Implementing Sets Without C++ STL Containers

A Set is a collection of distinct elements. Elements cannot be modified once added. There are various operations associated with sets such as union, intersection, power set, Cartesian Product, set difference, complement, and equality.

Methods of Set:

• add(data) – Adds ‘data’ to the set
• unionSet(s) – Returns union of set with set ‘s’
• intersectionSet(s) – Returns intersection set with set ‘s’
• complementSet(U) – Returns complement of set with Universal Set ‘U’
• operator -(s) – Returns difference of set and set ‘s’
• operator ==(s) – Returns whether the set is equal to set ‘s’
• displayProduct(s) – Prints the Cartesian Product of set and set ‘s’ to console
• displayPowerSet() – Prints power set of the set to console
• toArray() – Returns the set as an array of its elements
• contains(s) – Returns whether the set contains element ‘s’
• displaySet() – Prints the set to console
• getSize() – Returns the size of the set

Below is an implementation of a set using Binary Search Tree: 

C++

// C++ implementation of the approach
#include <algorithm>
#include <iostream>
#include <math.h>
#include <stack>
#include <string>
using namespace std;

// Structure to implement a node of a BST
template <typename T>
struct Node {

    // The data content of the node
    T data;

    // Link to the left child
    Node* left;

    // Link to the right child
    Node* right;

public:
    // Function to print the inorder
    // traversal of the BST
    void inorder(Node* r)
    {
        if (r == NULL) {
            return;
        }
        inorder(r->left);
        cout << r->data << " ";
        inorder(r->right);
    }

    /*
        Function to check if BST contains a node
        with the given data

        @param r pointer to the root node
        @param d the data to search
        @return 1 if the node is present else 0
    */
    int containsNode(Node* r, T d)
    {
        if (r == NULL) {
            return 0;
        }
        int x = r->data == d ? 1 : 0;
        return x | containsNode(r->left, d) | containsNode(r->right, d);
    }

    /*
        Function to insert a node with
        given data into the BST

        @param r pointer to the root node
        @param d the data to insert
        @return pointer to the root of the resultant BST
    */
    Node* insert(Node* r, T d)
    {

        // Add the node when NULL node is encountered
        if (r == NULL) {
            Node<T>* tmp = new Node<T>;
            tmp->data = d;
            tmp->left = tmp->right = NULL;
            return tmp;
        }

        // Traverse the left subtree if data
        // is less than the current node
        if (d < r->data) {
            r->left = insert(r->left, d);
            return r;
        }

        // Traverse the right subtree if data
        // is greater than the current node
        else if (d > r->data) {
            r->right = insert(r->right, d);
            return r;
        }
        else
            return r;
    }
};

// Class to implement a Set using BST
template <typename T>
class Set {

    // Pointer to the root of the
    // BST storing the set data
    Node<T>* root;

    // The number of elements in the set
    int size;

public:
    // Default constructor
    Set()
    {
        root = NULL;
        size = 0;
    }

    // Copy constructor
    Set(const Set& s)
    {
        root = s.root;
        size = s.size;
    }

    /*
        Function to Add an element to the set

        @param data the element to add to the set
    */
    void add(const T data)
    {
        if (!root->containsNode(root, data)) {
            root = root->insert(root, data);
            size++;
        }
    }

    /*
        Function to compute the union of two sets

        @param s set to find union with
        @return the union set
    */
    Set unionSet(Set& s)
    {
        Set<T> res;

        // Second set is returned
        // if first set is empty
        if (root == NULL)
            return res;

        // First set is returned
        // if second set is empty
        if (s.root == NULL)
            return *this;

        // The elements of the first set
        // are added to the resultant set
        stack<Node<T>*> nodeStack;
        nodeStack.push(root);

        // Preorder traversal of the BST
        while (!nodeStack.empty()) {
            Node<T>* node;
            node = nodeStack.top();
            nodeStack.pop();

            // The data is added to the resultant set
            res.add(node->data);

            if (node->right)
                nodeStack.push(node->right);
            if (node->left)
                nodeStack.push(node->left);
        }

