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/* Matrix Commutation test */ #include <stdio.h> #include <math.h> #include <stdlib.h> int main() { int i,j,n,m,p,k,a[20][20],b[20][20],e[20][20],g[20][20], flag=1; printf( "Enter the order of the matrix A:\n" ); scanf( "%d%d" , &m ,&n); printf( "Enter the order of the matrix B:\n" ); scanf( "%d%d" , &n, &p); printf( "Enter the elements of the matrix A:\n" ); for (i=0;i<m;i++) { for (j=0;j<n;j++) scanf( "%d" , &a[i][j]); printf( "\n" ); } printf( "Enter the elements of the matrix B:\n" ); for (i=0;i<n;i++) { for (j=0;j<p;j++) scanf( "%d" , &b[i][j]); printf( "\n" ); } /*matrix multiplication AB */ for (i=0;i<m;i++) { for (j=0;j<p;j++) { e[i][j]=0; for (k=0;k<n;k++) e[i][j]=e[i][j]+a[i][k]*b[k][j]; } } printf( "Product matrix AB...

/* Monte carlo random dot method */ #include <stdio.h> #include <stdlib.h> #include <math.h> #define a 1 #define b 2 #define cycle 5000 int main() { int counter=0, r1, r2, ymax, i, y; float f, A; ymax=3*2*2; for (i=0;i<cycle;i++) { r1=a+rand()%ymax; y=3*r1*r2; r2=rand()%ymax; if (y>=r2) counter++; } f=( float )counter/( float )cycle; A=f*( float )ymax*(( float )b-( float )a); printf( "The required integration is %f" , A); return (0); }

/* To find the area of a unit circle by Monte Carlo random dot method */ #include <stdio.h> #include <math.h> int main() { float x, y, r, sqr, ratio; float xmax=2, ymax=2, h=0.0005, k=0.0005, area, rad=1; float cnt_tot=0, cnt_acc=0, cnt_rej=0; for (x=0;x<=ymax;x+=h) { for (y=0;y<=ymax;y+=k) { sqr=(x-1)*(x-1)+(y-1)*(y-1); r=sqrt(sqr); if (r<=rad) { cnt_acc+=1; } else { cnt_rej+=1; } } } cnt_tot=cnt_acc+cnt_rej; printf( "Total random number of dots generated=%f" , cnt_tot); ratio=cnt_acc/cnt_tot; printf( "\nRatio=%f" , ratio); area=ratio*ymax*xmax; printf( "\nTotal area=%f" , ymax*xmax); printf( "\nArea of the circle = (Ratio) X (Total area)" ); printf( "\nArea of the circle = %f" ,area); return (0); }

/* Multiplication of two matices */ #include <stdio.h> #include <math.h> int main() { int i, j, n, m, p, k, a[20] [20], b[20] [20], e[20] [20]; printf( "Enter order of the matrix A(mxn):\n" ); scanf( "%d%d" , &m, &n); printf( "Enter order of the matrix B(nxp):\n" ); scanf( "%d%d" , &n, &p); printf( "Enter the elements of matrix A:\n" ); for (i=0;i<m;i++) { for (j=0;j<n;j++) scanf( "%d" , &a[i] [j]); printf( "\n" ); }     printf( "Entered Matrix A:\n" );     for (i=0;i<m;i++) { for (j=0;j<n;j++) printf( "%10d" ,a[i] [j]); printf( "\n" ); } printf( "\nEnter the elements of matrix B:\n" ); for (i=0;i<n;i++) {     for (j=0;j<p;j++) scanf( "%d" , &b[i] [j]); printf( "\n" ); } printf( "Entered Matrix B:\n" );     for (i=0;i...

/* Trace of a matrix */ #include <stdio.h> #include <math.h> int main() { int i, j, n, m,  a[20] [20], sum=0; printf( "Enter the order of matrix (mxn):\n" ); scanf( "%d%d" , &m, &n); printf( "Enter the elements of the matrix:\n" ); for (i=0;i<m;i++) { for (j=0;j<n;j++)        { scanf( "%d" , &a[i] [j]);        } } printf( "your matrix:\n" ); for (i=0;i<m;i++) {     for (j=0;j<n;j++)     { printf( "%20d" ,a[i][j]); } printf( "\n" ); } for (i=0;i<m;i++) { for (j=0;j<n;j++) { if (i==j) sum=sum+a[i][j];         }     }     printf( "\n\ntrace of the matrix=%d\n" ,sum); return (0); }

