A continuación se muestra una implementación recursiva típica de QuickSort para arreglos. La implementación usa el último elemento como pivote.
C++
/* A typical recursive implementation of Quicksort for array*/
/* This function takes last element as pivot, places the pivot element at its
correct position in sorted array, and places all smaller (smaller than
pivot) to left of pivot and all greater elements to right of pivot */
int partition (int arr[], int l, int h)
{
int x = arr[h];
int i = (l - 1);
for (int j = l; j <= h- 1; j++)
{
if (arr[j] <= x)
{
i++;
swap (&arr[i], &arr[j]);
}
}
swap (&arr[i + 1], &arr[h]);
return (i + 1);
}
/* A[] --> Array to be sorted, l --> Starting index, h --> Ending index */
void quickSort(int A[], int l, int h)
{
if (l < h)
{
int p = partition(A, l, h); /* Partitioning index */
quickSort(A, l, p - 1);
quickSort(A, p + 1, h);
}
}
Java
/* A typical recursive implementation of
Quicksort for array*/
/* This function takes last element as pivot,
places the pivot element at its correct
position in sorted array, and places all
smaller (smaller than pivot) to left of
pivot and all greater elements to right
of pivot */
static int partition (int []arr, int l, int h)
{
int x = arr[h];
int i = (l - 1);
for(int j = l; j <= h - 1; j++)
{
if (arr[j] <= x)
{
i++;
int tmp = arr[i];
arr[i] = arr[j];
arr[j] = tmp;
}
}
int tmp = arr[i + 1];
arr[i + 1] = arr[h];
arr[h] = tmp;
return(i + 1);
}
/* A[] --> Array to be sorted,
l --> Starting index,
h --> Ending index */
static void quickSort(int []A, int l,
int h)
{
if (l < h)
{
// Partitioning index
int p = partition(A, l, h);
quickSort(A, l, p - 1);
quickSort(A, p + 1, h);
}
}
// This code is contributed by pratham76.
Python3
"""A typical recursive implementation of Quicksort for array """ """ This function takes last element as pivot, places the pivot element at its correct position in sorted array, and places all smaller (smaller than pivot) to left of pivot and all greater elements to right of pivot """ """ i --> is the first index in the array x --> is the last index in the array tmp --> is a temporary variable for swapping values (integer) """ # array arr, integer l, integer h def partition (arr, l, h): x = arr[h] i = (l - 1) for j in range(l, h): if (arr[j] <= x): i +=1 tmp = arr[i] arr[i] = arr[j] arr[j] = tmp tmp = arr[i + 1] arr[i + 1] = arr[h] arr[h] = tmp return(i + 1) """ A --> Array to be sorted, l --> Starting index, h --> Ending index """ # array A, integer l, integer h def quickSort(A, l, h): if (l < h): p = partition(A, l, h) # pivot index quickSort(A, l, p - 1) # left quickSort(A, p + 1, h) # right # This code is contributed by humphreykibet.
C#
/* A typical recursive implementation of
Quicksort for array*/
/* This function takes last element as pivot,
places the pivot element at its correct
position in sorted array, and places all
smaller (smaller than pivot) to left of
pivot and all greater elements to right
of pivot */
static int partition (int []arr, int l, int h)
{
int x = arr[h];
int i = (l - 1);
for(int j = l; j <= h - 1; j++)
{
if (arr[j] <= x)
{
i++;
int tmp = arr[i];
arr[i] = arr[j];
arr[j] = tmp;
}
}
int tmp = arr[i + 1];
arr[i + 1] = arr[h];
arr[h] = tmp;
return(i + 1);
}
/* A[] --> Array to be sorted,
l --> Starting index,
h --> Ending index */
static void quickSort(int []A, int l,
int h)
{
if (l < h)
{
// Partitioning index
int p = partition(A, l, h);
quickSort(A, l, p - 1);
quickSort(A, p + 1, h);
}
}
// This code is contributed by rutvik_56
Javascript
<script>
/* A typical recursive implementation of
Quicksort for array*/
/* This function takes last element as pivot,
places the pivot element at its correct
position in sorted array, and places all
smaller (smaller than pivot) to left of
pivot and all greater elements to right
of pivot */
function partition (arr,l,h)
{
let x = arr[h];
let i = (l - 1);
for(let j = l; j <= h - 1; j++)
{
if (arr[j] <= x)
{
i++;
let tmp = arr[i];
arr[i] = arr[j];
arr[j] = tmp;
}
}
let tmp = arr[i + 1];
arr[i + 1] = arr[h];
arr[h] = tmp;
return(i + 1);
}
/* A[] --> Array to be sorted,
l --> Starting index,
h --> Ending index */
function quickSort(A,l,h)
{
if (l < h)
{
// Partitioning index
let p = partition(A, l, h);
quickSort(A, l, p - 1);
quickSort(A, p + 1, h);
}
}
// This code is contributed by unknown2108
</script>
¿Podemos usar el mismo algoritmo para la lista enlazada?
