Delete node at nth position from doubly linked list recursively? (C++)

I have been trying to practice a bit with some algorithms and in my code for a doubly linked list, I want to be able to delete a node at nth position recursively. I have tried doing this on my own but I cannot seem to find an effective way of doing so with recursion. If someone could possibly help me out in doing so that would be great. Here is the code I have so far.

Additionally, I am also aware that the current code I have for my delete function only works for a singly linked list. I figured this out on my own and just put it there as a placeholder / messing around with the code I have written below.

#include <cctype>

using namespace std;

struct Node{

  int data;
  Node* next;
  Node* prev;

};

Node* add(Node* head, int data);
void display(Node* head);
void displayReverse(Node* head);
Node* deleteNode(Node* head, int pos, Node* delNode);

int main(){


  Node* head = NULL;

  head = add(head, 1);
  head = add(head,2);
  head = add(head, 3);
  head = add(head, 4);
  head = add(head, 5);

  display(head);
  cout<<endl;
  displayReverse(head);

  cout<<endl;
  int del;
  cout<<"pos to delete: ";
  cin>>del;

  Node* delNode = NULL;
  head = deleteNode(head, del, delNode);
  display(head);
  return 0;
}

Node* add(Node* head, int data){

  if(head==NULL){ //if list is empty
    
    Node* newNode = new Node;
    newNode->data = data;
    newNode->next = NULL;
    newNode->prev = NULL;
    return newNode;
  }
  else if(head!=NULL && head->next == NULL){ //if the head points to a node that has a next that is not empty, but the node at the next is empty, then add to the end of list

    Node* newNode = new Node;
    head->next = newNode;
    newNode->data = data;
    newNode->next = NULL;
    newNode->prev = head;
  }
  else{ //if the head does not equal null, and the head next does not equal null either

    head->next = add(head->next, data);
  }
  return head;

}

void display(Node* head){

  if(head!=NULL){

    cout<<head->data<<" ";
    display(head->next);
    
  }
  return;
  

}

void displayReverse(Node* head){ //checks if the nodes are actually linked (this implementation works)

  while(head->next!=NULL){
    head = head->next;
  }

  while(head!=NULL){
    cout<<head->data<< " ";
    head = head->prev;

  }

}


Node* deleteNode(Node* head, int pos, Node* delNode){

  if(pos = 1){

    delNode = head->next;
    delete head;
    return delNode;

  }
  else{

    head->next = deleteNode(head->next, pos-1, delNode);
    return head;
  }


}

To delete n^th node from a doubly linked list recursively :

• Maintain a counter
• If counter is less than position of node to be delete then
  • Increment the counter and recursive call the delete function and pass the next of current processing node in the list.
  • Assign the return value of delete function to next pointer of current processing node.
  • Reset the previous pointer of returned node from delete function.
  • Return the current processing node.
• If counter is equal to the position that means the current node is to be delete from list
  • Record the next node of current processing node.
  • Reset next and previous links of current processing node to NULL.
  • Deallocate the current processing node node.
  • Reset the counter, so that (counter == position) condition will fail in further iterations.
  • Return the recorded node.

Implementation:

Node* deleteNode (Node* head, int pos) {
    static int cnt;

    if (head == NULL) {
        return NULL;
    }

    if (++cnt < pos) {
        head->next = deleteNode (head->next, pos);
        if (head->next) {
            // reset the pointer
            head->next->prev = head;
        }
    }

    if (cnt == pos) {
        Node *tmp = head->next;
        head->prev = NULL;
        head->next = NULL;
        free (head);
        // reset counter
        cnt = 0;
        if (tmp) {
            tmp->prev = NULL;
        }
        return tmp;
    }

    return head;
}

Output:

# ./a.out   
1 2 3 4 5 
5 4 3 2 1 
pos to delete: 2
1 3 4 5 

# ./a.out
1 2 3 4 5 
5 4 3 2 1 
pos to delete: 1
2 3 4 5 

# ./a.out
1 2 3 4 5 
5 4 3 2 1 
pos to delete: 5
1 2 3 4 

For invalid position :

# ./a.out
1 2 3 4 5 
5 4 3 2 1 
pos to delete: 8
1 2 3 4 5 

Additional:

1). Avoid adding using namespace std; in your program. Check this.