Matrix Operations

/* Subhranath Chunder - Matrix Operations */

/* A program to implement the following operation on two matrices:
   a. Addition
   b. Multiplication
   c. Transposition
   d. Determinant */

#include<stdio.h>
#include<conio.h>
#include<math.h>

/* Function declarations */
void print(int[][100],int,int);
void add(int[][100],int,int,int[][100],int,int);
void multiply(int[][100],int,int,int[][100],int,int);
void transpose(int[][100],int,int);
int determinant(int[][100],int);

/* Main Program */
void main()
{
   int inp1[100][100],inp2[100][100],m1,n1,m2,n2,i,j,option=0;
   clrscr();

   /* The values of the matrices are accepted */
   printf("Enter the dimensions of the first matrix in the form mXn: ");
   scanf("%dX%d",&m1,&n1);
   printf("Enter the values of the first matrix:\n");
   for(i=0;i<m1;++i)
   {
      for(j=0;j<n1;++j)
         scanf("%d",&inp1[i][j]);
   }
   printf("\n\nEnter the dimensions of the second matrix in the form mXn: ");
   scanf("%dX%d",&m2,&n2);
   printf("Enter the values of the second matrix:\n");
   for(i=0;i<m2;++i)
   {
      for(j=0;j<n2;++j)
         scanf("%d",&inp2[i][j]);
   }

   /* Main Menu - where the user chooses what he wants to do */
   while(option==0)
   {
      clrscr();
      printf("You can perform the following operations on the matrices:\n\n1. Addition\n2. Multiplication\n3. Transposition\n4. Determinant\n5. Exit\n\nEnter Choice: ");
      scanf("%d",&option);
      clrscr();

      /* Performs addition on the two matrices */
      if(option==1)
      {
         add(inp1,m1,n1,inp2,m2,n2);
         getch();
      }

      /* Performs multiplication on the two matrices */
      if(option==2)
      {
         multiply(inp1,m1,n1,inp2,m2,n2);
         getch();
      }

      /* Transposes a specified matrix */
      while(option==3)
      {
         printf("Which matrix would you like to transpose?\n\n1. First Matrix\n2. Second Matrix\n\nEnter Choice: ");
         scanf("%d",&option);
         clrscr();
         if(option==1 || option==2)
         {
            if(option==1)
               transpose(inp1,m1,n1);
            if(option==2)
               transpose(inp2,m2,n2);
            getch();
         }
         else
            option=3;
      }

      /* Finds the determinant of a specified matrix */
      while(option==4)
      {
         printf("Find the determinant of which matrix?\n\n1. First Matrix\n2. Second Matrix\n\nEnter Choice: ");
         scanf("%d",&option);
         clrscr();
         if(option==1 || option==2)
         {
            if(option==1)
            {
               if(m1==n1)
                  printf("The determinant of the matrix is: %d",determinant(inp1,m1));
               else
                  printf("The derterminant of the matrix cannot be determined.");
            }
            if(option==2)
            {
               if(m2==n2)
                  printf("The determinant of the matrix is: %d",determinant(inp2,m2));
               else
                  printf("The derterminant of the matrix cannot be determined.");
            }
            getch();
         }
         else
            option=4;
      }

      /* Exits the program */
      if(option==5)
         break;

      /* Returns the control back to main menu */
      option=0;
   }
}
/* Main Program Ends */

/* Performs addition on the two specified matrices */
void add(int arr1[][100],int m1,int n1,int arr2[][100],int m2,int n2)
{
   int arr3[100][100],i,j;
   if(m1==m2 && n1==n2)
   {
      for(i=0;i<m1;++i)
      {
         for(j=0;j<n1;++j)
            arr3[i][j]=arr1[i][j]+arr2[i][j];
      }
      printf("The sum of the two matrices is given below:\n\n");
      print(arr3,m1,n1);
   }
   else
      printf("The matrices cannot be added");
}