        // The elements of the second set
        // are added to the resultant set
        stack<Node<T>*> nodeStack1;
        nodeStack1.push(s.root);

        while (!nodeStack1.empty()) {
            Node<T>* node;
            node = nodeStack1.top();
            nodeStack1.pop();

            res.add(node->data);

            if (node->right)
                nodeStack1.push(node->right);
            if (node->left)
                nodeStack1.push(node->left);
        }

        return res;
    }

    /**
        Computes the intersection of two sets

        @param s the set to find intersection with
        @return the intersection set
    */
    Set intersectionSet(Set& s)
    {
        Set<T> res;
        stack<Node<T>*> nodeStack;
        nodeStack.push(root);

        while (!nodeStack.empty()) {
            Node<T>* node;
            node = nodeStack.top();
            nodeStack.pop();
            if (s.contains(node->data)) {
                res.add(node->data);
            }
            if (node->right)
                nodeStack.push(node->right);
            if (node->left)
                nodeStack.push(node->left);
        }
        return res;
    }

    /*
        Function to compute the complement of the set

        @param U the universal set
        @return the complement set
    */
    Set complementSet(Set& U)
    {
        return (U - *this);
    }

    /*
        Function to compute the difference of two sets

        @param s the set to be subtracted
        @return the difference set
    */
    Set operator-(Set& s)
    {
        Set<T> res;
        stack<Node<T>*> nodeStack;
        nodeStack.push(this->root);

        while (!nodeStack.empty()) {
            Node<T>* node;
            node = nodeStack.top();
            nodeStack.pop();
            if (!s.contains(node->data)) {
                res.add(node->data);
            }
            if (node->right)
                nodeStack.push(node->right);
            if (node->left)
                nodeStack.push(node->left);
        }
        return res;
    }

    /*
        Function that checks equality of two sets

        @param s set to check equality with
        @return boolean value denoting result of check
    */
    bool operator==(Set& s)
    {
        if (s.getSize() != size) {
            return false;
        }
        stack<Node<T>*> nodeStack;
        nodeStack.push(this->root);

        while (!nodeStack.empty()) {
            Node<T>* node;
            node = nodeStack.top();
            nodeStack.pop();
            if (!s.contains(node->data)) {
                return false;
            }
            if (node->right)
                nodeStack.push(node->right);
            if (node->left)
                nodeStack.push(node->left);
        }
        return true;
    }

    /*
        Function to print the cartesian product of two sets

        @param s the set to find product with
    */
    void displayProduct(Set& s)
    {
        int i, j, n2 = s.getSize();
        T* A = toArray();
        T* B = s.toArray();

        i = 0;

        cout << "{ ";
        for (i = 0; i < size; i++) {
            for (j = 0; j < n2; j++) {
                cout << "{ " << A[i] << " " << B[j] << " } ";
            }
        }
        cout << "}" << endl;
    }

    // Function to print power set of the set
    void displayPowerSet()
    {
        int n = pow(2, size);
        T* A = toArray();
        int i;
        while (n-- > 0) {
            cout << "{ ";
            for (int i = 0; i < size; i++) {
                if ((n & (1 << i)) == 0) {
                    cout << A[i] << " ";
                }
            }
            cout << "}" << endl;
        }
    }

    /*
        Function to convert the set into an array

        @return array of set elements
    */
    T* toArray()
    {
        T* A = new T[size];
        int i = 0;
        stack<Node<T>*> nodeStack;
        nodeStack.push(this->root);

        while (!nodeStack.empty()) {
            Node<T>* node;
            node = nodeStack.top();
            nodeStack.pop();

            A[i++] = node->data;

            if (node->right)
                nodeStack.push(node->right);
            if (node->left)
                nodeStack.push(node->left);
        }
        return A;
    }

    /*
        Function to check whether the set contains an element

        @param data the element to search
        @return relut of check
    */
    bool contains(T data)
    {
        return root->containsNode(root, data) ? true : false;
    }

