从双向链表中删除所有质节点

给定一个包含 N 个节点的双向链表，任务是从列表中删除所有质数节点。
例子：

Input: List = 15 <=> 16 <=> 6 <=> 7 <=> 17 
Output: Final List = 15 <=> 16 <=> 6
Input: List = 5 <=> 3 <=> 4 <=> 2 <=> 9 
Output: Final List = 5 <=> 4 <=> 9 
 

方法：思想是将双向链表的节点一一遍历，得到质数节点的指针。按照本文中使用的方法删除这些节点。
下面是上述想法的实现：

C++

// C++ implementation to delete all
// prime nodes from the doubly
// linked list
#include 
 
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 node
    Node* new_node = (Node*)malloc(sizeof(struct Node));
 
    // put in 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 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 to check if a number is prime
bool isPrime(int n)
{
    // Corner cases
    if (n <= 1)
        return false;
    if (n <= 3)
        return true;
 
    // This is checked so that we can skip
    // middle five numbers in below loop
    if (n % 2 == 0 || n % 3 == 0)
        return false;
 
    for (int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;
 
    return true;
}
 
// 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 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 delete all prime nodes
// from the doubly linked list
void deletePrimeNodes(Node** head_ref)
{
    Node* ptr = *head_ref;
    Node* next;
 
    while (ptr != NULL) {
        next = ptr->next;
        // if true, delete node 'ptr'
        if (isPrime(ptr->data))
            deleteNode(head_ref, ptr);
        ptr = next;
    }
}
 
// function to print nodes in a
// given doubly linked list
void printList(Node* head)
{
    while (head != NULL) {
        cout << head->data << " ";
        head = head->next;
    }
}
 
// Driver program
int main()
{
    // start with the empty list
    Node* head = NULL;
 
    // create the doubly linked list
    // 15 <-> 16 <-> 7 <-> 6 <-> 17
    push(&head, 17);
    push(&head, 6);
    push(&head, 7);
    push(&head, 16);
    push(&head, 15);
 
    cout << "Original List: ";
    printList(head);
 
    deletePrimeNodes(&head);
 
    cout << "\nModified List: ";
    printList(head);
}

Java

// Java implementation to delete all
// prime nodes from the doubly
// linked list
class GFG
{
     
 
// Node of the doubly linked list
static class Node
{
    int data;
    Node prev, next;
};
 
// function to insert a node at the beginning
// of the Doubly Linked List
static Node push(Node head_ref, int new_data)
{
    // allocate node
    Node new_node = new Node();
 
    // put in 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 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;
     
    return head_ref;
}
 
// Function to check if a number is prime
static boolean isPrime(int n)
{
    // Corner cases
    if (n <= 1)
        return false;
    if (n <= 3)
        return true;
 
    // This is checked so that we can skip
    // middle five numbers in below loop
    if (n % 2 == 0 || n % 3 == 0)
        return false;
 
    for (int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;
 
    return true;
}
 
// function to delete a node in a Doubly Linked List.
// head_ref -. pointer to head node pointer.
// del -. pointer to node to be deleted
static Node deleteNode(Node head_ref, Node del)
{
    // base case
    if (head_ref == null || del == null)
        return null;
 
    // If 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;
 
    return head_ref;
}
 
// function to delete all prime nodes
// from the doubly linked list
static Node deletePrimeNodes(Node head_ref)
{
    Node ptr = head_ref;
    Node next;
 
    while (ptr != null)
    {
        next = ptr.next;
         
        // if true, delete node 'ptr'
        if (isPrime(ptr.data))
            deleteNode(head_ref, ptr);
        ptr = next;
    }
    return head_ref;
}
 
// function to print nodes in a
// given doubly linked list
static void printList(Node head)
{
    while (head != null)
    {
        System.out.print( head.data + " ");
        head = head.next;
    }
}
 
// Driver program
public static void main(String args[])
{
    // start with the empty list
    Node head = null;
 