/* Performs multiplication on the two specified matrices */
void multiply(int arr1[][100],int m1,int n1,int arr2[][100],int m2,int n2)
{
   int arr3[100][100],i,j,k;
   if(n1==m2)
   {
      for(i=0;i<m1;++i)
      {
         for(j=0;j<n2;++j)
         {
            arr3[i][j]=0;
            for(k=0;k<n1;++k)
               arr3[i][j]+=arr1[i][k]*arr2[k][j];
         }
      }
      printf("The product of the two matrices is given below:\n\n");
      print(arr3,m1,n2);
   }
   else
      printf("The matrices cannot be multiplied");
}

/* Transposes a specified matrix */
void transpose(int arr[][100],int m,int n)
{
   int arr2[100][100],i,j;
   for(i=0;i<m;++i)
   {
      for(j=0;j<n;++j)
         arr2[j][i]=arr[i][j];
   }
   printf("The transpose of the matrix is given below:\n\n");
   print(arr2,n,m);
}

/* Finds the determinant of a specified matrix */
int determinant(int arr[][100],int n)
{
   int temp[100][100],a,b,result=0,i,j,k;
   if(n==1)
      return(arr[0][0]);
   else
   {
      for(i=0;i<n;++i)
      {
         a=0;
         b=0;
         for(j=1;j<n;++j)
         {
            for(k=0;k<n;++k)
            {
               if(k!=i)
               {
                  temp[a][b]=arr[j][k];
                  ++b;
               }
            }
            b=0;
            ++a;
         }
         result+=arr[0][i]*determinant(temp,n-1)*pow(-1,i);
      }
   }
   return result;
}

/* Prints a matrix of specified dimension */
void print(int arr[][100],int m,int n)
{
   int i,j;
   for(i=0;i<m;++i)
   {
      for(j=0;j<n;++j)
         printf("%d\t",arr[i][j]);
      printf("\n");
   }
}

A program demonstrating various operations on integer array

/* Subhranath Chunder - A program demonstrating various operations on integer array */

#include<stdio.h>
#include<conio.h>

/* Funtion declarations */
void printarray1(int[],int);
void printarray2(int[],int);
int maximum(int[],int);
int minimum(int[],int);
void ascend(int[],int);
void descend(int[],int);
int search(int,int[],int);
void insertion(int,int,int[],int);
void deletion(int,int[],int);
void merge(int,int[],int,int[]);
void reverse(int,int[]);

/* Main Program */
void main()
{
   int inp[100],n,option=0,i,temp1,temp2;
   clrscr();

   /* User inputs the elements of the array */
   printf("Enter the no. of elements you would like to enter: ");
   scanf("%d",&n);
   printf("\nEnter the numbers: ");
   for(i=0;i<n;++i)
      scanf("%d",&inp[i]);

   /* Main Menu - where the user chooses what he wants to do */
   while(option==0)
   {
      clrscr();
      printf("You can perform the following options on the array.\n\n1. Find the maximum and minimum elements.\n2. Sort.\n3. Search.\n4. Insertion.\n5. Deletion.\n6. Merging.\n7. Reversing.\n8. Exit\n\nEnter your option: ");
      scanf("%d",&option);

      /* Shows the maximum and minimum element of the array */
      if(option==1)
      {
         clrscr();
         printf("The maximum element of the array is: %d",maximum(inp,n));
         printf("\n\nThe minimum element of the array is: %d",minimum(inp,n));
         getch();
         option=0;
      }

      /* Sort the array either in ascending or descending order */
      while(option==2)
      {
         clrscr();
         printf("Sort the array:\n\n1. In Ascending Order.\n2. In Descending Order.\n\nEnter Choice: ");
         scanf("%d",&option);
         if(option==1 || option==2)
         {
            if(option==1)
               ascend(inp,n);
            if(option==2)
               descend(inp,n);
            printarray2(inp,n);
            getch();
            option=0;
         }
         else
            option=2;
      }

      /* Provides the option to search for the position of an element in the array */
      if(option==3)
      {
         clrscr();
         printf("Enter the value of the element you want to search: ");
         scanf("%d",&temp1);
         temp2=search(temp1,inp,n);
         if(temp2==-1)
            printf("\n\nValue not found.");
         else
            printf("\n\n%d was found at the following position: %d",temp1,temp2);
         getch();
         option=0;
      }

