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

• Difficulty Level : Easy
• Last Updated : 29 Oct, 2021

Given a linked list and a value x, partition it such that all nodes less than x come first, then all nodes with a value equal to x, and finally nodes with a 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 solve it on “PRACTICE” 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 the smaller list. If the value is equal to x, then at the end of the equal list. And if a value is greater, then at the end of the greater list.
• Now concatenate three lists.

Below is the implementation of the above idea.

C++

// C++ program to partition a linked list around a
// given value.
#include<bits/stdc++.h>
using namespace std;

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
struct Node *partition(struct Node *head, int x)
{
/* Let us initialize first and last nodes of
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
{
// If current node is equal to x, append it
// to the list of x values
{
else
{
equalLast = equalLast->next;
}
}

// If current node is less than X, append
// it to the list of smaller values
{
else
{
}
}
else // Append to the list of greater values
{
else
{
}
}

}

// 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 smaller list is not empty
// and equal list is empty
{
}

// If both smaller and equal list
// are non-empty
}

/* Function to print linked list */
{
while (temp != NULL)
{
printf("%d  ", temp->data);
temp = temp->next;
}
}

// Driver program to run the case
int main()
{

int x = 3;
return 0;
}

Java

// Java program to partition a
// linked list around a given value.
class GfG
{

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
static Node partition(Node head, int x)
{

/* Let us initialize first and last nodes of
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
{
// If current node is equal to x, append it
// to the list of x values
{
else
{
equalLast = equalLast.next;
}
}

// If current node is less than X, append
// it to the list of smaller values
{
else
{
}
}
else // Append to the list of greater values
{
else
{
}
}
}

// 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 smaller list is not empty
// and equal list is empty
{
}

// If both smaller and equal list
// are non-empty
}

/* Function to print linked list */
{
while (temp != null)
{
System.out.print(temp.data + " ");
temp = temp.next;
}
}

// Driver code
public static void main(String[] args)
{

int x = 3;
}
}

// This code is contributed by Prerna saini.

Python3

# Python3 program to partition a
# linked list around a given value.

class Node:
def __init__(self):
self.data = 0
self.next = None

# A utility function to create a new node
def newNode( data):

new_node = Node()
new_node.data = data
new_node.next = None
return new_node

# Function to make two separate lists and return

# Let us initialize first and last nodes of
# 1) Linked list of values smaller than x.
# 2) Linked list of values equal to x.
# 3) Linked list of values greater than x.
smallerLast = None
greaterLast = None
equalLast = None

# Now iterate original list and connect nodes

# If current node is equal to x, append it
# to the list of x values

else:

equalLast = equalLast.next

# If current node is less than X, append
# it to the list of smaller values

else:

else :
# Append to the list of greater values

else:

# Fix end of greater linked list to None if this
# list has some nodes
if (greaterLast != None) :
greaterLast.next = None

# Connect three lists

# If smaller list is empty

# If smaller list is not empty
# and equal list is empty

# If both smaller and equal list
# are non-empty

# Function to print linked list

while (temp != None):

print(temp.data ,end= " ")
temp = temp.next

# Driver code

x = 3

# This code is contributed by Arnab Kundu.

C#

// C# program to partition a
// linked list around a given value.
using System;

public class GfG
{

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
static Node partition(Node head, int x)
{

/* Let us initialize first and last nodes of
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
{
// If current node is equal to x, append it
// to the list of x values
{
else
{
equalLast = equalLast.next;
}
}

// If current node is less than X, append
// it to the list of smaller values
{
else
{
}
}
else // Append to the list of greater values
{
else
{
}
}
}

// 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 smaller list is not empty
// and equal list is empty
{
}

// If both smaller and equal list
// are non-empty
}

/* Function to print linked list */
{
while (temp != null)
{
Console.Write(temp.data + " ");
temp = temp.next;
}
}

// Driver code
public static void Main()
{

int x = 3;
}
}

/* This code contributed by PrinciRaj1992 */

Javascript

<script>

// Javascript program to partition a
// linked list around a given value.

class Node {
constructor() {
this.data = 0;
this.next = null;
}
}

// A utility function to create a new node
function newNode(data) {
var new_node = new Node();
new_node.data = data;
new_node.next = null;
return new_node;
}

// Function to make two separate lists and return

/*
Let us initialize first and last
of values smaller than x. 2) Linked list
of values equal to x. 3) Linked list
of values greater than x.
*/

var smallerHead = null, smallerLast = null;
var greaterLast = null, greaterHead = null;
var equalHead = null, equalLast = null;

// Now iterate original list and connect nodes
// If current node is equal to x, append it
// to the list of x values
else {
equalLast = equalLast.next;
}
}

// If current node is less than X, append
// it to the list of smaller values
else if (head.data < x) {
else {
}
} else // Append to the list of greater values
{
else {
}
}
}

// 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 smaller list is not empty
// and equal list is empty
}

// If both smaller and equal list
// are non-empty
}

/* Function to print linked list */
while (temp != null) {
document.write(temp.data + " ");
temp = temp.next;
}
}

// Driver code

var x = 3;

// This code contributed by aashish1995

</script>

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 write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.