A continuación se muestra la implementación de C++ para la lista doblemente enlazada. La idea es simple, primero encontramos el puntero al último Node. Una vez que tenemos un puntero al último Node, podemos ordenar recursivamente la lista enlazada usando punteros al primer y último Node de una lista enlazada, similar a la función recursiva anterior donde pasamos índices del primer y último elemento de la array. La función de partición para una lista enlazada también es similar a la partición para arrays. En lugar de devolver el índice del elemento pivote, devuelve un puntero al elemento pivote. En la siguiente implementación, quickSort() es solo una función contenedora, la principal función recursiva es _quickSort(), que es similar a quickSort() para la implementación de arrays.
Implementación:
C++
// A C++ program to sort a linked list using Quicksort
#include <bits/stdc++.h>
using namespace std;
/* a node of the doubly linked list */
class Node
{
public:
int data;
Node *next;
Node *prev;
};
/* A utility function to swap two elements */
void swap ( int* a, int* b )
{ int t = *a; *a = *b; *b = t; }
// A utility function to find
// last node of linked list
Node *lastNode(Node *root)
{
while (root && root->next)
root = root->next;
return root;
}
/* Considers last element as pivot,
places the pivot element at its
correct position in sorted array,
and places all smaller (smaller than
pivot) to left of pivot and all greater
elements to right of pivot */
Node* partition(Node *l, Node *h)
{
// set pivot as h element
int x = h->data;
// similar to i = l-1 for array implementation
Node *i = l->prev;
// Similar to "for (int j = l; j <= h- 1; j++)"
for (Node *j = l; j != h; j = j->next)
{
if (j->data <= x)
{
// Similar to i++ for array
i = (i == NULL)? l : i->next;
swap(&(i->data), &(j->data));
}
}
i = (i == NULL)? l : i->next; // Similar to i++
swap(&(i->data), &(h->data));
return i;
}
/* A recursive implementation
of quicksort for linked list */
void _quickSort(Node* l, Node *h)
{
if (h != NULL && l != h && l != h->next)
{
Node *p = partition(l, h);
_quickSort(l, p->prev);
_quickSort(p->next, h);
}
}
// The main function to sort a linked list.
// It mainly calls _quickSort()
void quickSort(Node *head)
{
// Find last node
Node *h = lastNode(head);
// Call the recursive QuickSort
_quickSort(head, h);
}
// A utility function to print contents of arr
void printList(Node *head)
{
while (head)
{
cout << head->data << " ";
head = head->next;
}
cout << endl;
}
/* Function to insert a node at the
beginning of the Doubly Linked List */
void push(Node** head_ref, int new_data)
{
Node* new_node = new Node; /* allocate node */
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;
}
/* Driver code */
int main()
{
Node *a = NULL;
push(&a, 5);
push(&a, 20);
push(&a, 4);
push(&a, 3);
push(&a, 30);
cout << "Linked List before sorting \n";
printList(a);
quickSort(a);
cout << "Linked List after sorting \n";
printList(a);
return 0;
}
// This code is contributed by rathbhupendra
C
// C program to sort a linked list using Quicksort
#include <stdio.h>
#include <stdlib.h>
/* a node of the doubly linked list */
struct Node
{
int data;
struct Node *next;
struct Node *prev;
};
/* A utility function to swap two elements */
void swap ( int* a, int* b )
{ int t = *a; *a = *b; *b = t; }
// A utility function to find last node of linked list
struct Node *lastNode(struct Node *root)
{
while (root && root->next)
root = root->next;
return root;
}
/* Considers last element as pivot, places the
pivot element at its correct position in sorted array,
and places all smaller (smaller than pivot) to left
of pivot and all greater elements to right of pivot */
struct Node* partition(struct Node *l, struct Node *h)
{
// set pivot as h element
int x = h->data;
// similar to i = l-1 for array implementation
struct Node *i = l->prev;
// Similar to "for (int j = l; j <= h- 1; j++)"
for (struct Node *j = l; j != h; j = j->next)
{
if (j->data <= x)
{
// Similar to i++ for array
i = (i == NULL) ? l : i->next;
swap(&(i->data), &(j->data));
}
}
i = (i == NULL) ? l : i->next; // Similar to i++
swap(&(i->data), &(h->data));
return i;
}
/* A recursive implementation of quicksort for linked list */
void _quickSort(struct Node* l, struct Node *h)
{
if (h != NULL && l != h && l != h->next)
{
struct Node *p = partition(l, h);
_quickSort(l, p->prev);
_quickSort(p->next, h);
}
}
// The main function to sort a linked list.
