Sort a nearly sorted doubly linked list
Last Updated :
31 Aug, 2024
Given a doubly linked list containing n nodes, each node is at most k-indices away from its target position. The problem is to sort the given doubly linked list. The distance can be assumed in either of the directions (left and right).
Examples:
Input: Doubly Linked List : 3 <-> 2 <-> 1 <-> 5 <-> 6 <-> 4 , k = 2
Output: 1 <-> 2 <-> 3 <-> 4 <-> 5 <-> 6
Input: Doubly Linked List : 5 <-> 6 <-> 7 <-> 3 <-> 4 <-> 4 , k = 3
Output: 3 <-> 4 <-> 4 <-> 5 <-> 6 <-> 7
[Naive Approach] Using Insertion sort - O(n*k) time and O(1) space
The idea is to use insertion sort to sort the doubly linked list. While inserting each element in the sorted part of the list, there will be atmost k swaps to place the element to its correct position since every node is is atmost k steps away from its correct position.
Below is the implementation of the above approach:
C++
// C++ implementation to sort a k sorted doubly
// linked list
#include <iostream>
using namespace std;
class Node {
public:
int data;
Node *next;
Node *prev;
Node(int x) {
data = x;
prev = nullptr;
next = nullptr;
}
};
// Function to sort a k-sorted doubly linked list
Node *sortAKSortedDLL(Node *head, int k) {
if (head == nullptr || head->next == nullptr)
return head;
Node *node = head->next;
// Perform on all the nodes in the list
while (node != nullptr) {
Node *next = node->next;
Node *curr = node;
while (curr->prev != nullptr &&
curr->data < curr->prev->data) {
// Swap curr and curr->prev node
Node *node1 = curr->prev->prev;
Node *node2 = curr->prev;
Node *node3 = curr->next;
if (node1 != nullptr)
node1->next = curr;
curr->prev = node1;
node2->next = node3;
if (node3 != nullptr)
node3->prev = node2;
curr->next = node2;
node2->prev = curr;
}
// If curr is now the new head,
// then reset head
if (curr->prev == nullptr)
head = curr;
node = next;
}
return head;
}
void printList(Node *curr) {
while (curr != nullptr) {
cout << curr->data << " ";
curr = curr->next;
}
cout << endl;
}
int main() {
// Create the doubly linked list:
// 3 <-> 2 <-> 1 <-> 5
Node *head = new Node(3);
head->next = new Node(2);
head->next->prev = head;
head->next->next = new Node(1);
head->next->next->prev = head->next;
head->next->next->next = new Node(5);
head->next->next->next->prev = head->next->next;
int k = 2;
head = sortAKSortedDLL(head, k);
printList(head);
return 0;
}
// C implementation to sort a k sorted doubly
// linked list
#include <stdio.h>
#include <stdlib.h>
struct Node {
int data;
struct Node *next;
struct Node *prev;
};
// Function to sort a k-sorted
// doubly linked list
struct Node *sortAKSortedDLL(struct Node *head, int k) {
if (head == NULL || head->next == NULL)
return head;
struct Node *node = head->next;
// Perform on all the nodes in the list
while (node != NULL) {
struct Node *next = node->next;
struct Node *curr = node;
while (curr->prev != NULL &&
curr->data < curr->prev->data) {
// Swap curr and curr->prev node
struct Node *node1 = curr->prev->prev;
struct Node *node2 = curr->prev;
struct Node *node3 = curr->next;
if (node1 != NULL)
node1->next = curr;
curr->prev = node1;
node2->next = node3;
if (node3 != NULL)
node3->prev = node2;
curr->next = node2;
node2->prev = curr;
}
// If curr is now the new head,
// then reset head
if (curr->prev == NULL)
head = curr;
node = next;
}
return head;
}
void printList(struct Node *node) {
struct Node *curr = node;
while (curr != NULL) {
printf("%d ", curr->data);
curr = curr->next;
}
printf("\n");
}
struct Node *createNode(int new_data) {
struct Node *new_node =
(struct Node *)malloc(sizeof(struct Node));
new_node->data = new_data;
new_node->next = NULL;
new_node->prev = NULL;
return new_node;
}
int main() {
// Create the doubly linked list:
// 3 <-> 2 <-> 1 <-> 5
struct Node *head = createNode(3);
head->next = createNode(2);