    // Function to print the contents of the set
    void displaySet()
    {
        cout << "{ ";
        root->inorder(root);
        cout << "}" << endl;
    }

    /*
        Function to return the current size of the Set

        @return size of set
    */
    int getSize()
    {
        return size;
    }
};

// Driver code
int main()
{

    // Create Set A
    Set<int> A;

    // Add elements to Set A
    A.add(1);
    A.add(2);
    A.add(3);
    A.add(2);

    // Display the contents of Set A
    cout << "A = ";
    A.displaySet();
    cout << "P(A) = " << endl;
    A.displayPowerSet();

    // Check if Set A contains some elements
    cout << "A " << (A.contains(3) ? "contains"
                                   : "does not contain")
         << " 3" << endl;
    cout << "A " << (A.contains(4) ? "contains"
                                   : "does not contain")
         << " 4" << endl;
    cout << endl;

    // Create Set B
    Set<int> B;

    // Insert elements to Set B
    B.add(1);
    B.add(2);
    B.add(4);

    // Display the contents of Set B
    cout << "B = ";
    B.displaySet();
    cout << "P(B) = " << endl;
    B.displayPowerSet();
    cout << endl;

    // Create Set C
    Set<int> C;
    C.add(1);
    C.add(2);
    C.add(4);

    // Display the contents of Set C
    cout << "C = ";
    C.displaySet();
    cout << endl;

    // Set F contains the difference
    // of the Sets A and B
    Set<int> F = A - B;
    cout << "A - B = ";
    F.displaySet();
    cout << endl;

    // Set D contains the union
    // of the Sets A and B
    Set<int> D = A.unionSet(B);
    cout << "A union B = ";
    D.displaySet();
    cout << endl;

    // Set E contains the intersection
    // of the Sets A and B
    Set<int> E = A.intersectionSet(B);
    cout << "A intersection B = ";
    E.displaySet();
    cout << endl;

    // Display the product
    cout << "A x B = ";
    A.displayProduct(B);
    cout << endl;

    // Equality tests
    cout << "Equality of Sets:" << endl;

    cout << "A "
         << ((A == B) ? "" : "!") << "= B"
         << endl;
    cout << "B "
         << ((B == C) ? "" : "!") << "= C"
         << endl;
    cout << "A "
         << ((A == C) ? "" : "!") << "= C"
         << endl;
    cout << endl;

    Set<int> U;
    U.add(1);
    U.add(2);
    U.add(3);
    U.add(4);
    U.add(5);
    U.add(6);
    U.add(7);

    // Complements of the respective Sets
    Set<int> A1 = A.complementSet(U);
    Set<int> B1 = B.complementSet(U);
    Set<int> C1 = C.complementSet(U);

    cout << "A' = ";
    A1.displaySet();
    cout << "B' = ";
    B1.displaySet();
    cout << "C' = ";
    C1.displaySet();

    return 0;
}

Output:

A = { 1 2 3 }
P(A) = 
{ }
{ 1 }
{ 2 }
{ 1 2 }
{ 3 }
{ 1 3 }
{ 2 3 }
{ 1 2 3 }
A contains 3
A does not contain 4

B = { 1 2 4 }
P(B) = 
{ }
{ 1 }
{ 2 }
{ 1 2 }
{ 4 }
{ 1 4 }
{ 2 4 }
{ 1 2 4 }

C = { 1 2 4 }

A - B = { 3 }

A union B = { 1 2 3 4 }

A intersection B = { 1 2 }

A x B = { { 1 1 } { 1 2 } { 1 4 } { 2 1 } { 2 2 } { 2 4 } { 3 1 } { 3 2 } { 3 4 } }

Equality of Sets:
A != B
B = C
A != C

A' = { 4 5 6 7 }
B' = { 3 5 6 7 }
C' = { 3 5 6 7 }

AVL Tree or Red-Black Tree can be used instead of simple BST to make worst case complexity of insertion and searching O(log(n)). 
For using STL set, refer to this article Set in C++ Standard Template Library (STL).