      /* Inserts an element at any user defined position of the array */
      if(option==4)
      {
         clrscr();
         printarray1(inp,n);
         printf("\n\nEnter the position of the array where you want to insert a new element: ");
         scanf("%d",&temp1);
         printf("\nEnter the element: ");
         scanf("%d",&temp2);
         insertion(temp2,temp1,inp,n);
         ++n;
         printarray2(inp,n);
         getch();
         option=0;
      }

      /* Removes an element from any given position of the array */
      if(option==5)
      {
         clrscr();
         printarray1(inp,n);
         printf("\n\nEnter the position of the element that you want to delete: ");
         scanf("%d",&temp1);
         deletion(temp1,inp,n);
         --n;
         printarray2(inp,n);
         getch();
         option=0;
      }

      /* Merges a set of elements with the existing array */
      if(option==6)
      {
         int inp2[100];
         clrscr();
         printarray1(inp,n);
         printf("\n\nEnter the no elements you would like to merge with the existing array: ");
         scanf("%d",&temp1);
         printf("Enter the elements: ");
         for(i=0;i<temp1;++i)
            scanf("%d",&inp2[i]);
         merge(n,inp,temp1,inp2);
         n=n+temp1;
         printarray2(inp,n);
         getch();
         option=0;
      }

      /* Reverses an element of the array */
      if(option==7)
      {
         clrscr();
         printarray1(inp,n);
         printf("\n\nEnter the position of the element that you want to reverse: ");
         scanf("%d",&temp1);
         reverse(temp1,inp);
         printarray2(inp,n);
         getch();
         option=0;
      }

      /* Exits the program */
      if(option==8)
         break;

      /* Returns the control back to main menu if an invalid option is selected from the main menu */
      else
         option=0;
   }
}
/* Main Program Ends */

/* Prints the structure of the array */
void printarray1(int a[],int n)
{
   int i;
   printf("\nThe structure of the array is given below:\n\n------------------\n%8s%10s\n------------------","Position","Element");
   for(i=0;i<n;++i)
      printf("\n%8d%10d",i,a[i]);
   printf("\n------------------\n");
}

/* Prints the structure of the array after any modification */
void printarray2(int a[],int n)
{
   int i;
   printf("\nThe structure of the modified array is given below:\n\n------------------\n%8s%10s\n------------------","Position","Element");
   for(i=0;i<n;++i)
      printf("\n%8d%10d",i,a[i]);
   printf("\n------------------\n\n<Press any key to continue>\n");
}

/* Returns the value of the maximum element of an array */
int maximum(int a[],int n)
{
   int max,i;
   max=a[0];
   for(i=1;i<n;++i)
   {
      if(a[i]>max)
         max=a[i];
   }
   return(max);
}

/* Returns the value of the minimum element of an array */
int minimum(int a[],int n)
{
   int min,i;
   min=a[0];
   for(i=1;i<n;++i)
   {
      if(a[i]<min)
         min=a[i];
   }
   return(min);
}

/* Sorts an array in ascending order */
void ascend(int a[],int n)
{
   int i,j,temp;
   for(i=0;i<n-1;++i)
   {
      for(j=0;j<n-1-i;++j)
      {
         if(a[j]>a[j+1])
         {
            temp=a[j];
            a[j]=a[j+1];
            a[j+1]=temp;
         }
      }
   }
}

/* Sorts an array in descending order */
void descend(int a[],int n)
{
   int i,j,temp;
   for(i=0;i<n-1;++i)
   {
      for(j=0;j<n-1-i;++j)
      {
         if(a[j]<a[j+1])
         {
            temp=a[j];
            a[j]=a[j+1];
            a[j+1]=temp;
         }
      }
   }
}

/* Searches for the position of any particular value from an array */
int search(int key,int a[],int n)
{
   int i;
   for(i=0;i<n;++i)
   {
      if(a[i]==key)
         return(i);
   }
   return(-1);
}

