12/7/19

Notes for computer science and engineering branch. Subject Computer programming through c language


UNIT: - 02

ALGORITHM FOR PROBLEM SOLVING

 02.01 Exchanging values of two variables.
02.02 Summation of a set of numbers.
 02.03 Reversing digits of an integer.
 02.04 GCD(Greatest Common Division) of two numbers.
 02.05 Test whether a number is prime or not.
 02.06 Organize numbers in ascending order.
 02.07 Find square root of a number.
02.08 Factorial computation.
 02.09 Fibonacci sequence.
02.10 Compute sine Series.
 02.11 Check whether a given num is Palindrome or not.
02.12 Find Square root of a quadratic equation.
 02.13 Multiplication of two matrices.

Q. What is an algorithm?
Answer: -
         Algorithm is a set step-by-step processor, which define a set of instructions to be executed in a certain order to get the desired output.
    1.   An algorithm is a set of rules for carrying out calculation.
    2.   It is a sequence of computational steps that transform the input into the output.

02.01 Exchanging values of two variables.

Step-1       START
Step-2       Declare variable a and b;
Step-3       Read value ‘a’
Step-4       Read value ‘b’
Step-5       temp=a;
Step-6       a=b;
Step-7       b=temp;
Step-8       Print the value of ‘a’ , ‘b’.
Step-9       END

PROGRAM: -

#include<stdio.h>
#include<conio.h>
void main()
{
         int a,b,temp;
         printf("Enter the value of a and b :-\n");
         scanf("%d %d",&a,&b);
         printf("Before Swapping a=%d, b=%d \n",a,b);
         temp=a;
         a=b;
         b=temp;
         printf("After swapping a=%d, b=%d",a,b);
         getch();
}







02.02 Summation of a set of numbers.(Sum of digits of given number)

Step-1       START
Step-2       Declare variable n,m,sum=0;
Step-3       read values n; n=m;
Step-4       while(n!=0)
                 {
                          rem=n%10;
                          sum= sum + rem;
                          n= n / 10;
                 }
Step-5       print sum
Step-6       STOP

PROGRAM: -
#include<stdio.h>
#include<conio.h>
void main()
{
         int n,sum=0,rem,m;
         printf("Enter a num: -");
         scanf("%d",&n);
         m=n;
         while(n != 0)
         {
                 rem = n % 10;
                 sum = sum + rem;
                 n=n / 10;
         }
         printf("Sum of %d num is %d",m,sum);
         getch();
}





02.03 Reversing digits of an integer.

Step-1       START
Step-2       Declare variable num, reverse =0;
Step-3       read values num
Step-4       if(num < 0)
                 {
                          printf (“-“);
                          num = -num;
                 }
Step-5       do
                  {
                          printf("%d", num % 10);
                          num = num / 10;
                  }
while(num !=0);
Step-6       STOP         

Note: - This algorithm is apply on both negative and positive number.

PROGRAM: -
#include<stdio.h>
#include<conio.h>
void main()
{
         long int num;
         printf("Enter  a number: -");
         scanf("%ld",&num);
         printf("Reverse of %d number is ",num);
         if(num < 0)
         {
                 printf("-");
                 num = -num;
         }
         do
         {
                 printf("%ld",num%10);
                 num=num/10;
         }while(num!=0);
        
         getch();
}



02.04 GCD(Greatest Common Division) of two numbers.(HCF- Highest Common Factor)

Step-1       START
Step-2       Declared variables num1, num2, gcd, i;
Step-3       Read values num1, num2;
Step-4       for(i=1; i <= num1 && i <= num2; ++i)
                 {
                             if(num1 % i ==0 && num2 % i==0)
                             gcd = i;
         }

Step-5       Display gcd;
Step-6       STOP

PROGRAM: - 

#include<stdio.h>
#include<conio.h>
void main()
{
    int num1, num2, i, gcd;
    printf("Enter two integers: ");
    scanf("%d %d", &num1, &num2);
    for(i=1; i <= num1 && i <= num2; ++i)
    {
        if(num1 % i ==0 && num2 % i==0)
            gcd = i;
    }
    printf("G.C.D of %d and %d is %d", num1, num2, gcd);
    getch();
}








02.05 Test whether a number is prime or not.

Step-1       START
Step-2       Declare variables num, i, prime;
Step-3       Initialize variables as
                 i <- 2
                 prime <- 1

Step-4       Take input from user as num
Step-5       Repeat the steps until i<(num/2)
Step-6       If remainder of num % i = 0
                 6.1    Prime <- 0
                         goto step 7
                 6.2    i++ or i <- i + 1
Step-7       if prime = 0
                          Display num is not a prime number.
                 else
                          Display num is a prime number.
Step-8       STOP

PROGRAM: - 

#include<stdio.h>
#include<conio.h>
int main()
{
    long int num;
         int prime=1, i=2;
    printf("Enter an integer: ");
    scanf("%ld", &num);
    while(i<(num/2))
    {
         if(num%i==0)
         prime=0;
         i++;
         }
         if(prime==0)
                 printf("Number %d is not a prime number",num);
         else
                 printf("Number %d is a prime number",num);
   
    getch();
}
 





02.06 Organize numbers in ascending order.

In this algorithm we are taking three inputs from user to arrange the input number into ascending order. For n numbers we have to go for shorting algorithm i.e selection short and merge short.

