C++ - Delete even nodes of the Circular Doubly Linked List

Deleting even nodes of a circular doubly linked list requires traverse through the list and deleting even nodes one by one. It requires creating two nodes - oddNode and evenNode. If the list contains more than one node, make oddNode to first odd node of list and evenNode to first even node of the list. Store the current odd node into temp node and delete the even node. Move both nodes to next set of odd-even nodes. Repeat the process till any of nodes reaches head. Finally, link the last node with the head.

The function deleteEvenNodes is created for this purpose. It is a 3-step process.

void deleteEvenNodes() {
  if(head != NULL && head->next != head) {
  
    //1. if the list has more than one element
    //   create evenNode node - pointing to head
    //   oddNode node - pointing to next of head
    //   temp node - to store last odd node
    Node* oddNode = head;
    Node* evenNode = head->next; 
    Node* temp = new Node();

    while(true) {
      
      //2. delete even node and update evenNode and 
      //   oddNode to next set of odd-even nodes
      //   update temp node to latest oddNode node
      //   continue the process till any of the node 
      //   reaches head
      temp = oddNode;
      oddNode->next = evenNode->next;
      oddNode->next->prev = oddNode;
      free(evenNode);
      oddNode = oddNode->next;
      evenNode = oddNode->next;
      if(oddNode == head || evenNode == head)
        break;
    }
    
    //3. if oddNode reaches head, make next of 
    //   temp as head else make next of oddNode
    //   as head
    if(oddNode == head) {
      temp->next = head;
      head->prev = temp;
    } else {
      oddNode->next = head;
      head->prev = oddNode;
    }
  }
}

The below is a complete program that uses above discussed concept of deleting even nodes of a circular doubly linked list.

#include <iostream>
using namespace std;

//node structure
struct Node {
    int data;
    Node* next;
    Node* prev;
};

class LinkedList {
  private:
    Node* head;
  public:
    LinkedList(){
      head = NULL;
    }
 
    //Add new element at the end of the list
    void push_back(int newElement) {
      Node* newNode = new Node();
      newNode->data = newElement;
      newNode->next = NULL;
      newNode->prev = NULL; 
      if(head == NULL) {
        head = newNode;
        newNode->next = head;
        newNode->prev = head;
      } else {
        Node* temp = head;
        while(temp->next != head)
          temp = temp->next;
        temp->next = newNode;
        newNode->next = head;
        newNode->prev = temp;
        head->prev = newNode;
      }    
    }
    
    //delete even nodes of the list
    void deleteEvenNodes() {
      if(head != NULL && head->next != head) {
        Node* oddNode = head;
        Node* evenNode = head->next; 
        Node* temp = new Node();
        while(true) {
          temp = oddNode;
          oddNode->next = evenNode->next;
          oddNode->next->prev = oddNode;
          free(evenNode);
          oddNode = oddNode->next;
          evenNode = oddNode->next;
          if(oddNode == head || evenNode == head)
            break;
        }
        if(oddNode == head) {
          temp->next = head;
          head->prev = temp;
        } else {
          oddNode->next = head;
          head->prev = oddNode;
        }
      }
    } 

    //display the content of the list
    void PrintList() {
      Node* temp = head;
      if(temp != NULL) {
        cout<<"The list contains: ";
        while(true) {
          cout<<temp->data<<" ";
          temp = temp->next;
          if(temp == head) 
            break;
        }
        cout<<endl;
      } else {
        cout<<"The list is empty.\n";
      }
    }     
};

// test the code 
int main() {
  LinkedList MyList;

  //Add five elements in the list.
  MyList.push_back(10);
  MyList.push_back(20);
  MyList.push_back(30);
  MyList.push_back(40);
  MyList.push_back(50);

  //Display the content of the list.
  MyList.PrintList();

  //delete even nodes of the list
  MyList.deleteEvenNodes();

  cout<<"After deleting even nodes.\n";
  //Display the content of the list.
  MyList.PrintList();
  
  return 0; 
}

The above code will give the following output:

The list contains: 10 20 30 40 50 
After deleting even nodes.
The list contains: 10 30 50