/* Inserts an element at any given position of an existing array */
void insertion(int element,int pos,int a[],int n)
{
   int i;
   for(i=n;i>pos;--i)
      a[i]=a[i-1];
   a[pos]=element;
}

/* Deletes an element from any given position of an existing array */
void deletion(int pos,int a[],int n)
{
   int i;
   for(i=pos;i<n-1;++i)
      a[i]=a[i+1];
}

/* Merges a set of elements with an existing array */
void merge(int n,int a[],int m,int b[])
{
   int i,j;
   for(i=n,j=0;i<m+n;++i,++j)
      a[i]=b[j];
}

/* Reverse the value of an element at any given position of an array */
void reverse(int pos,int a[])
{
   int i,sum=0;
   while(a[pos]>0)
   {
      sum=sum*10+a[pos]%10;
      a[pos]/=10;
   }
   a[pos]=sum;
}

Binary Search Using Recursion

/* Subhranath Chunder - Binary Search using Recursion */

#include<stdio.h>
#include<conio.h>

void sort(int a[],int n);
int search(int t,int a[],int lb,int ub);
void main()
{
   int n,inp[200],i,key,result;
   clrscr();
   printf("Enter the no. of terms: ");
   scanf("%d",&n);
   printf("Enter the values: ");
   for(i=0;i<n;++i)
      scanf("%d",&inp[i]);
   printf("Enter the value to search: ");
   scanf("%d",&key);
   sort(inp,n);
   printf("The sorted array is given below:\n");
   for(i=0;i<n;++i)
      printf("%d ",inp[i]);
   result=search(key,inp,0,n-1);
   if(result==-1)
      printf("\nValue Not Found");
   else
      printf("\nThe value was found at position %d of the sorted array.",result);
   getch();
}

void sort(int a[],int n)
{
   int i,j,temp;
   for(i=0;i<n-1;++i)
   {
      for(j=0;j<n-1-i;++j)
      {
         if(a[j]>a[j+1])
         {
            temp=a[j];
            a[j]=a[j+1];
            a[j+1]=temp;
         }
      }
   }
}

int search(int key,int a[],int lb,int ub)
{
   int middle;
   if(lb<=ub)
   {
      middle=(lb+ub)/2;
      if(a[middle]==key)
         return(middle);
      if(key<a[middle])
         return search(key,a,lb,middle-1);
      else
         return search(key,a,middle+1,ub);
   }
   return(-1);
}

Binary Search

/* Subhranath Chunder - Binary Search */

#include<stdio.h>
#include<conio.h>

void sort(int a[],int n);
int search(int t,int a[],int n);
void main()
{
   int n,inp[200],i,key,result;
   clrscr();
   printf("Enter the no. of terms: ");
   scanf("%d",&amp;n);
   printf("Enter the values: ");
   for(i=0;i<n;++i)
      scanf("%d",&amp;inp[i]);
   printf("Enter the value to search: ");
   scanf("%d",&amp;key);
   sort(inp,n);
   printf("The sorted array is given below:\n");
   for(i=0;i<n;++i)
      printf("%d ",inp[i]);
   result=search(key,inp,n);
   if(result==-1)
      printf("\nValue Not Found");
   else
      printf("\nThe value was found at position %d of the sorted array.",result);
   getch();
}

void sort(int a[],int n)
{
   int i,j,temp;
   for(i=0;i<n-1;++i)
   {
      for(j=0;j<n-1-i;++j)
      {
         if(a[j]>a[j+1])
         {
            temp=a[j];
            a[j]=a[j+1];
            a[j+1]=temp;
         }
      }
   }
}

int search(int key,int a[],int n)
{
   int lb,ub,middle;
   lb=0;
   ub=n-1;
   while(lb<=ub)
   {
      middle=(lb+ub)/2;
      if(a[middle]==key)
         return(middle);
      if(key<a[middle])
         ub=middle-1;
      else
         lb=middle+1;
   }
   return(-1);
}