head->next->prev = head;
head->next->next = createNode(1);
head->next->next->prev = head->next;
head->next->next->next = createNode(5);
head->next->next->next->prev = head->next->next;
int k = 2;
head = sortAKSortedDLL(head, k);
printList(head);
return 0;
}
// Java implementation to sort a k sorted doubly
// linked list
class Node {
int data;
Node next;
Node prev;
Node(int data) {
this.data = data;
this.next = null;
this.prev = null;
}
}
public class GfG {
// Function to sort a k-sorted doubly linked list
static Node sortAKSortedDLL(Node head, int k) {
if (head == null || head.next == null)
return head;
Node node = head.next;
while (node != null) {
Node next = node.next;
Node curr = node;
while (curr.prev != null
&& curr.data < curr.prev.data) {
// Swap curr and curr.prev node
Node node1 = curr.prev.prev;
Node node2 = curr.prev;
Node node3 = curr.next;
if (node1 != null)
node1.next = curr;
curr.prev = node1;
node2.next = node3;
if (node3 != null)
node3.prev = node2;
curr.next = node2;
node2.prev = curr;
}
// If curr is now the new head,
// then reset head
if (curr.prev == null)
head = curr;
node = next;
}
return head;
}
static void printList(Node curr) {
while (curr != null) {
System.out.print(curr.data + " ");
curr = curr.next;
}
System.out.println();
}
public static void main(String[] args) {
// Create the doubly linked list:
// 3 <-> 2 <-> 1 <-> 5
Node head = new Node(3);
head.next = new Node(2);
head.next.prev = head;
head.next.next = new Node(1);
head.next.next.prev = head.next;
head.next.next.next = new Node(5);
head.next.next.next.prev = head.next.next;
int k = 2;
head = sortAKSortedDLL(head, k);
printList(head);
}
}
# Python implementation to sort a k sorted doubly
# linked list
class Node:
def __init__(self, new_data):
self.data = new_data
self.next = None
self.prev = None
# Function to sort a k-sorted doubly linked list
def sort_k_sorted_dll(head, k):
if head is None or head.next is None:
return head
node = head.next
while node is not None:
next_node = node.next
curr = node
while curr.prev is not None \
and curr.data < curr.prev.data:
# Swap curr and curr.prev node
node1 = curr.prev.prev
node2 = curr.prev
node3 = curr.next
if node1 is not None:
node1.next = curr
curr.prev = node1
node2.next = node3
if node3 is not None:
node3.prev = node2
curr.next = node2
node2.prev = curr
# If curr is now the new head,
# then reset head
if curr.prev is None:
head = curr
node = next_node
return head
def print_list(curr):
while curr is not None:
print(curr.data, end=" ")
curr = curr.next
print()
if __name__ == "__main__":
# Create the doubly linked list:
# 3 <-> 2 <-> 1 <-> 5
head = Node(3)
head.next = Node(2)
head.next.prev = head
head.next.next = Node(1)
head.next.next.prev = head.next
head.next.next.next = Node(5)
head.next.next.next.prev = head.next.next
k = 2
head = sort_k_sorted_dll(head, k)
print_list(head)
// C# implementation to sort a k sorted doubly
// linked list
using System;
class Node {
public int Data;
public Node next;
public Node prev;
public Node(int newData) {
Data = newData;
next = null;
prev = null;
}
}
class GfG {
// Function to sort a k-sorted doubly linked list
static Node SortAKSortedDLL(Node head, int k) {
if (head == null || head.next == null)
return head;
Node node = head.next;
while (node != null) {
Node nextNode = node.next;
Node curr = node;
while (curr.prev != null &&
curr.Data < curr.prev.Data) {
// Swap curr and curr.prev node
Node node1 = curr.prev.prev;
Node node2 = curr.prev;
Node node3 = curr.next;
if (node1 != null)
node1.next = curr;
curr.prev = node1;
node2.next = node3;
if (node3 != null)
node3.prev = node2;
curr.next = node2;
node2.prev = curr;
}
// If curr is now the new head,
// then reset head
if (curr.prev == null)
head = curr;
node = nextNode;
}
return head;
}
static void PrintList(Node curr) {
while (curr != null) {