Algorithm will upload as soon as possible


PROGRAM: -

#include<stdio.h>
#include<conio.h>
int main()
{
int a[100],n,i,j,temp;
printf("enter array size [1-100] ");
scanf("%d",&n);
printf("enter %d integers ",n);
for(i=0;i<n;i++)
scanf("%d",&a[i]); /selection sort/
for(i=0;i<=n-2;i++)
{
for(j=i+1;j<=n-1;j++)
{
if(a[i]>a[j]) /this is ascending order/
{
temp=a[i]; a[i]=a[j]; a[j]=temp;
}
}
}
printf("sorted elements ");
for(i=0;i<n;i++)
printf("%4d",a[i]);
getch();

}

02.07 Find square root of a number.

In this we are using pre-defined function sqrt() which belong to math.h header file: -

Step-1       START
Step-2       declare variable n
Step-3       read values of n from the user
Step-4       use sqrt(n)
Step-5       print <- sqrt(n);
Step-8       STOP
PROGRAM: - 

#include<stdio.h>
#include<conio.h>
#include<math.h>
void main()
{
             int n,m;
             printf("Enter  an integer: ");
             scanf("%d",&n);
             printf(“Square root of %d is %.2f",n,sqrt(n)); 
             getch();
}
 




02.08 Factorial computation.

Step-1       START
Step-2       Declare variables num, temp;
Step-3       declare one more variable as long fact
Step-4       initialize fact<-1
Step-5       copy num <- temp;
Step-6       while(num>=1)
                 {
                          fact=fact*num;
                          num--;
                 }
Step-7       display the factorial i.e. fact           
Step-8       STOP

PROGRAM: - 

#include<stdio.h>
#include<conio.h>
void main()
{
             int num,temp;
             long fact=1;
             printf("Enter  an integer: ");
             scanf("%d",&num);
             temp=num;
             while(num>=1)
             {
                 fact=fact*num;
                 num--;
             }
             printf("%d factorial is %d",temp,fact); 
             getch();
}






02.09 Fibonacci sequence.

Step-1       START
Step-2       Declare variables num, f1, f2, f3
Step-3       initialize f1 <- 0, f2 <- 1;
Step-4       read values of num from user
Step-5       check below condition: -
                 if(num <=0)
                 printf("Series not possible");
                 else if(num==0)
                 printf("0");
Step-6       before displaying the series display 0, 1
Step-7       the below loop is used to find the Fibonacci series
                 for(i=3; i<=num; i++)
                 {                        
                          f3=f1+f2;
                          printf(", %d",f3);
                          f1=f2;
                          f2=f3;
                 }
Step-8       STOP

PROGRAM: -

#include<stdio.h>
#include<conio.h>
void main()
{
             int num,i,f1,f2,f3;
             f1=0;
             f2=1;
             printf("Enter  an integer: ");
             scanf("%d",&num);
             if(num <=0)
             printf("Series not possible");
             else if(num==0)
             printf("0");
             else
             {
                 printf("Series is=0, 1");
                 for(i=3; i<=num; i++)
                 {
                          f3=f1+f2;
                          printf(", %d",f3);
                          f1=f2;
                          f2=f3;
                 }
             }
             getch();
 }





02.10 Compute sine Series.
Sine Series:
 Series which is used to find the value of Sin(x) is known as sine series.
In which, x is the angle in degree i.e. converted into Radian.
The following formula is used to express the value of sin(x) as sine series: -
 
Expanding the above notation, the formula of Sine Series is
For example,
 Let the value of be 30.
 
So, Radian value for 30 degree is 0.52359.
So, the value of Sin(30) is 0.5.

Step-1       START
Step-2       Declare variables i, x, sum, t
Step-3       read the values of x from the user
Step-4       Convert x value into radian
                 x=x*3.14159/180;

Step-5       initialize t <- x and sum <- x
Step-6           /* Loop to calculate the value of Sine */
                      for(i=1;i<=2;i++)
                     {
                        t=(t*(-1)*x*x)/(2*i*(2*i+1));
                       sum=sum+t;
                      }
Step-7       display the sum as sin(x) values    
Step-8       STOP

PROGRAM: -

#include<stdio.h>
#include<conio.h>
int main()
{           
    int i;
    float x, sum, t;
    printf(" Enter the value for x : ");
    scanf("%f",&x);
    x=x*3.14159/180;
    t=x;
    sum=x;
    /* Loop to calculate the value of Sine */
    for(i=1;i<=2;i++)
    {
        t=(t*(-1)*x*x)/(2*i*(2*i+1));
        sum=sum+t;
    }
    printf(" The value of Sin(%f) = %.4f",x,sum);
    getch();
}







