Clone linked list with next and random pointer
Last Updated :
23 Jul, 2025
Given a linked list of size n where each node has two links: next pointer pointing to the next node and random pointer to any random node in the list. The task is to create a clone of this linked list.
[Naive Approach - 1] Using Hashing - O(2n) Time and O(2n) Space
The idea is to create a new node corresponding to each node in the original linked list and store the new nodes in a hash table. Now, again traverse the original linked list and update the next and random pointers of new nodes corresponding to every original node.
Illustration:
Steps to clone a linked list with next and random pointer:
- Create a hash table, say mp to store the new nodes corresponding to their original nodes.
- Traverse the original linked list and for every node, say curr,
- Create a new node corresponding to curr and push them into a hash table, mp[curr] = new Node().
- Again traverse the original linked list to update the next and random pointer of each new node, mp[curr]->next = mp[curr->next] and mp[curr]->random = mp[curr->random].
- Return mp[head] as the head of the cloned linked list.
Below is the implementation of the above approach:
C++14
// C++ code to Clone a linked list with next and random
// pointer using Hashing
#include <bits/stdc++.h>
using namespace std;
struct Node {
int data;
Node* next;
Node* random;
Node(int x) {
data = x;
next = random = NULL;
}
};
// Function to clone the linked list
Node* cloneLinkedList(Node* head) {
// Map to store new nodes corresponding to
// their original nodes
unordered_map<Node*, Node*> mp;
Node *curr = head;
// Traverse original linked list to store new
// nodes corresponding to original linked list
while (curr != NULL) {
mp[curr] = new Node(curr->data);
curr = curr->next;
}
curr = head;
// Loop to update the next and random pointers
// of new nodes
while (curr != NULL) {
// Update the next pointer of new node
mp[curr]->next = mp[curr->next];
// Update the random pointer of new node
mp[curr]->random = mp[curr->random];
curr = curr->next;
}
// Return the head of the clone
return mp[head];
}
// Function to print the linked list
void printList(Node* head) {
while (head != NULL) {
cout << head->data << "(";
if(head->random)
cout << head->random->data << ")";
else
cout << "null" << ")";
if(head->next != NULL)
cout << " -> ";
head = head->next;
}
cout << endl;
}
int main() {
// Creating a linked list with random pointer
Node* head = new Node(1);
head->next = new Node(2);
head->next->next = new Node(3);
head->next->next->next = new Node(4);
head->next->next->next->next = new Node(5);
head->random = head->next->next;
head->next->random = head;
head->next->next->random = head->next->next->next->next;
head->next->next->next->random = head->next->next;
head->next->next->next->next->random = head->next;
// Print the original list
cout << "Original linked list:\n";
printList(head);
// Function call
Node* clonedList = cloneLinkedList(head);
cout << "Cloned linked list:\n";
printList(clonedList);
return 0;
}
// Java code to Clone a linked list with next and random
// pointer using Hashing
import java.util.HashMap;
import java.util.Map;
// Define the Node class
class Node {
int data;
Node next;
Node random;
Node(int x) {
data = x;
next = null;
random = null;
}
}
class GfG {
// Function to clone the linked list
static Node cloneLinkedList(Node head) {
// Hash Map to store new nodes corresponding
// to their original nodes
Map<Node, Node> mp = new HashMap<>();
Node curr = head;
// Traverse original linked list to store new nodes
// corresponding to original linked list
while (curr != null) {
mp.put(curr, new Node(curr.data));
curr = curr.next;
}
curr = head;
// Loop to update the next and random pointers
// of new nodes
while (curr != null) {
// Update the next pointer of new node
Node newNode = mp.get(curr);
newNode.next = mp.get(curr.next);
// Update the random pointer of new node
newNode.random = mp.get(curr.random);
curr = curr.next;
}
// Return the head of the clone
return mp.get(head);
}
// Function to print the linked list
static void printList(Node head) {
while (head != null) {
System.out.print(head.data + "(");
if (head.random != null)
System.out.print(head.random.data + ")");
else
System.out.print("null" + ")");
if (head.next != null)
System.out.print(" -> ");
head = head.next;
}
System.out.println();
}
public static void main(String[] args) {
// Creating a linked list with random pointer
Node head = new Node(1);
head.next = new Node(2);
head.next.next = new Node(3);
head.next.next.next = new Node(4);
head.next.next.next.next = new Node(5);
head.random = head.next.next;
head.next.random = head;
head.next.next.random = head.next.next.next.next;
head.next.next.next.random = head.next.next;
