Partitioning a linked list around a given value and keeping the original order

Given a linked list and a value x, partition it such that all nodes less than x come first, then all nodes with value equal to x and finally nodes with value greater than or equal to x. The original relative order of the nodes in each of the three partitions should be preserved. The partition must work in-place.

Examples:

Input : 1->4->3->2->5->2->3, 
        x = 3
Output: 1->2->2->3->3->4->5

Input : 1->4->2->10 
        x = 3
Output: 1->2->4->10

Input : 10->4->20->10->3 
        x = 3
Output: 3->10->4->20->10

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

To solve this problem we can use partition method of Quick Sort but this would not preserve the original relative order of the nodes in each of the two partitions.

Below is the algorithm to solve this problem :

Initialize first and last nodes of below three linked lists as NULL.
1. Linked list of values smaller than x.
2. Linked list of values equal to x.
3. Linked list of values greater than x.
Now iterate through the original linked list. If a node’s value is less than x then append it at the end of smaller list. If the value is equal to x, then at the end of equal list. And if value is greater, then at the end of greater list.
Now concatenate three lists.

Below is the implementation of above idea.

C++

// C++ program to partition a linked list around a 
// given value. 
#include<bits/stdc++.h> 
using namespace std; 
  
/* Link list Node */
struct Node 
{ 
    int data; 
    struct Node* next; 
}; 
  
// A utility function to create a new node 
Node *newNode(int data) 
{ 
    struct Node* new_node = new Node; 
    new_node->data  = data; 
    new_node->next = NULL; 
    return new_node; 
} 
  
// Function to make two separate lists and return 
// head after concatinating 
struct Node *partition(struct Node *head, int x) 
{ 
    /* Let us initialize first and last nodes of 
      three linked lists 
        1) Linked list of values smaller than x. 
        2) Linked list of values equal to x. 
        3) Linked list of values greater than x.*/
    struct Node *smallerHead = NULL, *smallerLast = NULL; 
    struct Node *greaterLast = NULL, *greaterHead = NULL; 
    struct Node *equalHead = NULL, *equalLast = NULL; 
  
    // Now iterate original list and connect nodes 
    // of appropriate linked lists. 
    while (head != NULL) 
    { 
        // If current node is equal to x, append it 
        // to the list of x values 
        if (head->data == x) 
        { 
            if (equalHead == NULL) 
                equalHead = equalLast = head; 
            else
            { 
                equalLast->next = head; 
                equalLast = equalLast->next; 
            } 
        } 
  
        // If current node is less than X, append 
        // it to the list of smaller values 
        else if (head->data < x) 
        { 
            if (smallerHead == NULL) 
                smallerLast = smallerHead = head; 
            else
            { 
                smallerLast->next = head; 
                smallerLast = head; 
            } 
        } 
        else // Append to the list of greater values 
        { 
            if (greaterHead == NULL) 
                greaterLast = greaterHead = head; 
            else
            { 
                greaterLast->next  = head; 
                greaterLast = head; 
            } 
        } 
  
        head = head->next; 
    } 
  
    // Fix end of greater linked list to NULL if this 
    // list has some nodes 
    if (greaterLast != NULL) 
        greaterLast->next = NULL; 
  
    // Connect three lists 
  
    // If smaller list is empty 
    if (smallerHead == NULL) 
    { 
        if (equalHead == NULL) 
            return greaterHead; 
        equalLast->next = greaterHead; 
        return equalHead; 
    } 
  
    // If smaller list is not empty 
    // and equal list is empty 
    if (equalHead == NULL) 
    { 
        smallerLast->next = greaterHead; 
        return smallerHead; 
    } 
  
    // If both smaller and equal list 
    // are non-empty 
    smallerLast->next = equalHead; 
    equalLast->next = greaterHead; 
    return  smallerHead; 
} 
  
/* Function to print linked list */
void printList(struct Node *head) 
{ 
    struct Node *temp = head; 
    while (temp != NULL) 
    { 
        printf("%d  ", temp->data); 
        temp = temp->next; 
    } 
} 
  
// Driver program to run the case 
int main() 
{ 
    /* Start with the empty list */
    struct Node* head = newNode(10); 
    head->next = newNode(4); 
    head->next->next = newNode(5); 
    head->next->next->next = newNode(30); 
    head->next->next->next->next = newNode(2); 
    head->next->next->next->next->next = newNode(50); 
  
    int x = 3; 
    head = partition(head, x); 
    printList(head); 
    return 0; 
} 

Java

// Java program to partition a  
// linked list around a given value.  
class GfG  
{  
  
/* Link list Node */
static class Node  
{  
    int data;  
    Node next;  
} 
  
// A utility function to create a new node  
static Node newNode(int data)  
{  
    Node new_node = new Node();  
    new_node.data = data;  
    new_node.next = null;  
    return new_node;  
}  
  
// Function to make two separate lists and return  
// head after concatinating  
static Node partition(Node head, int x)  
{  
      
    /* Let us initialize first and last nodes of  
    three linked lists  
        1) Linked list of values smaller than x.  
        2) Linked list of values equal to x.  
        3) Linked list of values greater than x.*/
    Node smallerHead = null, smallerLast = null;  
    Node greaterLast = null, greaterHead = null;  
    Node equalHead = null, equalLast =null;  
  