Console.Write(curr.Data + " ");
curr = curr.next;
}
Console.WriteLine();
}
static void Main() {
// Create the doubly linked list:
// 3 <-> 2 <-> 1 <-> 5
Node head = new Node(3);
head.next = new Node(2);
head.next.prev = head;
head.next.next = new Node(1);
head.next.next.prev = head.next;
head.next.next.next = new Node(5);
head.next.next.next.prev = head.next.next;
int k = 2;
head = SortAKSortedDLL(head, k);
PrintList(head);
}
}
// C# implementation to sort a k sorted doubly
// linked list
class Node {
constructor(new_data) {
this.data = new_data;
this.next = null;
this.prev = null;
}
}
// Function to sort a k-sorted doubly linked list
function sortAKSortedDLL(head, k) {
if (head === null || head.next === null)
return head;
let node = head.next;
while (node !== null) {
let next = node.next;
let curr = node;
while (curr.prev !== null
&& curr.data < curr.prev.data) {
// Swap curr and curr.prev node
let node1 = curr.prev.prev;
let node2 = curr.prev;
let node3 = curr.next;
if (node1 !== null)
node1.next = curr;
curr.prev = node1;
node2.next = node3;
if (node3 !== null)
node3.prev = node2;
curr.next = node2;
node2.prev = curr;
}
// If curr is now the new head, then reset head
if (curr.prev === null)
head = curr;
node = next;
}
return head;
}
function printList(curr) {
while (curr !== null) {
process.stdout.write(curr.data + " ");
curr = curr.next;
}
console.log();
}
// Create the doubly linked list:
// 3 <-> 2 <-> 1 <-> 5
let head = new Node(3);
head.next = new Node(2);
head.next.prev = head;
head.next.next = new Node(1);
head.next.next.prev = head.next;
head.next.next.next = new Node(5);
head.next.next.next.prev = head.next.next;
let k = 2;
head = sortAKSortedDLL(head, k);
printList(head);
Time Complexity: O(n*k)
Auxiliary Space: O(1)
[Expected Approach] Using Min Heap - O(nlogk) time and O(k) space
We can sort the list using the Min Heap data structure. The approach is same as discussed in Sort a nearly sorted (or K sorted) array. We only have to be careful while traversing the input doubly linked list and adjusting the required next and previous links in the final sorted list.
Below is the implementation of the above approach:
C++
// C++ implementation to sort a k sorted doubly
// linked list using minHeap
#include <bits/stdc++.h>
using namespace std;
class Node {
public:
int data;
Node* next;
Node* prev;
Node(int x){
data = x;
next = nullptr;
prev = nullptr;
}
};
class Compare {
public:
bool operator()(Node* a, Node* b) {
return a->data > b->data;
}
};
// function to sort a k sorted doubly linked list
Node* sortAKSortedDLL(Node* head, int k) {
// if list is empty
if (head == nullptr)
return head;
// priority_queue 'pq' implemented as min heap with the
// help of 'compare' function
priority_queue<Node*, vector<Node*>, Compare> pq;
Node* newHead = nullptr, *last = nullptr;
// Create a Min Heap of first (k+1) elements from
// input doubly linked list
for (int i = 0; head != NULL && i < k+1; i++) {
pq.push(head);
head = head->next;
}
while (!pq.empty()) {
if (newHead == nullptr) {
newHead = pq.top();
newHead->prev = nullptr;
// 'last' points to the last node
// of the result sorted list so far
last = newHead;
}
else {
last->next = pq.top();
pq.top()->prev = last;
last = pq.top();
}
// remove element from 'pq'
pq.pop();
// if there are more nodes left
// in the input list
if (head != nullptr) {
pq.push(head);
head = head->next;
}
}
// making 'next' of last node point to NULL
last->next = nullptr;
// new head of the required sorted DLL
return newHead;
}
void printList(Node* curr) {
while (curr != nullptr) {
cout << curr->data << " ";
curr = curr->next;
}
}
int main() {
// Create the doubly linked list:
// 3 <-> 2 <-> 1 <-> 5
Node *head = new Node(3);
head->next = new Node(2);
head->next->prev = head;
head->next->next = new Node(1);
head->next->next->prev = head->next;
head->next->next->next = new Node(5);