head.next.next.next.next.random = head.next;
// Print the original list
System.out.println("Original linked list:");
printList(head);
// Function call
Node clonedList = cloneLinkedList(head);
System.out.println("Cloned linked list:");
printList(clonedList);
}
}
# Python code to Clone a linked list with next and random
# pointer using Hashing
class Node:
def __init__(self, x):
self.data = x
self.next = None
self.random = None
# Function to clone the linked list
def cloneLinkedList(head):
# Dictionary to store new nodes corresponding
# to their original nodes
nodeMap = {}
curr = head
# Traverse original linked list to store new nodes
# corresponding to original linked list
while curr is not None:
nodeMap[curr] = Node(curr.data)
curr = curr.next
curr = head
# Loop to update the next and random pointers
# of new nodes
while curr is not None:
newNode = nodeMap[curr]
# Update the next pointer of new node
newNode.next = nodeMap.get(curr.next)
# Update the random pointer of new node
newNode.random = nodeMap.get(curr.random)
curr = curr.next
# Return the head of the clone
return nodeMap.get(head)
def printList(head):
curr = head
while curr is not None:
print(f'{curr.data}(', end='')
if curr.random:
print(f'{curr.random.data})', end='')
else:
print('null)', end='')
if curr.next is not None:
print(' -> ', end='')
curr = curr.next
print()
if __name__ == "__main__":
# Creating a linked list with random pointer
head = Node(1)
head.next = Node(2)
head.next.next = Node(3)
head.next.next.next = Node(4)
head.next.next.next.next = Node(5)
head.random = head.next.next
head.next.random = head
head.next.next.random = head.next.next.next.next
head.next.next.next.random = head.next.next
head.next.next.next.next.random = head.next
# Print the original list
print("Original linked list:")
printList(head)
# Function call
clonedList = cloneLinkedList(head)
print("Cloned linked list:")
printList(clonedList)
// C# code to Clone a linked list with next and random
// pointer using Hashing
using System;
using System.Collections.Generic;
class Node {
public int Data;
public Node Next;
public Node Random;
public Node(int x) {
Data = x;
Next = null;
Random = null;
}
}
class GfG {
// Function to clone the linked list
public static Node CloneLinkedList(Node head) {
// Dictionary to store new nodes corresponding
// to their original nodes
Dictionary<Node, Node> mp = new Dictionary<Node, Node>();
Node curr = head;
// Traverse original linked list to store new nodes
// corresponding to original linked list
while (curr != null) {
mp[curr] = new Node(curr.Data);
curr = curr.Next;
}
curr = head;
// Loop to update the next and random pointers of new nodes
while (curr != null) {
Node newNode = mp[curr];
if(curr.Next != null)
newNode.Next = mp[curr.Next];
newNode.Random = mp[curr.Random];
curr = curr.Next;
}
// Return the head of the clone
return mp[head];
}
// Function to print the linked list
public static void PrintList(Node head) {
while (head != null) {
Console.Write(head.Data + "(");
if (head.Random != null)
Console.Write(head.Random.Data);
else
Console.Write("null");
Console.Write(")");
if (head.Next != null)
Console.Write(" -> ");
head = head.Next;
}
Console.WriteLine();
}
static void Main(string[] args) {
// Creating a linked list with random pointer
Node head = new Node(1);
head.Next = new Node(2);
head.Next.Next = new Node(3);
head.Next.Next.Next = new Node(4);
head.Next.Next.Next.Next = new Node(5);
head.Random = head.Next.Next;
head.Next.Random = head;
head.Next.Next.Random = head.Next.Next.Next.Next;
head.Next.Next.Next.Random = head.Next.Next;
head.Next.Next.Next.Next.Random = head.Next;
// Print the original list
Console.WriteLine("Original linked list:");
PrintList(head);
// Function call
Node clonedList = CloneLinkedList(head);
Console.WriteLine("Cloned linked list:");
PrintList(clonedList);
}
}
// JavaScript code to Clone a linked list with next
// and random pointer using Hashing
class Node {
constructor(data) {
this.data = data;
this.next = null;
this.random = null;
}
}
// Function to clone the linked list
function cloneLinkedList(head) {
// Map to store new nodes corresponding to
// their original nodes
const mp = new Map();
let curr = head;
// Traverse original linked list to store new nodes
// corresponding to original linked list
while (curr !== null) {
mp.set(curr, new Node(curr.data));
curr = curr.next;
}
curr = head;
// Loop to update the next and random pointers
// of new nodes
while (curr !== null) {
const newNode = mp.get(curr);
newNode.next = mp.get(curr.next) || null;
newNode.random = mp.get(curr.random) || null;
curr = curr.next;
}
// Return the head of the clone
return mp.get(head) || null;
}
// Function to print the linked list
function printList(head) {
