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 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
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.
- Linked list of values smaller than x.
- Linked list of values equal to x.
- 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++ 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 concatenating
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;
}
// This code is contributed by Aditya Kumar (adityakumar129)
// C++ program to partition a linked list around a
// given value.
#include <stdio.h>
#include <stdlib.h>
/* Link list Node */
typedef struct Node {
int data;
struct Node* next;
} Node;
// A utility function to create a new node
Node* newNode(int data)
{
Node* new_node = (Node*)malloc(sizeof(Node));
new_node->data = data;
new_node->next = NULL;
return new_node;
}
// Function to make two separate lists and return
// head after concatenating
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 */
void printList(Node* head)
{
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 */
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;
}
// This code is contributed by Aditya Kumar (adityakumar129)
// 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 concatenating
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 Aditya Kumar (adityakumar129)
# Python3 program to partition a
# linked list around a given value.
# Link list Node
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
# head after concatenating
def partition( head, 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.
smallerHead = None
smallerLast = None
greaterLast = None
greaterHead = None
equalHead = None
equalLast = None
# Now iterate original list and connect nodes
# of appropriate linked lists.
while (head != None) :
# If current node is equal to x, append it
# to the list of x values
if (head.data == x):
if (equalHead == None):
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 == None):
smallerLast = smallerHead = head
else:
smallerLast.next = head
smallerLast = head
else :
# Append to the list of greater values
if (greaterHead == None) :
greaterLast = greaterHead = head
else:
greaterLast.next = head
greaterLast = head
head = head.next
# 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 (smallerHead == None) :
if (equalHead == None) :
return greaterHead
equalLast.next = greaterHead
return equalHead
# If smaller list is not empty
# and equal list is empty
if (equalHead == None) :
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
def printList(head) :
temp = head
while (temp != None):
print(temp.data ,end= " ")
temp = temp.next
# Driver code
# Start with the empty list
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)
x = 3
head = partition(head, x)
printList(head)
# This code is contributed by Arnab Kundu.
// 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 concatenating
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 */
<script>
// Javascript program to partition a
// linked list around a given value.
/* Link list Node */
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
// head after concatenating
function partition(head , 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.
*/
var smallerHead = null, smallerLast = null;
var greaterLast = null, greaterHead = null;
var 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 */
function printList(head) {
var temp = head;
while (temp != null) {
document.write(temp.data + " ");
temp = temp.next;
}
}
// Driver code
/* Start with the empty list */
var 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);
var x = 3;
head = partition(head, x);
printList(head);
// This code contributed by aashish1995
</script>
Output
2 10 4 5 30 50
Time complexity: O(n) where n is the size of the linked list
Auxiliary Space: O(1)
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