    // create the doubly linked list
    // 15 <. 16 <. 7 <. 6 <. 17
    head = push(head, 17);
    head = push(head, 6);
    head = push(head, 7);
    head = push(head, 16);
    head = push(head, 15);
 
    System.out.print( "Original List: ");
    printList(head);
 
    head = deletePrimeNodes(head);
 
    System.out.print("\nModified List: ");
    printList(head);
}
}
 
// This code is contributed by Arnab Kundu

Python3

# Python3 implementation to delete all
# prime nodes from the doubly
# linked list
import math
 
# Node of the doubly linked list
class Node:
    def __init__(self, data):
        self.data = data
        self.next = None
         
# function to insert a node at the beginning
# of the Doubly Linked List
def push(head_ref, new_data):
     
    # allocate node
    new_node = Node(new_data)
 
    # put in the data
    new_node.data = new_data
 
    # since we are adding at the beginning,
    # prev is always None
    new_node.prev = None
 
    # link the old list off the new node
    new_node.next = head_ref
 
    # change prev of head node to new node
    if (head_ref != None):
        head_ref.prev = new_node
 
    # move the head to point to the new node
    head_ref = new_node
    return head_ref
 
# Function to check if a number is prime
def isPrime(n):
     
    # Corner cases
    if (n <= 1):
        return False
    if (n <= 3):
        return True
 
    # This is checked so that we can skip
    # middle five numbers in below loop
    if (n % 2 == 0 or n % 3 == 0):
        return False
    for i in range(5, n + 1, 6):
        if (i * i < n + 2 and
           (n % i == 0 or n % (i + 2) == 0)):
            return False
         
    return True
 
# function to delete a node in a Doubly Linked List.
# head_ref --> pointer to head node pointer.
# del --> pointer to node to be deleted
def deleteNode(head_ref, delete):
     
    # base case
    if (head_ref == None or delete == None):
        return None
 
    # If node to be deleted is head node
    if (head_ref == delete):
        head_ref = delete.next
 
    # Change next only if node to be
    # deleted is NOT the last node
    if (delete.next != None):
        delete.next.prev = delete.prev
 
    # Change prev only if node to be
    # deleted is NOT the first node
    if (delete.prev != None):
        delete.prev.next = delete.next
 
    # Finally, free the memory occupied by del
    return head_ref
 
# function to delete all prime nodes
# from the doubly linked list
def deletePrimeNodes(head_ref):
    ptr = head_ref
    #next
 
    while (ptr != None):
        next = ptr.next
         
        # if true, delete node 'ptr'
        if (isPrime(ptr.data)):
            deleteNode(head_ref, ptr)
        ptr = next
     
    return head_ref
 
# function to print nodes in a
# given doubly linked list
def printList(head):
    while (head != None) :
        print(head.data, end = " ")
        head = head.next
 
# Driver Code
if __name__=='__main__':
     
    # start with the empty list
    head = None
 
    # create the doubly linked list
    # 15 <-> 16 <-> 7 <-> 6 <-> 17
    head = push(head, 17)
    head = push(head, 6)
    head = push(head, 7)
    head = push(head, 16)
    head = push(head, 15)
 
    print("Original List: ", end = "")
    printList(head)
 
    deletePrimeNodes(head)
 
    print("\nModified List: ", end = "")
    printList(head)
 
# This code is contributed by AbhiThakur

C#

// C# implementation to delete all
// prime nodes from the doubly
// linked list
using System;
 
class GFG
{
     
// Node of the doubly linked list
public class Node
{
    public int data;
    public Node prev, next;
};
 
// function to insert a node at the beginning
// of the Doubly Linked List
static Node push(Node head_ref, int new_data)
{
    // allocate node
    Node new_node = new Node();
 
    // put in 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 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;
     
    return head_ref;
}
 
// Function to check if a number is prime
static Boolean isPrime(int n)
{
    // Corner cases
    if (n <= 1)
        return false;
    if (n <= 3)
        return true;
 
