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Implementing the sets without C++ STL containers

Many practical features and tools in C++ support us in programming competitions. One of these parts is a set from the Standard Template Library (STL), which offers an effective way to keep data sorted. All the fundamentals regarding implementing sets without STL containers are covered in this C++ set lesson.

In the C++ STL, sets are the containers used to store things in a certain order. A set must have distinct components. Each element in a set may be identified by the value alone, serving as the key itself. In C++, items can be added to or removed from sets, but they cannot be changed after being stored there since their values become constant.

What is a Set in C++ ?

As was already established, sets are the kind of STL containers used in C++ to store elements in an ordered manner. The operations that are allowed to be performed on the sets include insertion and deletion. In a set type container, the items are internally sorted in accordance with a rigid weak ordering. Users are unable to change or alter the values of the already-existing items in a set since they are constant in the containers. Sets are only permitted to contain unique values as a result.

In C++, we employ iterators to traverse sets. The couple of header files that are required to deal with sets in C++ are <set> and <iterators>. The < bits/stdc++> serves as a replacement to these two header files. Binary Search Trees (BST) are used for the implementation of sets internally.

Methods that can be performed on a set :

In C++, a broad range of operations may be carried out on sets. Let's examine some of the key set ways.

  • insert(value) :
    adds a key element with value to the set.
    Time Complexity : O(h), here the h represents the tree's height.
    Space Complexity : O(1)
  • _union(s) :
    returns a set that was produced by union with "set s".
    Time Complexity : O((n+m)*h), where n and m are the number of items in sets and h is the tree's height.
    Space complexity : O(n+m)
  • _intersection(s) :
    returns a set that was produced by intersection with "set s."
    Time Complexity : O(n*h), where n represents the number of items in sets and h is the tree's height.
    Space Complexity : O(n)
  • _complement(U) :
    Complementary set of a Universal set "Set U" is returned.
    Time Complexity : O(n*h), where n represents the number of items in sets and h is the tree's height.
    Space Complexity : O(n)
  • _array() :
    Returns an array that is made up of every element in the set.
    Time Complexity : O(n)
    Space Complexity : O(n)
  • _size() :
    Returns the set's total number of items.
    Time Complexity : O(1)
    Space Complexity : O(1)

Implementation of sets using the BST :

We have explained the implementation of sets using the BST procedure with the help of an example below :

Program :

#include <algorithm>  
#include <iostream>  
#include <math.h>  
#include <stack>  
#include <string>  
using namespace std;  
  
template <typename T>  
struct Node { // Creating the node of the BST  
  
    T data; // Node’s value  
  
    Node* leftwards; // Pointer to the left-hand side child  
  
    Node* rightwards; // Pointer to the right-hand side child  
  
public:  
    // inOrder() function prints the inorder traversal of the BST  
    void inOrder(Node* r)  
    {  
        if (r == NULL) { // If it reaches the last level  
            return;  
        }  
        inOrder(r->leftwards); // printing the left child  
        cout << r->data << " "; // printing the node value  
        inOrder(r->rightwards); // printing the right child  
    }  
  
    /* 
        Method to check whether the BST contains a node 
        with the given piece of data 
         
        r is the pointer towards the root node 
         d is the data to search in the BST 
        The function will return 1 if the node is present in the BST otherwise it will print 0 
    */  
    int containNode(Node* r, T d)  
    {  
        if (r == NULL) { // If it reaches the last level or the tree is empty  
            return 0;  
        }  
        int x = r->data == d ? 1 : 0; // Checking for duplicacy  
        // Traversing in the right and left subtree  
        return x | containNode(r->leftwards, d) | containNode(r->rightwards, d);  
    }  
  
    /* 
        Method to insert a node with the
        given data into BST 
         
        r is the pointer to the root node in BST  
        d is the data to be inserted in the BST 
        return the pointer to the root of resultant BST 
    */  
    Node* insert(Node* r, T d)  
    {  
  
        if (r == NULL) { // Adding where NULL is encountered meaning the space is present  
            Node<T>* temp = new Node<T>; // Creating a new node in the BST  
            temp->data = d; // inserting the data in BST  
            temp->leftwards = temp->rightwards = NULL; // Allocating the left and the right pointers a NULL  
            return temp; // returning the current node  
        }  
  
        //    Inserting the node in the left subtree if the data is lesser than the current node data  
        if (d < r->data) {  
            r->leftwards = insert(r->leftwards, d);  
            return r;  
        }  
  
        //   Inserting the node in the right subtree if the data is greater than the current node data  
        else if (d > r->data) {  
            r->rightwards = insert(r->rightwards, d);  
            return r;  
        }  
        else  
            return r;  
    }  
};  
  
template <typename T> // creating a class template for the implementation of a set in the BST  
class Set { // Creating the class set  
  
    Node<T>* root; // Root to store the data  
  
    int size; // this indicates the size of set  
  
public:  
    Set() // If no value is passed  
    {  
        root = NULL; // It points towards the NULL  
        size = 0; // this means the size will be zero  
    }  
  
    Set(const Set& s) // Copy constructor  
    {  
        root = s.root;  
        size = s.size;  
    }  
  
    void add(const T data) // It adds an element to set  
    {  
        if (!root->containNode(root, data)) { // Checking if it is the first element or not 
            root = root->insert(root, data); // Inserting of the data into the set  
            size++; // Increment the size of the set  
        }  
    }  
  
    bool contain(T data)  
    {  
        return root->containNode(root, data) ? true : false;  
    }  
  
    void displaysSet()  
    {  
        cout << "{ ";  
        root->inOrder(root);  
        cout << "}" << endl;  
    }  
  
    /* 
        Method for returning the current size of the Set 
          
        @return is the size of the set 
    */  
    int getSize()  
    {  
        return size;  
    }  
};  
  
int main()  
{  
  
    // Creating the Set X  
    Set<int> X;  
  
    // Adding elements to the Set X  
    X.add(10);  
    X.add(20);  
    X.add(30);  
    X.add(20);  
  
    // Displaying the contents of the Set X
    cout << "X = ";  
    X.displaysSet();  
  
    // Checking if the Set X contains some of the elements  
    cout << "X " << (X.contain(30) ? "contains"  
                                   : "does not contain")  
         << " 30" << endl;  
    cout << "X " << (X.contain(40) ? "contains"  
                                   : "does not contain")  
         << " 40" << endl;  
    cout << endl;  
  
    return 0;  
}  

Output :

X = { 1 2 3 }
X contains 30
X does not contain 40

Explanation :

In the above example, internally, the set data structure uses the BST (Binary Search Tree) data structure. In order to implement the Set, we added the components to the tree and utilised this tree template. We made a BST template. Three components made up the tree : the node's data, its left and right pointers, and its members.

We used the insert() function to add the nodes to the tree once it had been created. The BST placed the data that was lesser than the root on the left hand side of the tree and the bigger data on the right. The function ContainNode() was used to determine if a node is there in the tree or not. The BST's inorder traversal was printed using the inOrder() method. The BST template was put into action in the Set class. The set template was mainly made to implement the BST once the BST had been built for the set's internal operation. The size variable was used to return the size of the set, and it contained a root pointer node to hold the data. The Set class provided a copy constructor that copied a set into the other set and a default constructor that initialised the root of BST as NULL.

The values in the set were added using the method add(). By invoking the method containNode(), it did not add the already added data to the set. Then, if a new element was present, the set was expanded. The contain() method determined if a certain element was present in the set or not at that particular time. In the BST, contain() method internally called containNode(). The set items were printed using the displaysSet() method. Internally, it used the BST's inOrder() method. The size of the set was returned by the getSize() method.



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