    // Now iterate original list and connect nodes  
    // of appropriate linked lists.  
    while (head != null)  
    {  
        // If current node is equal to x, append it  
        // to the list of x values  
        if (head.data == x)  
        {  
            if (equalHead == null)  
                equalHead = equalLast = head;  
            else
            {  
                equalLast.next = head;  
                equalLast = equalLast.next;  
            }  
        }  
  
        // If current node is less than X, append  
        // it to the list of smaller values  
        else if (head.data < x)  
        {  
            if (smallerHead == null)  
                smallerLast = smallerHead = head;  
            else
            {  
                smallerLast.next = head;  
                smallerLast = head;  
            }  
        }  
        else // Append to the list of greater values  
        {  
            if (greaterHead == null)  
                greaterLast = greaterHead = head;  
            else
            {  
                greaterLast.next = head;  
                greaterLast = head;  
            }  
        }  
        head = head.next;  
    }  
  
    // Fix end of greater linked list to NULL if this  
    // list has some nodes  
    if (greaterLast != null)  
        greaterLast.next = null;  
  
    // Connect three lists  
  
    // If smaller list is empty  
    if (smallerHead == null)  
    {  
        if (equalHead == null)  
            return greaterHead;  
        equalLast.next = greaterHead;  
        return equalHead;  
    }  
  
    // If smaller list is not empty  
    // and equal list is empty  
    if (equalHead == null)  
    {  
        smallerLast.next = greaterHead;  
        return smallerHead;  
    }  
  
    // If both smaller and equal list  
    // are non-empty  
    smallerLast.next = equalHead;  
    equalLast.next = greaterHead;  
    return smallerHead;  
}  
  
/* Function to print linked list */
static void printList(Node head)  
{  
    Node temp = head;  
    while (temp != null)  
    {  
        System.out.print(temp.data + " ");  
        temp = temp.next;  
    }  
}  
  
// Driver code  
public static void main(String[] args)  
{  
    /* Start with the empty list */
    Node head = newNode(10);  
    head.next = newNode(4);  
    head.next.next = newNode(5);  
    head.next.next.next = newNode(30);  
    head.next.next.next.next = newNode(2);  
    head.next.next.next.next.next = newNode(50);  
  
    int x = 3;  
    head = partition(head, x);  
    printList(head);  
} 
}  
  
// This code is contributed by Prerna saini. 

C#

// C# program to partition a  
// linked list around a given value.  
using System; 
  
public class GfG  
{  
  
/* Link list Node */
public class Node  
{  
    public int data;  
    public Node next;  
} 
  
// A utility function to create a new node  
static Node newNode(int data)  
{  
    Node new_node = new Node();  
    new_node.data = data;  
    new_node.next = null;  
    return new_node;  
}  
  
// Function to make two separate lists and return  
// head after concatinating  
static Node partition(Node head, int x)  
{  
      
    /* Let us initialize first and last nodes of  
    three linked lists  
        1) Linked list of values smaller than x.  
        2) Linked list of values equal to x.  
        3) Linked list of values greater than x.*/
    Node smallerHead = null, smallerLast = null;  
    Node greaterLast = null, greaterHead = null;  
    Node equalHead = null, equalLast =null;  
  
    // Now iterate original list and connect nodes  
    // of appropriate linked lists.  
    while (head != null)  
    {  
        // If current node is equal to x, append it  
        // to the list of x values  
        if (head.data == x)  
        {  
            if (equalHead == null)  
                equalHead = equalLast = head;  
            else
            {  
                equalLast.next = head;  
                equalLast = equalLast.next;  
            }  
        }  
  
        // If current node is less than X, append  
        // it to the list of smaller values  
        else if (head.data < x)  
        {  
            if (smallerHead == null)  
                smallerLast = smallerHead = head;  
            else
            {  
                smallerLast.next = head;  
                smallerLast = head;  
            }  
        }  
        else // Append to the list of greater values  
        {  
            if (greaterHead == null)  
                greaterLast = greaterHead = head;  
            else
            {  
                greaterLast.next = head;  
                greaterLast = head;  
            }  
        }  
        head = head.next;  
    }  
  
    // Fix end of greater linked list to NULL if this  
    // list has some nodes  
    if (greaterLast != null)  
        greaterLast.next = null;  
  
    // Connect three lists  
  
    // If smaller list is empty  
    if (smallerHead == null)  
    {  
        if (equalHead == null)  
            return greaterHead;  
        equalLast.next = greaterHead;  
        return equalHead;  
    }  
  
    // If smaller list is not empty  
    // and equal list is empty  
    if (equalHead == null)  
    {  
        smallerLast.next = greaterHead;  
        return smallerHead;  
    }  
  
    // If both smaller and equal list  
    // are non-empty  
    smallerLast.next = equalHead;  
    equalLast.next = greaterHead;  
    return smallerHead;  
}  
  
/* Function to print linked list */
static void printList(Node head)  
{  
    Node temp = head;  
    while (temp != null)  
    {  
        Console.Write(temp.data + " ");  
        temp = temp.next;  
    }  
}  
  
// Driver code  
public static void Main()  
{  
    /* Start with the empty list */
    Node head = newNode(10);  
    head.next = newNode(4);  
    head.next.next = newNode(5);  
    head.next.next.next = newNode(30);  
    head.next.next.next.next = newNode(2);  
    head.next.next.next.next.next = newNode(50);  
  
    int x = 3;  
    head = partition(head, x);  
    printList(head);  
} 
} 
  
/* This code contributed by PrinciRaj1992 */

Output:

2 10 4 5 30 50

This article is contributed by Shashank Mishra ( Gullu ). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

C#

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