    // This is checked so that we can skip
    // middle five numbers in below loop
    if (n % 2 == 0 || n % 3 == 0)
        return false;
 
    for (int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;
 
    return true;
}
 
// function to delete a node in a Doubly Linked List.
// head_ref -. pointer to head node pointer.
// del -. pointer to node to be deleted
static Node deleteNode(Node head_ref, Node del)
{
    // base case
    if (head_ref == null || del == null)
        return null;
 
    // If 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;
 
    return head_ref;
}
 
// function to delete all prime nodes
// from the doubly linked list
static Node deletePrimeNodes(Node head_ref)
{
    Node ptr = head_ref;
    Node next;
 
    while (ptr != null)
    {
        next = ptr.next;
         
        // if true, delete node 'ptr'
        if (isPrime(ptr.data))
            deleteNode(head_ref, ptr);
        ptr = next;
    }
    return head_ref;
}
 
// function to print nodes in a
// given doubly linked list
static void printList(Node head)
{
    while (head != null)
    {
        Console.Write(head.data + " ");
        head = head.next;
    }
}
 
// Driver program
public static void Main()
{
    // start with the empty list
    Node head = null;
 
    // create the doubly linked list
    // 15 <. 16 <. 7 <. 6 <. 17
    head = push(head, 17);
    head = push(head, 6);
    head = push(head, 7);
    head = push(head, 16);
    head = push(head, 15);
 
    Console.Write( "Original List: ");
    printList(head);
 
    head = deletePrimeNodes(head);
 
    Console.Write("\nModified List: ");
    printList(head);
}
}
 
// This code is contributed by Rajput-Ji

Javascript

// javascript implementation to delete all
// prime nodes from the doubly
// linked list     // Node of the doubly linked list
class Node {
    constructor(val) {
        this.data = val;
        this.prev = null;
        this.next = null;
    }
}
 
    // function to insert a node at the beginning
    // of the Doubly Linked List
    function push(head_ref , new_data) {
        // allocate node
var new_node = new Node();
 
        // put in 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 prev of head node to new node
        if ((head_ref) != null)
            (head_ref).prev = new_node;
 
        // move the head to povar to the new node
        (head_ref) = new_node;
 
        return head_ref;
    }
 
    // Function to check if a number is prime
    function isPrime(n) {
        // Corner cases
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;
 
        // This is checked so that we can skip
        // middle five numbers in below loop
        if (n % 2 == 0 || n % 3 == 0)
            return false;
 
        for (i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
 
        return true;
    }
 
    // function to delete a node in a Doubly Linked List.
    // head_ref -. pointer to head node pointer.
    // del -. pointer to node to be deleted
    function deleteNode(head_ref,  del) {
        // base case
        if (head_ref == null || del == null)
            return null;
 
        // If 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;
 
        return head_ref;
    }
 
    // function to delete all prime nodes
    // from the doubly linked list
    function deletePrimeNodes(head_ref) {
var ptr = head_ref;
var next;
 
        while (ptr != null) {
            next = ptr.next;
 
            // if true, delete node 'ptr'
            if (isPrime(ptr.data))
                deleteNode(head_ref, ptr);
            ptr = next;
        }
        return head_ref;
    }
 
    // function to prvar nodes in a
    // given doubly linked list
    function printList(head) {
        while (head != null) {
            document.write(head.data + " ");
            head = head.next;
        }
    }
 
    // Driver program
     
        // start with the empty list
var head = null;
 
        // create the doubly linked list
        // 15 <. 16 <. 7 <. 6 <. 17
        head = push(head, 17);
        head = push(head, 6);
        head = push(head, 7);
        head = push(head, 16);
        head = push(head, 15);
 
        document.write("Original List: ");
        printList(head);
 
        head = deletePrimeNodes(head);
 
        document.write("<br/>Modified List: ");
        printList(head);
 
// This code contributed by Rajput-Ji

输出：

Original List: 15 16 7 6 17 
Modified List: 15 16 6

时间复杂度： O(N)，其中 N 是节点总数。

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