head->next->next->next->prev = head->next->next;
int k = 2;
head = sortAKSortedDLL(head, k);
printList(head);
return 0;
}
// Java implementation to sort a k sorted doubly
// linked list using minHeap
import java.util.PriorityQueue;
class Node {
int data;
Node next, prev;
Node(int new_data) {
data = new_data;
next = null;
prev = null;
}
}
class Compare implements java.util.Comparator<Node> {
public int compare(Node a, Node b) {
return a.data - b.data;
}
}
public class GfG {
// function to sort a k sorted doubly linked list
static Node sortAKSortedDLL(Node head, int k) {
// if list is empty
if (head == null)
return head;
// priority_queue 'pq' implemented as min
// heap with the help of 'compare' function
PriorityQueue<Node> pq =
new PriorityQueue<>(new Compare());
Node newHead = null, last = null;
// Create a Min Heap of first (k+1)
// elements from input doubly linked list
for (int i = 0; head != null &&
i < k + 1; i++) {
pq.add(head);
head = head.next;
}
while (!pq.isEmpty()) {
if (newHead == null) {
newHead = pq.poll();
newHead.prev = null;
// 'last' points to the last node
// of the result sorted list so far
last = newHead;
} else {
last.next = pq.poll();
last.next.prev = last;
last = last.next;
}
// if there are more nodes left in
// the input list
if (head != null) {
pq.add(head);
head = head.next;
}
}
// making 'next' of last node point to NULL
last.next = null;
// new head of the required sorted DLL
return newHead;
}
static void printList(Node curr) {
while (curr != null) {
System.out.print(curr.data + " ");
curr = curr.next;
}
}
public static void main(String[] args) {
// Create the doubly linked list:
// 3 <-> 2 <-> 1 <-> 5
Node head = new Node(3);
head.next = new Node(2);
head.next.prev = head;
head.next.next = new Node(1);
head.next.next.prev = head.next;
head.next.next.next = new Node(5);
head.next.next.next.prev = head.next.next;
int k = 2;
head = sortAKSortedDLL(head, k);
printList(head);
}
}
# Python implementation to sort a k sorted doubly
# linked list using minHeap
import heapq
class Node:
def __init__(self, new_data):
self.data = new_data
self.next = None
self.prev = None
class Compare:
def __call__(self, a, b):
return a.data > b.data
# function to sort a k sorted doubly linked list
def sort_k_sorted_dll(head, k):
# if list is empty
if head is None:
return head
# priority_queue 'pq' implemented as
# min heap with the
# help of 'compare' function
pq = []
heapq.heapify(pq)
def heap_push(node):
heapq.heappush(pq, (node.data, node))
def heap_pop():
return heapq.heappop(pq)[1]
new_head = None
last = None
# Create a Min Heap of first (k+1) elements from
# input doubly linked list
for i in range(k + 1):
if head is None:
break
heap_push(head)
head = head.next
while pq:
# place root or top of 'pq' at the end of the
# result sorted list so far having the first node
# pointed to by 'newHead'
# and adjust the required links
if new_head is None:
new_head = heap_pop()
new_head.prev = None
last = new_head
else:
last.next = heap_pop()
last.next.prev = last
last = last.next
# if there are more nodes left in the input list
if head is not None:
heap_push(head)
head = head.next
# making 'next' of last node point to NULL
last.next = None
# new head of the required sorted DLL
return new_head
def print_list(curr):
while curr is not None:
print(curr.data, end=" ")
curr = curr.next
print()
if __name__ == "__main__":
# Create the doubly linked list:
# 3 <-> 2 <-> 1 <-> 5
head = Node(3)
head.next = Node(2)
head.next.prev = head
head.next.next = Node(1)
head.next.next.prev = head.next
head.next.next.next = Node(5)
head.next.next.next.prev = head.next.next
k = 2
head = sort_k_sorted_dll(head, k)
print_list(head)
// C# implementation to sort a k sorted doubly
// linked list using minHeap
using System;
using System.Collections.Generic;
class Node {
public int Data;
public Node next;
public Node prev;
public Node(int newData) {
Data = newData;
next = null;
prev = null;
}
}
class NodeComparer : IComparer<Node> {
public int Compare(Node a, Node b) {
return a.Data.CompareTo(b.Data);
}
}
class GfG {
// function to sort a k sorted doubly linked list
static Node SortAKSortedDLL(Node head, int k) {
// if list is empty
if (head == null)
return head;
// priority_queue 'pq' implemented as min heap with
// the help of 'compare' function
SortedSet<Node> pq
= new SortedSet<Node>(new NodeComparer());
Node newHead = null, last = null;
// Create a Min Heap of first (k+1) elements from
// input doubly linked list
for (int i = 0; head != null && i < k + 1; i++) {
pq.Add(head);
head = head.next;
}
while (pq.Count > 0) {
// place root or top of 'pq' at the end of the
// result sorted list so far having the first
// node pointed to by 'newHead' and adjust the
// required links
if (newHead == null) {
newHead = pq.Min;
newHead.prev = null;
// 'last' points to the last node
// of the result sorted list so far
last = newHead;
}
else {
last.next = pq.Min;
pq.Min.prev = last;
last = pq.Min;
}
// remove element from 'pq'
pq.Remove(pq.Min);
// if there are more nodes left in the input
// list
if (head != null) {
pq.Add(head);
head = head.next;
}
}
// making 'next' of last node point to NULL
last.next = null;
// new head of the required sorted DLL
return newHead;
}
static void PrintList(Node curr) {
while (curr != null) {
Console.Write(curr.Data + " ");
curr = curr.next;
}
Console.WriteLine();
}
static void Main() {
// Create the doubly linked list:
// 3 <-> 2 <-> 1 <-> 5
Node head = new Node(3);
head.next = new Node(2);
head.next.prev = head;
head.next.next = new Node(1);
head.next.next.prev = head.next;
head.next.next.next = new Node(5);
head.next.next.next.prev = head.next.next;
int k = 2;
head = SortAKSortedDLL(head, k);
PrintList(head);
}
}
// JavaScript implementation to sort a k sorted doubly
// linked list using minHeap
class Node {
constructor(newData) {
this.data = newData;
this.next = null;
this.prev = null;
}
}
class Compare {
compare(a, b) { return a.data - b.data; }
}
// function to sort a k sorted doubly linked list
function sortAKSortedDLL(head, k) {
// if list is empty
if (head === null)
return head;
// priority_queue 'pq' implemented as min heap with the
// help of 'compare' function
let pq = [];
let compare = new Compare();
// Helper function to maintain heap property
function heapify() {
pq.sort((a, b) => compare.compare(a, b));
}
let newHead = null, last = null;
// Create a Min Heap of first (k+1) elements from
// input doubly linked list
for (let i = 0; head !== null && i < k + 1; i++) {
pq.push(head);
head = head.next;
}
heapify();
while (pq.length > 0) {
if (newHead === null) {
newHead = pq.shift();
newHead.prev = null;
// 'last' points to the last node
// of the result sorted list so far
last = newHead;
}
else {
last.next = pq.shift();
last.next.prev = last;
last = last.next;
}
// if there are more nodes left in the input list
if (head !== null) {
pq.push(head);
head = head.next;
heapify();
}
}
// making 'next' of last node point to NULL
if (last !== null) {
last.next = null;
}
return newHead;
}
function printList(curr) {
while (curr !== null) {
console.log(curr.data + " ");
curr = curr.next;
}
console.log();
}
// Create the doubly linked list:
// 3 <-> 2 <-> 1 <-> 5
let head = new Node(3);
head.next = new Node(2);
head.next.prev = head;
head.next.next = new Node(1);
head.next.next.prev = head.next;
head.next.next.next = new Node(5);
head.next.next.next.prev = head.next.next;
let k = 2;
head = sortAKSortedDLL(head, k);
printList(head);
Time Complexity: O(n*log k)
Auxiliary Space: O(k)
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Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
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