Question

Objective: Help the students understand the basic operations on sets and also know the importance of choosing suitable data structures to implement programs. Requirements: (1) Input three sets, i.e., universal set U set A and set B, and then calculate the following sets: ANB,AUB, A-B, A. (2) To input a set, give the size of the set first and then input the elements in the set one by one. The sequence of the input set is U, A, and then B. (3) Provide the output according to the format in the sample output. (4) The program should be implemented in Cor C++. Sample input: 10 1,2,3,4,5,6,7,8,9,10 1,2,4,6,7 1,3,5,6,7,9 Sample output: Intersection(A,B): (1,6,7) Union(A,B): {1,2,3,4,5,6,7,9) Difference(A,B): (2.4) Complement(A): (3,5,8,9,10 Comments on this experiment: In this part, you may state your comments, including but not limited to the following issues: (1) What difficulties you met during the programming, whether the difficulty level of this program is ok for you. (2) Whether this programming helps you in your discrete mathematics learning. If so, how does it help? (3) Suggestions on introducing programming to discrete mathematics learning.

Answer 1

#include<stdio.h>
#include<conio.h>
#define MAX 100
int printUnion (int arr1[], int arr2[], int m, int n)
{
int i = 0, j = 0;
while (i < m && j < n)
{
if (arr1[i] < arr2[j])
printf (" %d ", arr1[i++]);
else if (arr2[j] < arr1[i])
printf (" %d ", arr2[j++]);
else
   {
printf (" %d ", arr2[j++]);
i++;
}
}
/* Print remaining elements of the larger array */
while (i < m)
{
printf (" %d ", arr1[i++]);   
}
while (j < n)
{
printf (" %d ", arr2[j++]);
}
}
int printIntersection(int arr1[], int arr2[], int m, int n)
{
int i = 0, j = 0;
while (i < m && j < n)
{
if (arr1[i] < arr2[j])
i++;
else if (arr2[j] < arr1[i])
j++;
else /* if arr1[i] == arr2[j] */
{
printf(" %d ", arr2[j++]);
i++;
}
}
}
int findDifference(int arr1[], int arr2[], int m, int n)
{
int i=0,j=0,k=0,flag=0;
for(i=0;i<m;i++) //traverse 1st set element
{
for(j=0;j<n;j++) //traverse 1st set element
{
if(arr1[i]==arr2[j])
{
flag=0;
break;
}
else
{
flag=1;
}
}
if(flag==1)
{
printf("%d ",arr1[i]); //assign arr1 to arr3
k++;
}
}
}
int findCompliment(int arr1[],int arr2[],int m,int n)
{
int i=0,j=0,k=0,flag=0;
for(i=0;i<m;i++) //traverse 1st set element
{
for(j=0;j<n;j++) //traverse 1st set element
{
if(arr1[i]==arr2[j])
{
flag=0;
break;
}
else
{
flag=1;
}
}
if(flag==1)
{
printf("%d ",arr1[i]);
k++;
}
}   
}
/* Driver program to test above function */
int main ()
{
int U[MAX],A[MAX],B[MAX],C[MAX],D[MAX];
int p,q,r;
printf("Enter size of u");
scanf("%d",&p);
printf("Enter elements in u");
for(int i=0;i<p;i++)
{
scanf("%d",&U[i]);
}
printf("Enter size of A");
scanf("%d",&q);
printf("Enter elements of A");
for(int i=0;i<q;i++)
{
scanf("%d",&A[i]);
}
printf("Enter size of B");
scanf("%d",&r);
printf("Enter elements of B");
for(int i=0;i<r;i++)
{
scanf("%d",&B[i]);
}
printf("Union of {A,B}\n");
printUnion (A, B, q, r);
printf("\nIntersection of {A,B}\n");
printIntersection(A,B,q,r);
printf("\nDifference of {A,B}\n");
findDifference(A,B,q,r);
printf("\nfindCompliment of A\n");
findCompliment(U,A,p,q);
getch();
return 0;
}

output:

Enter size of u5
Enter elements in u1 3 5 7 9
Enter size of A2
Enter elements of A1 4
Enter size of B3
Enter elements of B1 5 6 9
Union of {A,B}
1 4 6 9
Intersection of {A,B}
1
Difference of {A,B}
4
findCompliment of A
3 5 7 9