Union of Two Sets using C and Python

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Objective

To write a program in C and Python to create two sets and perform the Union operation on them.

Prerequisites

• Basic knowledge of Set Theory.
• Knowledge of Arrays.
• Basic understanding of C Programming.
• Basic understanding of Python Programming.

Introduction

A Set is a collection of unique elements. The Union operation combines all distinct elements from two sets. If an element exists in both sets, it is stored only once in the Union Set.

The mathematical symbol used for Union is ∪.

Mathematical Representation

The Union contains every element that belongs to Set A, Set B or both.

Example

Algorithm

Program Logic

The program first stores all the elements of the first set. Next, it checks every element of the second set. If an element is not already available in the Result Set, it is inserted. Finally, the program displays all the unique elements present in both sets.

C Program

#include<stdio.h>

int main()
{
    int setA[20], setB[20], unionSet[40];
    int m, n;
    int i, j;
    int k = 0;
    int found;

    /* Read Set A */

    printf("Enter number of elements in Set A : ");
    scanf("%d", &m);

    printf("\nEnter elements of Set A\n");

    for(i = 0; i < m; i++)
    {
        scanf("%d", &setA[i]);
        unionSet[k++] = setA[i];
    }

    /* Read Set B */

    printf("\nEnter number of elements in Set B : ");
    scanf("%d", &n);

    printf("\nEnter elements of Set B\n");

    for(i = 0; i < n; i++)
    {
        scanf("%d", &setB[i]);
    }

    /* Perform Union */

    for(i = 0; i < n; i++)
    {
        found = 0;

        for(j = 0; j < k; j++)
        {
            if(setB[i] == unionSet[j])
            {
                found = 1;
                break;
            }
        }

        if(found == 0)
        {
            unionSet[k++] = setB[i];
        }
    }

    /* Display Result */

    printf("\nUnion of the Two Sets is : ");

    for(i = 0; i < k; i++)
    {
        printf("%d ", unionSet[i]);
    }

    printf("\n");

    return 0;
}

The program first reads all the elements of Set A and stores them in the Result Set. After that, every element of Set B is compared with the elements already present in the Result Set. If the element is not found, it is inserted into the Result Set. Finally, the Result Set is displayed, which represents the Union of the two sets.

Enter number of elements in Set A : 4

Enter elements of Set A

1
2
3
4

Enter number of elements in Set B : 4

Enter elements of Set B

3
4
5
6

Union of the Two Sets is :

1 2 3 4 5 6

# Program to perform Union of Two Sets

# Read Set A

setA = set()

n = int(input("Enter number of elements in Set A : "))

print("Enter elements of Set A")

for i in range(n):
    value = int(input())
    setA.add(value)

# Read Set B

setB = set()

m = int(input("\nEnter number of elements in Set B : "))

print("Enter elements of Set B")

for i in range(m):
    value = int(input())
    setB.add(value)

# Perform Union

unionSet = setA.union(setB)

# Display Result

print("\nSet A =", setA)
print("Set B =", setB)
print("Union =", unionSet)

The Python program first creates two empty sets. The user enters the elements of both sets. Python provides a built-in union() method that automatically combines both sets and removes duplicate elements. Finally, the resulting Union Set is displayed.

Enter number of elements in Set A : 4

Enter elements of Set A

1
2
3
4

Enter number of elements in Set B : 4

Enter elements of Set B

3
4
5
6

Set A = {1, 2, 3, 4}

Set B = {3, 4, 5, 6}

Union = {1, 2, 3, 4, 5, 6}

Dry Run

Suppose the user enters the following sets.

Time Complexity

Space Complexity

Working of the Program

The program first stores all the elements of the first set. It then compares every element of the second set with the Result Set. If the element is not already present, it is added to the Result Set. After all comparisons are completed, the final Union Set containing only unique elements is displayed.

Applications of Union of Sets

• Database management systems for combining records from multiple tables.
• Data analysis and data mining applications.
• Social networking applications to combine friend lists.
• Search engines for merging search results.
• Library management systems.
• Student information management systems.
• Artificial Intelligence and Machine Learning for combining datasets.
• Compiler design and formal language processing.

Advantages

• Simple and easy to understand.
• Eliminates duplicate elements automatically.
• Provides a complete collection of unique elements.
• Useful in mathematics as well as computer science.
• Python provides a built-in union() function, making implementation very easy.

Disadvantages

• The C implementation requires nested loops, increasing execution time for large datasets.
• Extra memory is required to store the resulting union set.
• For very large datasets, manual duplicate checking becomes less efficient.

Comparison of C and Python Implementations

Frequently Asked Viva Questions

1. What is a Set?
2. What is the Union of two Sets?
3. Which symbol represents Union?
4. Can duplicate elements exist in a Set?
5. Why is Union useful in computer science?
6. How is Union implemented in C?
7. Which Python function performs the Union operation?
8. What is the time complexity of the C implementation?
9. What is the difference between Union and Intersection?
10. Give two real-life applications of Union.

Interview Questions

1. Write a C program to perform the Union of two Sets.
2. Write a Python program using the union() method.
3. How can duplicate elements be removed without using the set data type?
4. Compare Union and Symmetric Difference.
5. Explain the time complexity of the Union algorithm.
6. Can Union be performed on more than two Sets? Explain.
7. What are the advantages of Python's built-in Set data structure?
8. Explain the difference between mathematical Sets and arrays.

Practice Questions

1. Write a program to find the Union of three Sets.
2. Modify the C program to accept character Sets.
3. Implement the Union operation without using an additional array.
4. Write a menu-driven program to perform all Set operations.
5. Write a Python program to find the Union of multiple Sets entered by the user.

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