02.11 Check whether a given num is Palindrome or not.

Step-1       START
Step-2       declares variable num, m, rev and r;      
Step-3       read values of num from the user
Step-4       initialized m <- n and rev <- 0
Step-5       while(num!=0)
                  {
                           r=num % 10;
                           rev = rev * 10 + r;
                          num = num / 10;
                  }

Step-6       if (m== rev)
                  {
                          printf("The entered integer is a palindrome");
                  }      
Step-7       else
                  {
                          printf("The entered integer is not a palindrome");
                  }

Step-8       STOP

PROGRAM: -

#include<stdio.h>
#include<conio.h>
void main()
{
         long num, m, rev=0;
         int r;
         printf("Enter an integer:");
         scanf("%d",&num);
         m=num;
         while(num!=0)
         {
                 r=num % 10;
                 rev = rev * 10 + r;
                 num = num / 10;
         }
         if (m== rev)
         {
                 printf("The %d integer is a palindrome", num);
         }    
         else
         {
                 printf("The %d integer is not a palindrome", num);
         }
         getch();
 }





02.12 Find Square root of a quadratic equation.

Step-1       START
Step-2       declare variables a, b, and c 
Step-3       read values of a, b and c
Step-4       if a =0 go to step-9
Step-5       calculate value of discriminate=b*b – 4*a*c
Step-6       From step-6 to step-8 we will find the nature of discriminate
                 if(discriminate > 0)
   {
                  root1 = (-b + sqrt(discriminate)) / (2*a);
                 root2 = (-b - sqrt(discriminate)) / (2*a);
 printf("Two distinct and real roots exists: %.2f and %.2f", root1, root2);
             }
Step-7       else if(discriminate == 0)
    {
                   root1 = root2 = -b / (2 * a);
  printf("Two equal and real roots exists: %.2f and %.2f", root1, root2);
            }

Step-8   else if(discriminate < 0)
          {
              root1 = root2 = -b / (2 * a);
                imaginary = sqrt(-discriminate) / (2 * a);

                printf("Two distinct complex roots exists: %.2f + i%.2f and %.2f i%.2f",
                root1, imaginary, root2, imaginary);
             }
Step-9   STOP

PROGRAM: -

#include <stdio.h>
#include<conio.h>
#include <math.h> /* Used for sqrt() */
int main()
{
    float a, b, c;
    float root1, root2, imaginary;
    float discriminate;
   
    printf("Enter values of a, b, c of quadratic equation (aX^2 + bX + c): ");
    scanf("%f%f%f", &a, &b, &c);
   
    /* Find discriminate of the equation */
    discriminate = (b * b) - (4 * a * c);
   
  
    /* Find the nature of discriminate */
    if(discriminate > 0)
    {
        root1 = (-b + sqrt(discriminate)) / (2*a);
        root2 = (-b - sqrt(discriminate)) / (2*a);

        printf("Two distinct and real roots exists: %.2f and %.2f", root1, root2);
    }
    else if(discriminate == 0)
    {
        root1 = root2 = -b / (2 * a);

        printf("Two equal and real roots exists: %.2f and %.2f", root1, root2);
    }
    else if(discriminate < 0)
    {
        root1 = root2 = -b / (2 * a);
        imaginary = sqrt(-discriminate) / (2 * a);

        printf("Two distinct complex roots exists: %.2f + i%.2f and %.2f - i%.2f",
                root1, imaginary, root2, imaginary);
    }

    getch();
}










02.13 Multiplication of two matrices.

Step-1       START
Step-2       declare variables a[100][100], b[100][100], nr, nc, r, c, k;
Step-3       read values of nr, nc, a[100], b[100][100] from users
Step-4       Use this for loop for performing matrix multiplication          
                      for(r=0;r<nr; r++)
                   {        
                          for(c=0;c<nc; c++)
                   {
                           int s=0;
                           for(k=0;k<nr; k++)
                   {
                           s=s+a[r][k]*b[k][c];
                   }
                           printf("%4d",s);
                   }
                          printf("\n");
                                                                   
                   }
Step-5       STOP

PROGRAM: -      

#include<stdio.h>
#include<conio.h>
int main()
{
int a[100][100], b[100][100],nr,nc,r, c, k;
printf("Enter Number of rows and columns of matrix-a and matrix-b:-");
                   scanf("%d %d",&nr,&nc);
                   printf("enter %d integers for a - matrix ", nr*nc);
                   for(r=0; r<nr; r++)
                   for(c=0; c<nc;c++)
                   scanf("%d",&a[r][c]);
                   printf("enter %d integers for b- matrix", nr*nc);
                   for(r=0; r<nr; r++)
                   for(c=0; c<nc;c++)
                   scanf("%d",&b[r][c]);
                   puts(" Multiplications of matrixes are: -");
                   for(r=0;r<nr;r++)
                   {        
                          for(c=0;c<nc;c++)
                   {
                           int s=0;
                           for(k=0;k<nr;k++)
                   {
                           s=s+a[r][k]*b[k][c];
                   }
                           printf("%4d",s);
                   }
                          printf("\n");
                                                                   
                   }
                   getch();
}


















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