let result = "";
while (head !== null) {
result += head.data + "(";
result += head.random ? head.random.data : "null";
result += ")";
if (head.next !== null) {
result += " -> ";
}
head = head.next;
}
console.log(result);
}
// Creating a linked list with random pointer
const head = new Node(1);
head.next = new Node(2);
head.next.next = new Node(3);
head.next.next.next = new Node(4);
head.next.next.next.next = new Node(5);
head.random = head.next.next;
head.next.random = head;
head.next.next.random = head.next.next.next.next;
head.next.next.next.random = head.next.next;
head.next.next.next.next.random = head.next;
// Print the original list
console.log("Original linked list:");
printList(head);
// Function call
const clonedList = cloneLinkedList(head);
console.log("Cloned linked list:");
printList(clonedList);
OutputOriginal linked list:
1(3) -> 2(1) -> 3(5) -> 4(3) -> 5(2)
Cloned linked list:
1(3) -> 2(1) -> 3(5) -> 4(3) -> 5(2)
Time Complexity: O(2n), as we are traversing the linked list twice.
Auxiliary Space: O(2n), extra O(n) space as we are using a hash table to store the new nodes.
[Naive Approach - 2] Using Hashing and Recursion- O(n) Time and O(3n) Space
The idea is to create a new node corresponding to each node in the original linked list and store the new nodes in a hash table. While traversing the original linked list we also use recursion to update the next and random pointers of new nodes corresponding to every original node.
For a more detailed solution and code checkout, this article Clone a linked list with next and random pointer using Recursion
Time Complexity: O(n) , where n is the number of nodes in linked list.
Auxiliary Space: O(3n) , extra O(n) space as we are using a hash table to store the new nodes as well for recursion stack space.
[Expected Approach] By Inserting Nodes In-place - O(3n) Time and O(1) Space
The idea is to create duplicate of a node and instead of storing in a separate hash table, we can insert it in between the original node and the next node. Now, we will have new nodes at alternate positions.
Now for a node X its duplicate will be X->next and the random pointer of the duplicate should point to X->random->next (as that is the duplicate of X->random). So, iterate over the entire linked list to update the random pointer of all the cloned nodes and then iterate again to separate the original linked list and the cloned linked list.
Illustration:
Follow the steps mentioned below to implement the idea:
- Create the copy of node 1 and insert it between node 1 and node 2 in the original Linked List, create the copy of node 2 and insert it between 2nd and 3rd node and so on. Add the copy of N after the Nth node
- Connect the clone node by updating the random pointers.
- Separate the cloned linked list from the original list by updating the next pointers.
C++
// C++ code to Clone a linked list with next and random
// pointer by Inserting Nodes In-place
#include <bits/stdc++.h>
using namespace std;
struct Node {
int data;
Node *next, *random;
Node(int x) {
data = x;
next = random = NULL;
}
};
Node* cloneLinkedList(Node* head) {
if (head == NULL) {
return NULL;
}
// Create new nodes and insert them next to
// the original nodes
Node* curr = head;
while (curr != NULL) {
Node* newNode = new Node(curr->data);
newNode->next = curr->next;
curr->next = newNode;
curr = newNode->next;
}
// Set the random pointers of the new nodes
curr = head;
while (curr != NULL) {
if (curr->random != NULL)
curr->next->random = curr->random->next;
curr = curr->next->next;
}
// Separate the new nodes from the original nodes
curr = head;
Node* clonedHead = head->next;
Node* clone = clonedHead;
while (clone->next != NULL) {
// Update the next nodes of original node
// and cloned node
curr->next = curr->next->next;
clone->next = clone->next->next;
// Move pointers of original as well as
// cloned linked list to their next nodes
curr = curr->next;
clone = clone->next;
}
curr->next = NULL;
clone->next = NULL;
return clonedHead;
}
// Function to print the linked list
void printList(Node* head) {
while (head != NULL) {
cout << head->data << "(";
if(head->random)
cout << head->random->data << ")";
else
cout << "null" << ")";
if(head->next != NULL)
cout << " -> ";
head = head->next;
}
cout << endl;
}
int main() {
// Creating a linked list with random pointer
Node* head = new Node(1);
head->next = new Node(2);
head->next->next = new Node(3);
head->next->next->next = new Node(4);
head->next->next->next->next = new Node(5);
head->random = head->next->next;
head->next->random = head;
head->next->next->random = head->next->next->next->next;
head->next->next->next->random = head->next->next;
head->next->next->next->next->random = head->next;
// Print the original list
