iterations, Recursions, Syntax, Pseudo code, examples, algorithm, flow chart - Simple Strategies For Developing Algorithms | Problem Solving and Python Programming : Algorithmic Problem Solving

Chapter: Problem Solving and Python Programming : Algorithmic Problem Solving

Simple Strategies For Developing Algorithms

1. iterations 2. Recursions

SIMPLE STRATEGIES FOR DEVELOPING ALGORITHMS:

1. iterations

2. Recursions

1. Iterations:

A sequence of statements is executed until a specified condition is true is called iterations.

1. for loop

2. While loop

Syntax for For:

FOR( start-value to end-value) DO

Statement

...

ENDFOR

Example: Print n natural numbers

BEGIN

GET n

INITIALIZE i=1

FOR (i<=n) DO

PRINT i

i=i+1

ENDFOR

END

Syntax for While:

WHILE (condition) DO

Statement

...

ENDWHILE

Example: Print n natural numbers

BEGIN

GET n

INITIALIZE i=1

WHILE(i<=n) DO

PRINT i

i=i+1

ENDWHILE

END

Recursions:

v A function that calls itself is known as recursion.

v Recursion is a process by which a function calls itself repeatedly until some specified condition has been satisfied.

Algorithm for factorial of n numbers using recursion:

Main function:

Step1: Start

Step2: Get n

Step3: call factorial(n)

Step4: print fact

Step5: Stop

Sub function factorial(n):

Step1: if(n==1) then fact=1 return fact

Step2: else fact=n*factorial(n-1) and return fact

Pseudo code for factorial using recursion:

Main function:

BEGIN

GET n

CALL factorial(n)

PRINT fact

BIN

Sub function factorial(n):

IF(n==1) THEN

fact=1

RETURN fact

ELSE

RETURN fact=n*factorial(n-1)

More examples:

Write an algorithm to find area of a rectangle

Step 1: Start

Step 2: get l,b values

Step 3: Calculate A=l*b

Step 4: Display A

Step 5: Stop

BEGIN

READ l,b

CALCULATE A=l*b

DISPLAY A

END

Write an algorithm for Calculating area and circumference of circle

Step 1: Start

Step 2: get r value

Step 3: Calculate A=3.14*r*r

Step 4: Calculate C=2.3.14*r

Step 5: Display A,C

Step 6: Stop

BEGIN

READ r

CALCULATE A and C

A=3.14*r*r

C=2*3.14*r

DISPLAY A

END

Write an algorithm for Calculating simple interest

Step 1: Start

Step 2: get P, n, r value

Step3:Calculate

SI=(p*n*r)/100

Step 4: Display S

Step 5: Stop

BEGIN

READ P, n, r

CALCULATE S

SI=(p*n*r)/100

DISPLAY SI

END

Write an algorithm for Calculating engineering cutoff

Step 1: Start

Step2: get P,C,M value

Step3:calculate

Cutoff= (P/4+C/4+M/2)

Step 4: Display Cutoff

Step 5: Stop

BEGIN

READ P,C,M

CALCULATE

Cutoff= (P/4+C/4+M/2)

DISPLAY Cutoff

END

To check greatest of two numbers

Step 1: Start

Step 2: get a,b value

Step 3: check if(a>b) print a is greater

Step 4: else b is greater

Step 5: Stop

BEGIN

READ a,b

IF (a>b) THEN

DISPLAY a is greater

ELSE

DISPLAY b is greater

END IF

END

To check leap year or not

Step 1: Start

Step 2: get y

Step 3: if(y%4==0) print leap year

Step 4: else print not leap year

Step 5: Stop

BEGIN

READ y

IF (y%4==0) THEN

DISPLAY leap year

ELSE

DISPLAY not leap year

END IF

END

To check positive or negative number

Step 1: Start

Step 2: get num

Step 3: check if(num>0) print a is positive

Step 4: else num is negative

Step 5: Stop

BEGIN

READ num

IF (num>0) THEN

DISPLAY num is positive

ELSE

DISPLAY num is negative

END IF

END

To check odd or even number

Step 1: Start

Step 2: get num

Step 3: check if(num%2==0) print num is even

Step 4: else num is odd

Step 5: Stop

BEGIN

READ num

IF (num%2==0) THEN

DISPLAY num is even

ELSE

DISPLAY num is odd

END IF

END

To check greatest of three numbers

Step1: Start

Step2: Get A, B, C

Step3: if(A>B) goto Step4 else goto step5

Step4: If(A>C) print A else print C

Step5: If(B>C) print B else print C

Step6: Stop

BEGIN

READ a, b, c

IF (a>b) THEN

IF(a>c) THEN

DISPLAY a is greater

ELSE

DISPLAY c is greater

END IF

ELSE

IF(b>c) THEN

DISPLAY b is greater

ELSE

DISPLAY c is greater

END IF

END

Write an algorithm to check whether given number is +ve, -ve or zero.