/* Transpose of a matrix */ #include <stdio.h> #include <math.h> int main() { int matrix[10][10], transpose[10][10]; int m, n, c, r; printf( "Enter the number of rows and columns of matrix:\n" ); scanf( "%d%d" , &m, &n); printf( "Enter the %d elements of matrix:\n" , m*n); for (r=0;r<m;r++) { for (c=0;c<n;c++) { printf( "\nEnter value in %dth row and %dth column:" , r+1, c+1); scanf( "%d" , &matrix[r][c]); } } printf( "your matrix:\n" ); for (r=0;r<m;r++) { for (c=0;c<n;c++) { printf( "%10d" , matrix[r][c]); } printf( "\n\n" ); } for (r=0;r<m;r++) { for (c=0;c<n;c++) { transpose[c][r]=matrix[r][c]; } } printf( "Transpose of entered matrix :\n" ); for (r=0;r<n;r++) { for (c=0;c<m;c++) { printf( "%10d" , transpose[r][c]); } printf( ...

/* Addition and subtraction of two matrices */ #include <stdio.h> #include <math.h> int main() { int i, j, n, m, a[20] [20], b[20] [20], c[20] [20], d[20] [20]; printf( "Enter order of the matrices:\n" ); scanf( "%d%d" , &m, &n); printf( "Enter the elements of matrix A:\n" ); for (i=0;i<m;i++) { for (j=0;j<n;j++) scanf( "%d" , &a[i] [j]); printf( "\n" ); }     printf( "Entered Matrix A:\n" );     for (i=0;i<m;i++) { for (j=0;j<n;j++) printf( "%10d" ,a[i] [j]); printf( "\n" ); } printf( "\nEnter the elements of matrix B:\n" ); for (i=0;i<m;i++) {     for (j=0;j<n;j++) scanf( "%d" , &b[i] [j]); printf( "\n" ); } printf( "Entered Matrix B:\n" );     for (i=0;i<m;i++) { for (j=0;j<n;j++) printf( "%10d" ,b[i] [j]); printf( ...

/*To integrate a fn. by Simpson's 1/3 Rule*/ #include <stdio.h> #include <math.h> /*Define your function here*/ float f( float x) { float d; d=x/1+x; return (d); } int main () { /*denoting a and b as integral lower and upper limits respectively*/ float a, b, h, s; int i, n; printf( "Input values of a, b and no. of steps:\n" ); scanf( "%f%f%d" ,&a,&b,&n); h=(b-a)/n; s=f(a)+f(b)+4*f(a+h); for (i=3;i<=n-1;i=i+2) { s=s+4*f(a+i*h)+2*f(a+(i-1)*h); } s=(h/3)*s; printf( "\nValue of the integral =%f" ,s); return (0); }

/* Integration of a function by Trapezoidal rule */ #include <stdio.h> #include <math.h> /*define your function here*/ float y( float x) { return x/1+x; } int main() { float a, b, h, s; int i, n; printf( "Enter a, b and no. of subintervals:\n" ); scanf( "%f%f%d" , &a, &b, &n); h=(b-a)/n; s=y(a) + y(b); for (i=0;i<n;i++) { s=2*y(a+i*h); } printf( "Value of integral is %f" ,(h/2)*s); return (0); }

/*Mean, Median and Mode calculation*/ #include <stdio.h> #include <math.h> int main() { int i,j,n; float a[100],t,sum=0.0,mean,median,mode; printf( "Number of data:" ); scanf( "%d" ,&n); printf( "Type the input data:\n" ); for (i=0;i<n;i++) { scanf( "%f" ,&a[i]); sum=sum+a[i]; } mean=sum/n; printf( "Mean=%f\n" ,mean); /*sorting of the array*/ for (j=0;j<n;j++) { for (i=0;i<n;i++) { if (a[i]>a[j]) { t=a[i]; a[i]=a[j]; a[j]=t; } } } if (n%2==0) median=(a[n/2]+a[(n-2)/2])/2; else median=a[(n-1)/2]; mode=3*median-2*mean; printf( "Median=%f\n" ,median); printf( "Mode=%f\n" ,mode); return (0); }