// It mainly calls _quickSort()
void quickSort(struct Node *head)
{
// Find last node
struct Node *h = lastNode(head);
// Call the recursive QuickSort
_quickSort(head, h);
}
// A utility function to print contents of arr
void printList(struct Node *head)
{
while (head)
{
printf("%d ", head->data);
head = head->next;
}
printf("\n");
}
/* Function to insert a node at the
beginning of the Doubly Linked List */
void push(struct Node** head_ref, int new_data)
{
struct Node* new_node = (struct Node*)
malloc(sizeof(struct Node)); /* allocate node */
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;
}
// Driver Code
int main(int argc, char **argv)
{
struct Node *a = NULL;
push(&a, 5);
push(&a, 20);
push(&a, 4);
push(&a, 3);
push(&a, 30);
printf("Linked List before sorting \n");
printList(a);
quickSort(a);
printf("Linked List after sorting \n");
printList(a);
return 0;
}
Java
// A Java program to sort a linked list using Quicksort
class QuickSort_using_Doubly_LinkedList{
Node head;
/* a node of the doubly linked list */
static class Node{
private int data;
private Node next;
private Node prev;
Node(int d){
data = d;
next = null;
prev = null;
}
}
// A utility function to find last node of linked list
Node lastNode(Node node){
while(node.next!=null)
node = node.next;
return node;
}
/* Considers last element as pivot, places the pivot element at its
correct position in sorted array, and places all smaller (smaller than
pivot) to left of pivot and all greater elements to right of pivot */
Node partition(Node l,Node h)
{
// set pivot as h element
int x = h.data;
// similar to i = l-1 for array implementation
Node i = l.prev;
// Similar to "for (int j = l; j <= h- 1; j++)"
for(Node j=l; j!=h; j=j.next)
{
if(j.data <= x)
{
// Similar to i++ for array
i = (i==null) ? l : i.next;
int temp = i.data;
i.data = j.data;
j.data = temp;
}
}
i = (i==null) ? l : i.next; // Similar to i++
int temp = i.data;
i.data = h.data;
h.data = temp;
return i;
}
/* A recursive implementation of quicksort for linked list */
void _quickSort(Node l,Node h)
{
if(h!=null && l!=h && l!=h.next){
Node temp = partition(l,h);
_quickSort(l,temp.prev);
_quickSort(temp.next,h);
}
}
// The main function to sort a linked list. It mainly calls _quickSort()
public void quickSort(Node node)
{
// Find last node
Node head = lastNode(node);
// Call the recursive QuickSort
_quickSort(node,head);
}
// A utility function to print contents of arr
public void printList(Node head)
{
while(head!=null){
System.out.print(head.data+" ");
head = head.next;
}
}
/* Function to insert a node at the beginning of the Doubly Linked List */
void push(int new_Data)
{
Node new_Node = new Node(new_Data); /* allocate node */
// if head is null, head = new_Node
if(head==null){
head = new_Node;
return;
}
/* link the old list off the new node */
new_Node.next = head;
/* change prev of head node to new node */
head.prev = new_Node;
/* since we are adding at the beginning, prev is always NULL */
new_Node.prev = null;
/* move the head to point to the new node */
head = new_Node;
}
/* Driver program to test above function */
public static void main(String[] args){
QuickSort_using_Doubly_LinkedList list = new QuickSort_using_Doubly_LinkedList();
list.push(5);
list.push(20);
list.push(4);
list.push(3);
list.push(30);
System.out.println("Linked List before sorting ");
list.printList(list.head);
System.out.println("\nLinked List after sorting");
list.quickSort(list.head);
list.printList(list.head);
}
}
// This code has been contributed by Amit Khandelwal
Python3
# A Python program to sort a linked list using Quicksort
head = None
# a node of the doubly linked list
class Node:
def __init__(self, d):
self.data = d
self.next = None
self.prev = None
# A utility function to find last node of linked list
def lastNode(node):
while(node.next != None):
node = node.next;
return node;
# Considers last element as pivot, places the pivot element at its
# correct position in sorted array, and places all smaller (smaller than
# pivot) to left of pivot and all greater elements to right of pivot
def partition(l, h):
# set pivot as h element
x = h.data;
# similar to i = l-1 for array implementation
i = l.prev;
j = l
# Similar to "for (int j = l; j <= h- 1; j++)"
while(j != h):
if(j.data <= x):
# Similar to i++ for array
i = l if(i == None) else i.next;
temp = i.data;
i.data = j.data;
j.data = temp;
j = j.next
i = l if (i == None) else i.next; # Similar to i++
temp = i.data;
i.data = h.data;
h.data = temp;
return i;
# A recursive implementation of quicksort for linked list
def _quickSort(l,h):
if(h != None and l != h and l != h.next):
temp = partition(l, h);
_quickSort(l,temp.prev);
_quickSort(temp.next, h);
# The main function to sort a linked list. It mainly calls _quickSort()
def quickSort(node):
# Find last node
head = lastNode(node);
# Call the recursive QuickSort
_quickSort(node,head);
# A utility function to print contents of arr
def printList(head):
while(head != None):
print(head.data, end=" ");
head = head.next;
# Function to insert a node at the beginning of the Doubly Linked List
def push(new_Data):
global head;
new_Node = Node(new_Data); # allocate node
# if head is null, head = new_Node
if(head == None):
head = new_Node;
return;
# link the old list off the new node
new_Node.next = head;
# change prev of head node to new node
head.prev = new_Node;
# since we are adding at the beginning, prev is always NULL
new_Node.prev = None;
# move the head to point to the new node
head = new_Node;
# Driver program to test above function
push(5);
push(20);
push(4);
push(3);
push(30);
print("Linked List before sorting ");
printList(head);
print("\nLinked List after sorting");
quickSort(head);
printList(head);
# This code is contributed by _saurabh_jaiswal
C#
// A C# program to sort a linked list using Quicksort
using System;
/* a node of the doubly linked list */
public class Node
{
public int Data;
public Node Next;
public Node Prev;
public Node(int d)
{
Data = d;
/* Prev and Next are left Null */
}
}
public class DoublyLinkedList
{
private Node _head;
public Node Head
{
get => _head;
set => _head = value;
}
// A utility function to find the last node of linked list
private Node LastNode(Node node)
{
while (node.Next != null)
node = node.Next;
return node;
}
/* Considers last element as pivot,
places the pivot element at its
correct position in a sorted array,
and places all smaller (smaller than
pivot) to left of pivot and all
greater elements to right of pivot */
private Node Partition(Node last, Node head)
{
// set pivot as h element
int pivot = head.Data;
// similar to i = l-1 for array implementation
Node i = last.Prev;
int temp;
// Similar to "for (int j = l; j <= h- 1; j++)"
for (Node j = last; j != head; j = j.Next)
{
if (j.Data <= pivot)
{
// Similar to i++ for array
i = (i == null) ? last : i.Next;
temp = i.Data;
i.Data = j.Data;
j.Data = temp;
}
}
i = (i == null) ? last : i.Next; // Similar to i++
temp = i.Data;
i.Data = head.Data;
head.Data = temp;
return i;
}
/* A recursive implementation of
quicksort for linked list */
private void RecursiveQuickSort(Node last, Node head)
{
if (head != null && last != head && last != head.Next)
{
Node temp = Partition(last, head);
RecursiveQuickSort(last, temp.Prev);
RecursiveQuickSort(temp.Next, head);
}
}
// The main function to sort a linked list.
