not

Step 1: START

Step 2: PRINT “Enter any number”

Step 3: INPUT n

Step 4: LET i = 2

Step 5: WHILE (i < = n-1)

            {

                        IF (n % i = = 0)

PRINT “Number is not prime!”

ELSE

i = i + 1

            }

Step 6: IF (n = = i)

PRINT “Number is prime!”

Step 7: STOP

15.  To print first N Fibonacci numbers.

Algorithm: To generate first n-Fibonacci numbers

Step 1: START

Step 2: PRINT “Enter the range”

Step 3: INPUT n

Step 4: LET a = 0, b = 1, i = 1

Step 5: PRINT a

PRINT b

Step 6: FOR (i = 1 to n-2)

{

c = a + b

PRINT c

a = b

b = c
i = i + 1

}

Step 7: STOP