cout << "Original linked list:\n";
printList(head);
// Function call
Node* clonedList = cloneLinkedList(head);
cout << "Cloned linked list:\n";
printList(clonedList);
return 0;
}
// Java code to Clone a linked list with next and random
// pointer by Inserting Nodes In-place
class Node {
int data;
Node next, random;
Node(int x) {
data = x;
next = random = null;
}
}
class GfG {
// Function to clone the linked list
static Node cloneLinkedList(Node head) {
if (head == null) {
return null;
}
// Create new nodes and insert them next to the original nodes
Node curr = head;
while (curr != null) {
Node newNode = new Node(curr.data);
newNode.next = curr.next;
curr.next = newNode;
curr = newNode.next;
}
// Set the random pointers of the new nodes
curr = head;
while (curr != null) {
if (curr.random != null) {
curr.next.random = curr.random.next;
}
curr = curr.next.next;
}
// Separate the new nodes from the original nodes
curr = head;
Node clonedHead = head.next;
Node clone = clonedHead;
while (clone.next != null) {
// Update the next nodes of original node
// and cloned node
curr.next = curr.next.next;
clone.next = clone.next.next;
// Move pointers of original and cloned
// linked list to their next nodes
curr = curr.next;
clone = clone.next;
}
curr.next = null;
clone.next = null;
return clonedHead;
}
// Function to print the linked list
public static void printList(Node head) {
while (head != null) {
System.out.print(head.data + "(");
if (head.random != null) {
System.out.print(head.random.data);
} else {
System.out.print("null");
}
System.out.print(")");
if (head.next != null) {
System.out.print(" -> ");
}
head = head.next;
}
System.out.println();
}
public static void main(String[] args) {
// Creating a linked list with random pointer
Node head = new Node(1);
head.next = new Node(2);
head.next.next = new Node(3);
head.next.next.next = new Node(4);
head.next.next.next.next = new Node(5);
head.random = head.next.next;
head.next.random = head;
head.next.next.random = head.next.next.next.next;
head.next.next.next.random = head.next.next;
head.next.next.next.next.random = head.next;
// Print the original list
System.out.println("Original linked list:");
printList(head);
// Function call
Node clonedList = cloneLinkedList(head);
System.out.println("Cloned linked list:");
printList(clonedList);
}
}
# Python code to Clone a linked list with next and random
# pointer by Inserting Nodes In-place
class Node:
def __init__(self, x):
self.data = x
self.next = None
self.random = None
# Function to clone the linked list
def cloneLinkedList(head):
if head is None:
return None
# Create new nodes and insert them next to
# the original nodes
curr = head
while curr is not None:
newNode = Node(curr.data)
newNode.next = curr.next
curr.next = newNode
curr = newNode.next
# Set the random pointers of the new nodes
curr = head
while curr is not None:
if curr.random is not None:
curr.next.random = curr.random.next
curr = curr.next.next
# Separate the new nodes from the original nodes
curr = head
clonedHead = head.next
clone = clonedHead
while clone.next is not None:
# Update the next nodes of original node
# and cloned node
curr.next = curr.next.next
clone.next = clone.next.next
# Move pointers of original as well as
# cloned linked list to their next nodes
curr = curr.next
clone = clone.next
curr.next = None
clone.next = None
return clonedHead
# Function to print the linked list
def printList(head):
while head is not None:
print(f"{head.data}(", end="")
if head.random:
print(f"{head.random.data})", end="")
else:
print("null)", end="")
if head.next is not None:
print(" -> ", end="")
head = head.next
print()
if __name__ == "__main__":
# Creating a linked list with random pointer
head = Node(1)
head.next = Node(2)
head.next.next = Node(3)
head.next.next.next = Node(4)
head.next.next.next.next = Node(5)
head.random = head.next.next
head.next.random = head
head.next.next.random = head.next.next.next.next
head.next.next.next.random = head.next.next
head.next.next.next.next.random = head.next
# Print the original list
print("Original linked list:")
printList(head)
# Function call
clonedList = cloneLinkedList(head)
print("Cloned linked list:")
printList(clonedList)
// C# code to Clone a linked list with next and random
// pointer by Inserting Nodes In-place
using System;
using System.Collections.Generic;
public class Node {
public int Data;
public Node Next, Random;
public Node(int x) {
Data = x;
Next = Random = null;
}
}
public class GfG {
public static Node CloneLinkedList(Node head) {
if (head == null)
return null;
// Create new nodes and insert them next to
// the original nodes
Node curr = head;
while (curr != null) {
Node newNode = new Node(curr.Data);
newNode.Next = curr.Next;
curr.Next = newNode;
curr = newNode.Next;