// It mainly calls _quickSort()
public void QuickSort(Node node)
{
// Find last node
Node head = LastNode(node);
// Call the recursive QuickSort
RecursiveQuickSort(node, head);
}
// A utility function to print contents of arr
public void PrintList(Node head)
{
while (head != null)
{
Console.Write(head.Data + " ");
head = head.Next;
}
}
/* Function to insert a node at the
beginning of the Doubly Linked List */
public void Push(int new_Data)
{
Node new_Node = new Node(new_Data); /* allocate node */
// if head is null, head = new_Node
if (_head == null)
{
_head = new_Node;
return;
}
/* link the old list off the new node */
new_Node.Next = _head;
/* change prev of head node to new node */
_head.Prev = new_Node;
/* since we are adding at the
beginning, prev is always NULL */
/* move the head to point to the new node */
_head = new_Node;
}
/* Driver code */
}
public class QuickSort_using_Doubly_LinkedList
{
public static void Main(String[] args)
{
var list = new DoublyLinkedList();
list.Push(5);
list.Push(20);
list.Push(4);
list.Push(3);
list.Push(30);
Console.WriteLine("Linked List before sorting ");
list.PrintList(list.Head);
Console.WriteLine("\nLinked List after sorting");
list.QuickSort(list.Head);
list.PrintList(list.Head);
}
}
Javascript
<script>
// A Javascript program to sort a linked list using Quicksort
let head;
/* a node of the doubly linked list */
class Node
{
constructor(d)
{
this.data = d;
this.next = null;
this.prev = null;
}
}
// A utility function to find last node of linked list
function lastNode(node)
{
while(node.next != null)
node = node.next;
return node;
}
/* Considers last element as pivot, places the pivot element at its
correct position in sorted array, and places all smaller (smaller than
pivot) to left of pivot and all greater elements to right of pivot */
function partition(l, h)
{
// set pivot as h element
let x = h.data;
// similar to i = l-1 for array implementation
let i = l.prev;
// Similar to "for (int j = l; j <= h- 1; j++)"
for(let j=l; j!=h; j=j.next)
{
if(j.data <= x)
{
// Similar to i++ for array
i = (i == null) ? l : i.next;
let temp = i.data;
i.data = j.data;
j.data = temp;
}
}
i = (i == null) ? l : i.next; // Similar to i++
let temp = i.data;
i.data = h.data;
h.data = temp;
return i;
}
/* A recursive implementation of quicksort for linked list */
function _quickSort(l,h)
{
if(h != null && l!=h && l != h.next){
let temp = partition(l, h);
_quickSort(l,temp.prev);
_quickSort(temp.next,h);
}
}
// The main function to sort a linked list. It mainly calls _quickSort()
function quickSort(node)
{
// Find last node
let head = lastNode(node);
// Call the recursive QuickSort
_quickSort(node,head);
}
// A utility function to print contents of arr
function printList(head)
{
while(head!=null){
document.write(head.data+" ");
head = head.next;
}
}
/* Function to insert a node at the beginning of the Doubly Linked List */
function push(new_Data)
{
let new_Node = new Node(new_Data); /* allocate node */
// if head is null, head = new_Node
if(head==null){
head = new_Node;
return;
}
/* link the old list off the new node */
new_Node.next = head;
/* change prev of head node to new node */
head.prev = new_Node;
/* since we are adding at the beginning, prev is always NULL */
new_Node.prev = null;
/* move the head to point to the new node */
head = new_Node;
}
/* Driver program to test above function */
push(5);
push(20);
push(4);
push(3);
push(30);
document.write("Linked List before sorting <br>");
printList(head);
document.write("<br>Linked List after sorting<br>");
quickSort(head);
printList(head);
// This code is contributed by patel2127
</script>
Producción
Linked List before sorting 30 3 4 20 5 Linked List after sorting 3 4 5 20 30
Complejidad de tiempo: la complejidad de tiempo de la implementación anterior es la misma que la complejidad de tiempo de QuickSort() para arreglos. Toma tiempo O(n^2) en el peor de los casos y O(nLogn) en el promedio y en el mejor de los casos. El peor caso ocurre cuando la lista enlazada ya está ordenada.
¿Podemos implementar una ordenación rápida aleatoria para una lista enlazada?
Quicksort se puede implementar para la lista enlazada solo cuando podemos elegir un punto fijo como pivote (como el último elemento en la implementación anterior). Random QuickSort no se puede implementar de manera eficiente para las listas vinculadas seleccionando un pivote aleatorio.
Espacio Auxiliar: O(n)
El espacio adicional se debe a la pila de llamadas de función.
Ejercicio:
La implementación anterior es para una lista doblemente enlazada. Modifíquelo para una lista enlazada individualmente. Tenga en cuenta que no tenemos un puntero anterior en una lista enlazada individualmente.
Consulte QuickSort en Single Linked List para obtener una solución.
Publicación traducida automáticamente
Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA