Remove all even parity nodes from a Doubly and Circular Singly Linked List

Given a Doubly linked list and Circular singly linked list containing N nodes, the task is to remove all the nodes from each list which contains elements whose parity is even.

Example:

Input: CLL = 9 -> 11 -> 34 -> 6 -> 13 -> 21
Output: 11 -> 13 -> 21
Explanation:
The circular singly linked list contains :
11 -> 1011, parity = 3
9 -> 1001, parity = 2
34 -> 100010, parity = 2
6 -> 110, parity = 2
13 -> 1101, parity = 3
21 -> 10101, parity = 3
Here, parity for nodes containing 9, 34, and 6 are even.
Hence, these nodes have been deleted.



Input: DLL = 18 <=> 15 <=> 8 <=> 9 <=> 14
Output: 8 <=> 14
Explanation:
The linked list contains :
18 -> 10010, parity = 2
15 -> 1111, parity = 4
8 -> 1000, parity = 1
9 -> 1001, parity = 2
14 -> 1110, parity = 3
Here, parity for nodes containing 18, 15 and 9 are even.
Hence, these nodes have been deleted.

Approach:
A simple approach is to traverse the nodes of the list one by one and for each node first, find the parity for the value present in the node by iterating through each bit and then finally remove the nodes whose parity is even.

Doubly Linked List

Below is the implementation of the above approach:

C++

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// C++ implementation to remove all
// the Even Parity Nodes from a
// doubly linked list
  
#include <bits/stdc++.h>
  
using namespace std;
  
// Node of the doubly linked list
struct Node {
    int data;
    Node *prev, *next;
};
  
// Function to insert a node at the beginning
// of the Doubly Linked List
void push(Node** head_ref, int new_data)
{
    // Allocate the node
    Node* new_node
        = (Node*)malloc(sizeof(struct Node));
  
    // Insert the data
    new_node->data = new_data;
  
    // Since we are adding at the beginning,
    // prev is always NULL
    new_node->prev = NULL;
  
    // Link the old list off the new node
    new_node->next = (*head_ref);
  
    // Change the prev of
    // head node to new node
    if ((*head_ref) != NULL)
        (*head_ref)->prev = new_node;
  
    // Move the head to point
    // to the new node
    (*head_ref) = new_node;
}
  
// Function that returns true if count
// of set bits in x is even
bool isEvenParity(int x)
{
    // parity will store the
    // count of set bits
    int parity = 0;
    while (x != 0) {
        if (x & 1)
            parity++;
        x = x >> 1;
    }
  
    if (parity % 2 == 0)
        return true;
    else
        return false;
}
  
// Function to delete a node
// in a Doubly Linked List.
// head_ref --> pointer to head node pointer.
// del --> pointer to node to be deleted
void deleteNode(Node** head_ref, Node* del)
{
    // Base case
    if (*head_ref == NULL || del == NULL)
        return;
  
    // If the node to be
    // deleted is head node
    if (*head_ref == del)
        *head_ref = del->next;
  
    // Change next only if node to be
    // deleted is not the last node
    if (del->next != NULL)
        del->next->prev = del->prev;
  
    // Change prev only if node to be
    // deleted is not the first node
    if (del->prev != NULL)
        del->prev->next = del->next;
  
    // Finally, free the memory
    // occupied by del
    free(del);
  
    return;
}
  
// Function to to remove all
// the Even Parity Nodes from a
// doubly linked list
void deleteEvenParityNodes(
    Node** head_ref)
{
    Node* ptr = *head_ref;
    Node* next;
  
    // Iterating through
    // the linked list
    while (ptr != NULL) {
        next = ptr->next;
  
        // If node's data's parity
        // is even
        if (isEvenParity(ptr->data))
            deleteNode(head_ref, ptr);
  
        ptr = next;
    }
}
  
// Function to print nodes in a
// given doubly linked list
void printList(Node* head)
{
    if (head == NULL) {
        cout << "Empty list\n";
        return;
    }
  
    while (head != NULL) {
        cout << head->data << " ";
        head = head->next;
    }
}
  