Step 1: Start

Step 2: Get n value.

Step 3: if (n ==0) print “Given number is Zero” Else goto step4

Step 4: if (n > 0) then Print “Given number is +ve”

Step 5: else Print “Given number is -ve”

Step 6: Stop

BEGIN

GET n

IF(n==0) THEN

DISPLAY “ n is zero”

ELSE

IF(n>0) THEN

DISPLAY “n is positive”

ELSE

DISPLAY “n is positive”

END IF

END

Write an algorithm to print all natural numbers up to n

Step 1: Start

Step 2: get n value.

Step 3: initialize i=1

Step 4: if (i<=n) go to step 5 else go to step 8

Step 5: Print i value

step 6 : increment i value by 1

Step 7: go to step 4

Step 8: Stop

BEGIN

GET n

INITIALIZE i=1

WHILE(i<=n) DO

PRINT i

i=i+1

ENDWHILE

END

Write an algorithm to print n odd numbers

Step 1: start

step 2: get n value

step 3: set initial value i=1

step 4: check if(i<=n) goto step 5 else goto step 8

step 5: print i value

step 6: increment i value by 2

step 7: goto step 4

step 8: stop

BEGIN

GET n

INITIALIZE i=1

WHILE(i<=n) DO

PRINT i

i=i+2

ENDWHILE

END

Write an algorithm to print n even numbers

Step 1: start

step 2: get n value

step 3: set initial value i=2

step 4: check if(i<=n) goto step 5 else goto step8

step 5: print i value

step 6: increment i value by 2

step 7: goto step 4

step 8: stop

BEGIN

GET n

INITIALIZE i=2

WHILE(i<=n) DO

PRINT i

i=i+2

ENDWHILE

END

Write an algorithm to print squares of a number

Step 1: start

step 2: get n value

step 3: set initial value i=1

step 4: check i value if(i<=n) goto step 5 else goto step8

step 5: print i*i value

step 6: increment i value by 1

step 7: goto step 4

step 8: stop

BEGIN

GET n

INITIALIZE i=1

WHILE(i<=n) DO

PRINT i*i

i=i+2

ENDWHILE

END

Write an algorithm to print to print cubes of a number

Step 1: start

step 2: get n value

step 3: set initial value i=1

step 4: check i value if(i<=n) goto step 5 else goto step8

step 5: print i*i *i value

step 6: increment i value by 1

step 7: goto step 4

step 8: stop

BEGIN

GET n

INITIALIZE i=1

WHILE(i<=n) DO

PRINT i*i*i

i=i+2

ENDWHILE

END

Write an algorithm to find sum of a given number

Step 1: start

step 2: get n value

step 3: set initial value i=1, sum=0

Step 4: check i value if(i<=n) goto step 5 else goto step8

step 5: calculate sum=sum+i

step 6: increment i value by 1

step 7: goto step 4

step 8: print sum value

step 9: stop

BEGIN

GET n

INITIALIZE i=1,sum=0

WHILE(i<=n) DO

sum=sum+i

i=i+1

ENDWHILE

PRINT sum

END

Write an algorithm to find factorial of a given number

Step 1: start

step 2: get n value

step 3: set initial value i=1, fact=1

Step 4: check i value if(i<=n) goto step 5 else goto step8

step 5: calculate fact=fact*i

step 6: increment i value by 1

step 7: goto step 4

step 8: print fact value

step 9: stop

BEGIN

GET n

INITIALIZE i=1,fact=1

WHILE(i<=n) DO

fact=fact*i

i=i+1

ENDWHILE

PRINT fact

END

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Problem Solving and Python Programming : Algorithmic Problem Solving : Simple Strategies For Developing Algorithms | iterations, Recursions, Syntax, Pseudo code, examples, algorithm, flow chart