/* Solution of an algebraic equation x*x-n=0 by Newton-Raphson method */ #include <stdio.h> #include <math.h> int main() { int count=0; float x0, xn, fx, dfx, n; printf( "Enter the number whose sq. root is required:" ); scanf( "%f" , &n); printf( "Initial guess value x0:" ); scanf( "%f" , &x0); /* Iteraion begins */ label: fx=x0*x0-n; dfx=2*x0; xn=x0-fx/dfx; if (fabs(xn-x0)<0.0001) printf( "The square root of %f is:%f" , n, xn); else { x0=xn; count=count+1; if (count>100) printf( "Solution does not converge" ); else goto label; } return (0); }

/* Solution of an algebraic equation x^5+3x^2-10=0 by Newton-Raphson method */ #include<stdio.h> #include<math.h> int main() {     int count=0;     float x0, xn, fx, dfx;     printf("Initial guess value x0:");     scanf("%f", &x0);     /* Iteraion begins */     label:         fx=pow(x0,5)+3*x0*x0-10;         dfx=5*pow(x0,4)+6*x0;         xn=x0-fx/dfx;         if(fabs(xn-x0)<0.0001)         printf("The final root is:%f\n",xn);         else         {             x0=xn;             count=count+1;             if(count>100)    ...

/* Least Square Fit */ #include<stdio.h> #include<math.h> int main() {     int i, n;     float m, c, X[50], Y[50], Sx=0, Sy=0, Sxy=0, Sx2=0;     printf("Enter the no. of input data=");     scanf("%d", &n);     printf("\n Enter the values of x:\n");     for (i=0;i<n;i++)     {         scanf("%f", &X[i]);     }     printf("\n Enter the values of y:\n");     for (i=0;i<n;i++)     {     scanf("%f", &Y[i]);     }     for (i=0;i<n;i++)     {         Sx=Sx+X[i];         Sy=Sy+Y[i];         Sx2=X[i]*X[i];         Sxy=Sxy+X[i]*Y[i];         }     m=(...

/*Selection Sort*/ #include<stdio.h> #include<math.h> int main() {     int n,i,j,position,swap;     float a[100];     printf("enter no. of elements:");     scanf("%d",&n);     printf("enter %d numbers:\n",n);     for(i=0;i<n;i++)     scanf("%f",&a[i]);     for(i=0;i<n-1;i++)     {         position=i;         for(j=i+1;j<n;j++)         {             if(a[position]>a[j])             position=j;         }         if(position!=i)         {             swap=a[i];       ...

/*Solution of a quadratic equation*/ #include<math.h> #include<stdio.h> int main() {     float a, b, c, d, x1, x2, rp, imp; /*consider the quadratic equation as ax^2+bx+c=0*/     printf("Enter the values of a:");     scanf("%f", &a);     printf("Enter the values of b:");     scanf("%f", &b);     printf("Enter the values of c:");     scanf("%f", &c);     d=b*b-4*a*c;     printf("\n The value of discriminant is : %f",d);     if(d>=0)     {         printf("\n The root is real");         x1=(-b+sqrt(d))/(2*a);         x2=(-b-sqrt(d))/(2*a);         printf("\n The 1st root is: %f", x1);         printf("\n The 2nd root is: %f\n", x2);     } ...

/* To arrange the series in descending order */ #include<stdio.h> #include<math.h> int main() {     int i, j, n;     float A[50], t;     printf("Input the no. of data:");     scanf("%d",&n);     printf("\nEnter the data:\n");     for(i=0;i<n;i++)     scanf("%f",&A[i]);     for(i=0;i<n;i++)     {         for(j=0;j<n-1;j++)         {             if(A[i]>A[j])             {                 t=A[i];                 A[i]=A[j];                 A[j]=t;       ...

/* To arrange the series in ascending order */ #include<stdio.h> #include<math.h> int main() {     int i, j, n;     float A[50], t;     printf("Input the no. of data:");     scanf("%d",&n);     printf("\nEnter the data:\n");     for(i=0;i<n;i++)     scanf("%f",&A[i]);     for(i=0;i<n;i++)     {         for(j=0;j<n-1;j++)         {             if(A[i]<A[j])             {                 t=A[i];                 A[i]=A[j];                 A[j]=t;       ...