// Driver Code
int main()
{
  
    Node* head = NULL;
  
    // Create the doubly linked list
    // 18 <-> 15 <-> 8 <-> 9 <-> 14
    push(&head, 14);
    push(&head, 9);
    push(&head, 8);
    push(&head, 15);
    push(&head, 18);
  
    // Uncomment to view the list
    // cout << "Original List: ";
    // printList(head);
  
    deleteEvenParityNodes(&head);
  
    // Modified List
    printList(head);
}

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Output:

8 14

Circular Singly Linked List

Below is the implementation of the above approach:

C++

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// C++ program to remove all
// the Even Parity Nodes from a
// circular singly linked list
  
#include <bits/stdc++.h>
using namespace std;
  
// Structure for a node
struct Node {
    int data;
    struct Node* next;
};
  
// Function to insert a node at the beginning
// of a Circular linked list
void push(struct Node** head_ref, int data)
{
    // Create a new node
    // and make head as next
    // of it.
    struct Node* ptr1
        = (struct Node*)malloc(
            sizeof(struct Node));
  
    struct Node* temp = *head_ref;
    ptr1->data = data;
    ptr1->next = *head_ref;
  
    // If linked list is not NULL then
    // set the next of last node
    if (*head_ref != NULL) {
  
        // Find the node before head
        // and update next of it.
        while (temp->next != *head_ref)
            temp = temp->next;
  
        temp->next = ptr1;
    }
    else
  
        // Point for the first node
        ptr1->next = ptr1;
  
    *head_ref = ptr1;
}
  
// Function to delete the node from a
// Circular Linked list
void deleteNode(
    Node*& head_ref, Node* del)
{
    // If node to be deleted is head node
    if (head_ref == del)
        head_ref = del->next;
  
    struct Node* temp = head_ref;
  
    // Traverse list till not found
    // delete node
    while (temp->next != del) {
        temp = temp->next;
    }
  
    // Copy the address of the node
    temp->next = del->next;
  
    // Finally, free the memory
    // occupied by del
    free(del);
  
    return;
}
  
// Function that returns true if count
// of set bits in x is even
bool isEvenParity(int x)
{
    // parity will store the
    // count of set bits
    int parity = 0;
    while (x != 0) {
        if (x & 1)
            parity++;
        x = x >> 1;
    }
  
    if (parity % 2 == 0)
        return true;
    else
        return false;
}
  
// Function to delete all
// the Even Parity Nodes
// from the singly circular linked list
void deleteEvenParityNodes(Node*& head)
{
    if (head == NULL)
        return;
  
    if (head == head->next) {
        if (isEvenParity(head->data))
            head = NULL;
        return;
    }
  
    struct Node* ptr = head;
  
    struct Node* next;
  
    // Traverse the list till the end
    do {
        next = ptr->next;
  
        // If the node's data has even parity,
        // delete node 'ptr'
        if (isEvenParity(ptr->data))
            deleteNode(head, ptr);
  
        // Point to the next node
        ptr = next;
  
    } while (ptr != head);
  
    if (head == head->next) {
        if (isEvenParity(head->data))
            head = NULL;
        return;
    }
}
  
// Function to print nodes in a
// given Circular linked list
void printList(struct Node* head)
{
    if (head == NULL) {
        cout << "Empty List\n";
        return;
    }
  
    struct Node* temp = head;
    if (head != NULL) {
        do {
            printf("%d ", temp->data);
            temp = temp->next;
        } while (temp != head);
    }
}
  
// Driver code
int main()
{
    // Initialize lists as empty
    struct Node* head = NULL;
  
    // Created linked list will be
    // 11->9->34->6->13->21
    push(&head, 21);
    push(&head, 13);
    push(&head, 6);
    push(&head, 34);
    push(&head, 9);
    push(&head, 11);
  
    deleteEvenParityNodes(head);
  
    printList(head);
  
    return 0;
}

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Output:

11 13 21

Time Complexity: O(K*N), where N is the size of the linked list and K is the number of bits in the maximum number present in the linked list.

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