}
// Set the random pointers of the new nodes
curr = head;
while (curr != null) {
if (curr.Random != null)
curr.Next.Random = curr.Random.Next;
curr = curr.Next.Next;
}
// Separate the new nodes from the original nodes
curr = head;
Node clonedHead = head.Next;
Node clone = clonedHead;
while (clone.Next != null) {
// Update the next nodes of original node
// and cloned node
curr.Next = curr.Next.Next;
clone.Next = clone.Next.Next;
// Move pointers of original as well as
// cloned linked list to their next nodes
curr = curr.Next;
clone = clone.Next;
}
curr.Next = null;
clone.Next = null;
return clonedHead;
}
// Function to print the linked list
public static void PrintList(Node head) {
while (head != null) {
Console.Write(head.Data + "(");
if (head.Random != null)
Console.Write(head.Random.Data + ")");
else
Console.Write("null)");
if (head.Next != null)
Console.Write(" -> ");
head = head.Next;
}
Console.WriteLine();
}
public static void Main() {
// Creating a linked list with random pointer
Node head = new Node(1);
head.Next = new Node(2);
head.Next.Next = new Node(3);
head.Next.Next.Next = new Node(4);
head.Next.Next.Next.Next = new Node(5);
head.Random = head.Next.Next;
head.Next.Random = head;
head.Next.Next.Random = head.Next.Next.Next.Next;
head.Next.Next.Next.Random = head.Next.Next;
head.Next.Next.Next.Next.Random = head.Next;
// Print the original list
Console.WriteLine("Original linked list:");
PrintList(head);
Node clonedList = CloneLinkedList(head);
Console.WriteLine("Cloned linked list:");
PrintList(clonedList);
}
}
// JavaScript code to Clone a linked list with next and random
// pointer by Inserting Nodes In-place
class Node {
constructor(data) {
this.data = data;
this.next = null;
this.random = null;
}
}
function cloneLinkedList(head) {
if (head === null) {
return null;
}
// Create new nodes and insert them next to the
// original nodes
let curr = head;
while (curr !== null) {
let newNode = new Node(curr.data);
newNode.next = curr.next;
curr.next = newNode;
curr = newNode.next;
}
// Set the random pointers of the new nodes
curr = head;
while (curr !== null) {
if (curr.random !== null) {
curr.next.random = curr.random.next;
}
curr = curr.next.next;
}
// Separate the new nodes from the original nodes
curr = head;
let clonedHead = head.next;
let clone = clonedHead;
while (clone.next !== null) {
// Update the next nodes of original node and cloned node
curr.next = curr.next.next;
clone.next = clone.next.next;
// Move pointers of original as well as cloned
// linked list to their next nodes
curr = curr.next;
clone = clone.next;
}
curr.next = null;
clone.next = null;
return clonedHead;
}
// Function to print the linked list
function printList(head) {
let result = "";
while (head !== null) {
result += head.data + "(";
result += head.random ? head.random.data : "null";
result += ")";
if (head.next !== null) {
result += " -> ";
}
head = head.next;
}
console.log(result);
}
// Creating a linked list with random pointer
let head = new Node(1);
head.next = new Node(2);
head.next.next = new Node(3);
head.next.next.next = new Node(4);
head.next.next.next.next = new Node(5);
head.random = head.next.next;
head.next.random = head;
head.next.next.random = head.next.next.next.next;
head.next.next.next.random = head.next.next;
head.next.next.next.next.random = head.next;
// Print the original list
console.log("Original linked list:");
printList(head);
let clonedList = cloneLinkedList(head);
console.log("Cloned linked list:");
printList(clonedList);
OutputOriginal linked list:
1(3) -> 2(1) -> 3(5) -> 4(3) -> 5(2)
Cloned linked list:
1(3) -> 2(1) -> 3(5) -> 4(3) -> 5(2)
Time Complexity: O(3n), because we are traversing the linked list three times.
Auxiliary Space: O(1), as we are storing all the cloned nodes in the original linked list itself, no extra space is required.
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String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
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Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
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Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
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Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
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Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
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Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
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Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
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Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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