/*To expand (1+x)^m series*/ #include<stdio.h> #include<math.h> int main() {     float sum, term, x;     int n, i, m;     printf("Enter the values of x & No. of countable terms(n):\n");     scanf("%f %d", &x, &n);     printf("Enter the power(m):");     scanf("%d", &m);     sum=1+m*x;         term=m*x;            for(i=1;i<=(n-1);i++)     {         term =term*x*(m-i)/(i+1);         sum=sum+term;     }     printf("\n(1+(%f))^%d=%f \n", x, m, sum);     return(0); }

/*To expand (1-x)^m series*/ #include<stdio.h> #include<math.h> int main() {     float sum, term, x;     int n, i, m;     printf("Enter the values of x & No. of countable terms(n):\n");     scanf("%f %d", &x, &n);     printf("Enter the power(m):");     scanf("%d", &m);     sum=1-m*x;     term=-m*x;            for(i=1;i<=(n-1);i++)     {         term =-term*x*(m-i)/(i+1);         sum=sum+term;     }     printf("\n(1-(%f))^%d=%f \n", x, m, sum);     return(0); }

/* To evaluate the value of e^-x */ #include<stdio.h> #include<math.h> int main() {     float  sum, t;     int i, x;     printf("Value of x:\n");     scanf("%d", &x);     sum=1.0;     t=1;     i=0;     label:         i=i+1;         t=-t*x/i; /*Setting a predefined accuracy=0.00001*/         if(fabs(t)>0.00001)     {         sum=sum+t;         goto label;     }     else     printf("e^-%d=%f\n", x, sum);     return(0); }

/* To evaluate the value of e^x */ #include<stdio.h> #include<math.h> int main() {     float  sum, t;     int i,x;     printf("Value of x:\n");     scanf("%d", &x);     sum=1.0;     t=1;     i=0;     label:         i=i+1;         t=t*x/i; /*Setting a predefined accuracy=0.00001*/         if(fabs(t)>0.00001)     {         sum=sum+t;         goto label;     }     else     printf("e^%d=%f\n", x, sum);     return(0); }

/* To evaluate the value of Cosx */ #include<stdio.h> #include<math.h> int main() {     int i, n;     float x, sum, t, x1; /*n=counting upto n terms in expansion of cosx series*/     printf("Enter the value of x in degree & n:\n");     scanf("%f%d", &x, &n);         x1=x; /*To convert the angle from degree to Radian*/     x=x*3.14159/180;     sum=1;     t=1;     for(i=1;i<=(n-1);i++)     {         t=-t*x*x/((2*i-1)*2*i);         sum=sum+t;     }     printf("Cos(%f)=%f\n",x1,sum);     return(0); }

 In the program below, we will learn about how the if-else statement works. I wanted to calculate 4th power of a given number if and only if it is greater than 2, else if the value of given number lowers than and equal to 2, it always shows result by adding up with 3.         /*To verify the if else statement */         #include<stdio.h>         #include<math.h>         int main()         {             float a, b;             printf("Enter the value of a:");             scanf("%f", &a);             if (a>2)             b=pow(a,4);          ...

In the program below, we will learn about how the if statement works. I wanted to calculate square root value of a given number if and only if it is greater than equal to zero. If, however, the value of given number lowers than zero, it always print a zero.            /*To verify the if statement */         #include<stdio.h>         #include<math.h>         int main()         {             float a, b;             printf("Enter the value of a:");             scanf("%f", &a);             if (a>=0)             b=sqrt(a);             printf("\n The square r...

/*To find area of the triangle*/ #include<math.h> #include<stdio.h> int main() {     int a, b;     float area;     printf("Enter the value of height: ");     scanf("%d", &a);     printf("Enter the value of base: ");     scanf("%d", &b);     area=.5*a*b;     printf("\n The area of the triangle is: %f\n",area);     return(0); }

/*Sum of infinite series with specified accuracy*/ #include<stdio.h> #include<math.h> int main() {     int i;     float x, sum, t, x1;     printf("Value of x in degrees:");     scanf("%f",&x);     x1=x;     x=x*3.14159/180;     sum=x;     t=x;     i=1;     label: i=i+2;     t=(-t)*x*x/(i*(i-1));     if (fabs (t)>0.00001)     {         sum=sum+t;         goto label;     }     else     printf("sin(%f)=%f\n",x1,sum);     return(0); }

/*To Convert given temperature from celsius to fahrenheit*/ #include<math.h> #include<stdio.h> int main() {     float C, F;     printf("Enter the value of temperature in celsius:");     scanf("%f", &C);     F=(C+17.776)/.5555;     printf("The value of temperaure in fahrenheit: %f\n",F);     return(0); }

/*To find the area of a circle having finite radius*/ #include<stdio.h> #include<math.h> int main() { float a, area; printf("Enter the value of Radius: "); scanf("%f", &a); area=3.1415927*a*a; printf("\n The area of the circle is: %f\n",area); return(0); }

/* Bubble Sort */ #include<stdio.h> #include<math.h> int main() {     float a[100], temp;     int i, j, n;     printf("Enter the # of elements are to be sorted:");     scanf("%d", &n);     printf("---: Put value of the elements :---\n");     for(i=0;i<n;i++)     {         scanf("%f", &a[i]);     }     for(i=0;i<n;i++)     {         for(j=0;j<n-i-1;j++)         {             if(a[j]>a[j+1])             {                 temp=a[j];                 a[j]=a[j+1];           ...

/* To find angle between two vectors */ #include<stdio.h> #include<math.h> int main() {     float ax, ay, az, bx, by, bz, AdotB, ModA, ModB, ModAModB, AngleAB;     printf("Enter the values of ax, ay, az:\n");     scanf("%f%f%f", &ax, &ay, &az);     printf("A=(%f)i+(%f)j+(%f)k", ax, ay, az);     printf("\nEnter the values of bx, by, bz:\n");     scanf("%f%f%f", &bx, &by, &bz);     printf("B=(%f)i+(%f)j+(%f)k", bx, by,bz);     AdotB=ax*bx+ay*by+az*bz;     printf("\nA.B=%f", AdotB);     ModA=sqrt(ax*ax+ay*ay+az*az);     ModB=sqrt(bx*bx+by*by+bz*bz);     ModAModB=ModA*ModB;     AngleAB=AdotB/ModAModB;     AngleAB=AngleAB*180/3.14159;     printf("\nAngle between A and B in degree is  Cos/_A,B=%f\n", AngleAB);     r...

/* To determine dot product, cross product and resultant of two vectors */ #include<stdio.h> #include<math.h> int main() {     float a1, a2, a3, b1, b2, b3, AdotB, AXBx, AXBy, AXBz, AplusBx, AplusBy, AplusBz;     printf("Enter the 1st vector components:\n");     scanf("%f%f%f", &a1, &a2, &a3);     printf("Enter the 2nd vector components:\n");     scanf("%f%f%f", &b1, &b2, &b3);     AdotB=a1*b1+a2*b2+a3*b3;     AXBx=(a2*b3-a3*b2);     AXBy=(a3*b1-a1*b3);     AXBz=(a1*b2-a2*b1);     AplusBx=(a1+b1);     AplusBy=(a2+b2);     AplusBz=(a3+b3);     printf("The dot product of the vectors is: A.B=%f", AdotB);     printf("\nThe cross product of the vectors is: AXB=%fi+%fj+%fk", AXBx, AXBy, AXBz);     printf("\nThe resultant of the vectors...

/* Sum of GP series term by term */ #include<stdio.h> #include<math.h> int main() {     float a, r, sum=0;     int n, i;     printf("Enter the values of a, r, n:\n");     scanf("%f%f%d", &a, &r, &n);     for(i=0;i<=n;i++)     {         sum=sum+a*pow(r,i);     }     printf("Sum of GP series:%f\n", sum);     return(0); }

Factorial of n is the product of all positive descending integers. Factorial of n is denoted by n!. For example: 5! = 5*4*3*2*1 = 120   3! = 3*2*1 = 6   Here, 5! is pronounced as "5 factorial", it is also called "5 bang" or "5 shriek". The factorial is normally used in Combinations and Permutations (mathematics).  /* To find factorial of a integer */ #include<math.h> #include<stdio.h> int main() {     int n, i, fact=1;     printf("Enter the No.:");     scanf("%d", &n);     for (i=1;i<=n;i++)     fact=fact*i;     printf("\n The factorial of %d is : %d\n", n,fact);     return(0); }

Comparing two integer variables is one of the simplest programs you can write at ease. In this program, you can either take input from user using  scanf()  function or statically define in the program itself. We expect it to be a simple program for you as well. We are just comparing two integer variables.  /*To evaluate greater or lesser numbers*/ #include<math.h> #include<stdio.h> int main() {     float x, y;     printf("Enter the value of x:");     scanf("%f", &x);     printf("Enter the value of y:");     scanf("%f", &y);     if(x==y)     printed("x is equal to y\n");     elseif(x>y)     printf("x is greater than y\n");     else     printf("y is greater than x\n");     return(0); } Output: