Bubble Sort On Doubly Linked List
Last Updated :
12 Sep, 2024
Given a doubly linked list, the task is to sort the linked list in non-decreasing order by using bubble sort.
Examples:
Input : head: 5<->3<->4<->1<->2
Output : head: 1<->2<->3<->4<->5
Input : head: 5<->4<->3<->2
Output : head: 2<->3<->4<->5
[Expected Approach - 1] Swapping node Values - O(n^2) Time and O(1) Space:
The bubble sort algorithm for a doubly linked list works by repeatedly traversing the list and comparing adjacent nodes. If two adjacent nodes do not follow the sorted order, their data is swapped. After each complete pass through the list, the largest unsorted element is moved to the end of the list. With each successive pass, the number of nodes that need to be checked decreases as the largest elements is positioned to its correct place. This process continues until the entire list is sorted.
Below is the implementation of the above approach:
C++
// C++ program to sort a doubly linked list
// using bubble sort
#include <iostream>
using namespace std;
class Node {
public:
int data;
Node* next;
Node* prev;
Node(int x) {
data = x;
next = nullptr;
prev = nullptr;
}
};
// Function to sort the doubly linked list
// using bubble sort
Node* bubbleSort(Node* head) {
if (head == nullptr) return head;
bool swapped;
Node* curr;
Node* last = nullptr;
// Keep going until no swaps occur in a pass
do {
swapped = false;
curr = head;
// Traverse through the list and swap adjacent
// nodes if they are in the wrong order
while (curr->next != last) {
if (curr->data > curr->next->data) {
// Swap the data of the current node
// and next node
int swap_data = curr->data;
curr->data = curr->next->data;
curr->next->data = swap_data;
swapped = true;
}
curr = curr->next;
}
// Reduce the effective list size after
// each pass
last = curr;
} while (swapped);
return head;
}
void printList(Node* node) {
Node* curr = node;
while (curr != nullptr) {
cout << " " << curr->data;
curr = curr->next;
}
}
int main() {
// Create a hard-coded doubly linked list:
// 5 <-> 3 <-> 4 <-> 1 <-> 2
Node* head = new Node(5);
head->next = new Node(3);
head->next->prev = head;
head->next->next = new Node(4);
head->next->next->prev = head->next;
head->next->next->next = new Node(1);
head->next->next->next->prev = head->next->next;
head->next->next->next->next = new Node(2);
head->next->next->next->next->prev
= head->next->next->next;
head = bubbleSort(head);
printList(head);
return 0;
}
// C program to sort a doubly linked list
// using bubble sort
#include <stdio.h>
#include <stdlib.h>
struct Node {
int data;
struct Node* next;
struct Node* prev;
};
// Function to sort the doubly linked list using
// bubble sort
struct Node* bubbleSort(struct Node* head) {
if (head == NULL) return head;
int swapped;
struct Node* curr;
struct Node* last = NULL;
// Keep going until no swaps occur in a pass
do {
swapped = 0;
curr = head;
// Traverse through the list and swap adjacent
// nodes if they are in the wrong order
while (curr->next != last) {
if (curr->data > curr->next->data) {
// Swap the data of the current node
// and next node
int swap_data = curr->data;
curr->data = curr->next->data;
curr->next->data = swap_data;
swapped = 1;
}
curr = curr->next;
}
last = curr;
} while (swapped);
return head;
}
void printList(struct Node* node) {
struct Node* curr = node;
while (curr != NULL) {
printf("%d ", curr->data);
curr = curr->next;
}
}
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 a hard-coded doubly linked list:
// 5 <-> 3 <-> 4 <-> 1 <-> 2
struct Node* head = createNode(5);
head->next = createNode(3);
head->next->prev = head;
head->next->next = createNode(4);
head->next->next->prev = head->next;
head->next->next->next = createNode(1);
head->next->next->next->prev
= head->next->next;
head->next->next->next->next = createNode(2);
head->next->next->next->next->prev
= head->next->next->next;
head = bubbleSort(head);
printList(head);
return 0;
}
// Java program to sort a doubly linked list
// using bubble sort
class Node {
int data;
Node next, prev;
Node(int x) {
data = x;
next = null;
prev = null;
}
}
public class GfG {
// Function to sort the linked list using bubble sort
static Node bubbleSort(Node head) {
if (head == null) return head;
boolean swapped;
Node curr;
Node last = null;
// Keep going until no swaps occur in a pass
do {
swapped = false;
curr = head;
// Traverse through the list and swap adjacent
// nodes if they are in the wrong order
while (curr.next != last) {
if (curr.data > curr.next.data) {
// Swap the data of the current node
// and next node
int swap_data = curr.data;
curr.data = curr.next.data;
curr.next.data = swap_data;
swapped = true;
}
curr = curr.next;
}
// Reduce the effective list size
// after each pass
last = curr;
} while (swapped);
return head;
}
static void printList(Node node) {
Node curr = node;
while (curr != null) {
System.out.print(" " + curr.data);
curr = curr.next;
}
}
public static void main(String[] args) {
// Create a hard-coded doubly linked list:
// 5 <-> 3 <-> 4 <-> 1 <-> 2
Node head = new Node(5);
head.next = new Node(3);
head.next.prev = head;
head.next.next = new Node(4);
head.next.next.prev = head.next;
head.next.next.next = new Node(1);
head.next.next.next.prev = head.next.next;
head.next.next.next.next = new Node(2);
head.next.next.next.next.prev
= head.next.next.next;
head = bubbleSort(head);
printList(head);
}
}
# Python program to sort a doubly linked list using
# bubble sort
class Node:
def __init__(self, data):
self.data = data
self.next = None
self.prev = None
# Function to sort the linked list using bubble sort
def bubble_sort(head):
if not head:
return head
swapped = True
last = None
# Keep going until no swaps occur in a pass
while swapped:
swapped = False
curr = head
# Traverse through the list and swap adjacent
# nodes if they are in the wrong order
while curr.next != last:
if curr.data > curr.next.data:
# Swap the data of the current node
# and next node
curr.data, curr.next.data = (
curr.next.data, curr.data
)
swapped = True
curr = curr.next
# Reduce the effective list size after each pass
last = curr
return head
def print_list(node):
curr = node
while curr:
print(curr.data, end=" ")
curr = curr.next
if __name__ == '__main__':
# Create a hard-coded doubly linked list:
# 5 <-> 3 <-> 4 <-> 1 <-> 2
head = Node(5)
head.next = Node(3)
head.next.prev = head
head.next.next = Node(4)
head.next.next.prev = head.next
head.next.next.next = Node(1)
head.next.next.next.prev = head.next.next
head.next.next.next.next = Node(2)
head.next.next.next.next.prev = head.next.next.next
head = bubble_sort(head)
print_list(head)
// C# program to sort a doubly linked list using
// bubble sort
using System;
public class Node {
public int data;
public Node next;
public Node(int new_data) {
data = new_data;
next = null;
}
}
class GfG {
// Function to sort the linked list using bubble sort
static Node BubbleSort(Node head) {
if (head == null) return head;
bool swapped;
Node curr;
Node last = null;
// Keep going until no swaps occur in a pass
do {
swapped = false;
curr = head;
// Traverse through the list and swap adjacent
// nodes if they are in the wrong order
while (curr.next != last) {
if (curr.data > curr.next.data) {
// Swap the data of the current node
// and next node
int swap_data = curr.data;
curr.data = curr.next.data;
curr.next.data = swap_data;
swapped = true;
}
curr = curr.next;
}
// Reduce the effective list size
// after each pass
last = curr;
} while (swapped);
return head;
}
static void PrintList(Node node) {
Node curr = node;
while (curr != null) {
Console.Write(" " + curr.data);
curr = curr.next;
}
}
static void Main(string[] args) {
// Create a hard-coded linked list:
// 5 -> 3 -> 4 -> 1 -> 2
Node head = new Node(5);
head.next = new Node(3);
head.next.next = new Node(4);
head.next.next.next = new Node(1);
head.next.next.next.next = new Node(2);
head = BubbleSort(head);
PrintList(head);
}
}
// JavaScript program to sort a doubly linked list
// using bubble sort
class Node {
constructor(data) {
this.data = data;
this.next = null;
this.prev = null;
}
}
// Function to sort the doubly linked list
// using bubble sort
function bubbleSort(head) {
if (!head) return head;
let swapped;
let last = null;
// Keep going until no swaps occur in a pass
do {
swapped = false;
let curr = head;
// Traverse through the list and swap adjacent
// nodes if they are in the wrong order
while (curr.next !== last) {
if (curr.data > curr.next.data) {
// Swap the data of the current node
// and next node
let swap_data = curr.data;
curr.data = curr.next.data;
curr.next.data = swap_data;
swapped = true;
}
curr = curr.next;
}
// Reduce the effective list size
// after each pass
last = curr;
} while (swapped);
return head;
}
function printList(node) {
let curr = node;
while (curr !== null) {
process.stdout.write(" " + curr.data);
curr = curr.next;
}
}
// Create a hard-coded doubly
// linked list: 5 <-> 3 <-> 4 <-> 1 <-> 2
let head = new Node(5);
head.next = new Node(3);
head.next.prev = head;
head.next.next = new Node(4);
head.next.next.prev = head.next;
head.next.next.next = new Node(1);
head.next.next.next.prev = head.next.next;
head.next.next.next.next = new Node(2);
head.next.next.next.next.prev = head.next.next.next;
head = bubbleSort(head);
printList(head);
Time Complexity: O(n^2), as we are using nested loops for sorting, where n is the number of nodes in the linked list.
Auxiliary Space: O(1)
[Expected Approach - 2] Changing node Links - O(n^2) Time and O(1) Space:
The idea is to sort the doubly linked list by rearranging its nodes rather than swapping their values. We start by traversing the list from the head. For each pass through the list, we compare adjacent nodes and rearrange their links if the nodes are not in sorted order. Instead of swapping the node values, we adjust the next and previous pointers of the nodes to change their positions. This process continues until the entire list is sorted.
Below is the implementation of the above approach:
C++
// C++ program to sort a doubly linked list using
// bubble sort by interchanging links
#include <iostream>
using namespace std;
class Node {
public:
int data;
Node* next;
Node* prev;
Node(int x) {
data = x;
next = nullptr;
prev = nullptr;
}
};
// Function to sort the linked list using bubble sort
Node* bubbleSort(Node* head) {
if (head == nullptr) return head;
bool swapped;
Node* curr;
Node* last = nullptr;
// Keep going until no swaps occur in a pass
do {
swapped = false;
curr = head;
// Traverse through the list and swap adjacent
// nodes if they are in the wrong order
while (curr->next != last) {
if (curr->data > curr->next->data) {
// Swap the nodes by rearranging the links
Node* nextNode = curr->next;
curr->next = nextNode->next;
nextNode->prev = curr->prev;
if (curr->next != nullptr) {
curr->next->prev = curr;
}
if (nextNode->prev != nullptr) {
nextNode->prev->next = nextNode;
} else {
head = nextNode;
}
nextNode->next = curr;
curr->prev = nextNode;
swapped = true;
} else {
curr = curr->next;
}
}
// Reduce the effective list size
// after each pass
last = curr;
} while (swapped);
return head;
}
void printList(Node* node) {
Node* curr = node;
while (curr != nullptr) {
cout << " " << curr->data;
curr = curr->next;
}
}
int main() {
// Create a hard-coded linked list:
// 5 <-> 3 <-> 4 <-> 1 <-> 2
Node* head = new Node(5);
head->next = new Node(3);
head->next->prev = head;
head->next->next = new Node(4);
head->next->next->prev = head->next;
head->next->next->next = new Node(1);
head->next->next->next->prev = head->next->next;
head->next->next->next->next = new Node(2);
head->next->next->next->next->prev
= head->next->next->next;
head = bubbleSort(head);
printList(head);
return 0;
}
// C program to sort a doubly linked list
// using bubble sort by interchanging links
#include <stdio.h>
#include <stdlib.h>
struct Node {
int data;
struct Node* next;
struct Node* prev;
};
// Function to sort the linked list using bubble sort
struct Node* bubbleSort(struct Node* head) {
if (head == NULL) return head;
int swapped;
struct Node* last = NULL;
// Keep going until no swaps occur in a pass
do {
swapped = 0;
struct Node* curr = head;
// Traverse through the list and swap adjacent
// nodes if they are in the wrong order
while (curr->next != last) {
if (curr->data > curr->next->data) {
// Nodes to be swapped
struct Node* nextNode = curr->next;
// Perform the swap
if (curr->prev == NULL) {
// Swapping the head node with next node
head = nextNode;
}
else {
// Linking previous node to next node
curr->prev->next = nextNode;
}
if (nextNode->next != NULL) {
nextNode->next->prev = curr;
}
// Re-linking nodes to complete swap
curr->next = nextNode->next;
nextNode->prev = curr->prev;
nextNode->next = curr;
curr->prev = nextNode;
// Update swapped
swapped = 1;
}
else {
// Move to the next pair of nodes
curr = curr->next;
}
}
// Update the last sorted element
last = curr;
} while (swapped);
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 a hard-coded linked list:
// 5 <-> 3 <-> 4 <-> 1 <-> 2
struct Node* head = createNode(5);
head->next = createNode(3);
head->next->prev = head;
head->next->next = createNode(4);
head->next->next->prev = head->next;
head->next->next->next = createNode(1);
head->next->next->next->prev = head->next->next;
head->next->next->next->next = createNode(2);
head->next->next->next->next->prev
= head->next->next->next;
head = bubbleSort(head);
printList(head);
return 0;
}
// Java program to sort a doubly linked list using
// bubble sort by interchanging links
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 the linked list using bubble sort
static Node bubbleSort(Node head) {
if (head == null) return head;
boolean swapped;
Node last = null;
// Keep going until no swaps occur in a pass
do {
swapped = false;
Node curr = head;
// Traverse through the list and swap adjacent
// nodes if they are in the wrong order
while (curr.next != last) {
if (curr.data > curr.next.data) {
// Nodes to be swapped
Node nextNode = curr.next;
// Perform the swap
if (curr.prev == null) {
// Swapping the head node
// with next node
head = nextNode;
}
else {
// Linking previous
// node to next node
curr.prev.next = nextNode;
}
if (nextNode.next != null) {
nextNode.next.prev = curr;
}
// Re-linking nodes to complete swap
curr.next = nextNode.next;
nextNode.prev = curr.prev;
nextNode.next = curr;
curr.prev = nextNode;
// Update swapped
swapped = true;
}
else {
// Move to the next pair of nodes
curr = curr.next;
}
}
// Update the last sorted element
last = curr;
} while (swapped);
return head;
}
static void printList(Node node) {
Node curr = node;
while (curr != null) {
System.out.print(" " + curr.data);
curr = curr.next;
}
System.out.println();
}
public static void main(String[] args) {
// Create a hard-coded linked list:
// 5 <-> 3 <-> 4 <-> 1 <-> 2
Node head = new Node(5);
head.next = new Node(3);
head.next.prev = head;
head.next.next = new Node(4);
head.next.next.prev = head.next;
head.next.next.next = new Node(1);
head.next.next.next.prev = head.next.next;
head.next.next.next.next = new Node(2);
head.next.next.next.next.prev
= head.next.next.next;
head = bubbleSort(head);
printList(head);
}
}
# Python program to sort a doubly linked list using
# bubble sort by interchanging links
class Node:
def __init__(self, data):
self.data = data
self.next = None
self.prev = None
def bubble_sort(head):
if head is None:
return head
swapped = True
last = None
# Keep going until no swaps occur in a pass
while swapped:
swapped = False
curr = head
# Traverse through the list and swap adjacent
# nodes if they are in the wrong order
while curr.next != last:
if curr.data > curr.next.data:
# Nodes to be swapped
next_node = curr.next
# Perform the swap
if curr.prev is None:
# Swapping the head node with
# next node
head = next_node
else:
# Linking previous node to next node
curr.prev.next = next_node
if next_node.next is not None:
next_node.next.prev = curr
# Re-linking nodes to complete swap
curr.next = next_node.next
next_node.prev = curr.prev
next_node.next = curr
curr.prev = next_node
# Update swapped
swapped = True
else:
# Move to the next pair of nodes
curr = curr.next
# Update the last sorted element
last = curr
return head
def print_list(node):
curr = node
while curr:
print(curr.data, end=" ")
curr = curr.next
print()
if __name__ == "__main__":
# Create a hard-coded linked list:
# 5 <-> 3 <-> 4 <-> 1 <-> 2
head = Node(5)
head.next = Node(3)
head.next.prev = head
head.next.next = Node(4)
head.next.next.prev = head.next
head.next.next.next = Node(1)
head.next.next.next.prev = head.next.next
head.next.next.next.next = Node(2)
head.next.next.next.next.prev = head.next.next.next
head = bubble_sort(head)
print_list(head)
// C# program to sort a doubly linked list using
// bubble sort by interchanging links
using System;
class Node {
public int Data;
public Node next;
public Node prev;
public Node(int data) {
Data = data;
next = null;
prev = null;
}
}
class GfG {
// Function to sort the linked list using
// bubble sort
static Node BubbleSort(Node head) {
if (head == null) return head;
bool swapped;
Node last = null;
// Keep going until no swaps occur in a pass
do {
swapped = false;
Node curr = head;
// Traverse through the list and swap
// adjacent nodes if they are in
// the wrong order
while (curr.next != last) {
if (curr.Data > curr.next.Data) {
// Nodes to be swapped
Node nextNode = curr.next;
// Perform the swap
if (curr.prev == null) {
// Swapping the head node
// with next node
head = nextNode;
}
else {
// Linking previous node
// to next node
curr.prev.next = nextNode;
}
if (nextNode.next != null) {
nextNode.next.prev = curr;
}
// Re-linking nodes to complete swap
curr.next = nextNode.next;
nextNode.prev = curr.prev;
nextNode.next = curr;
curr.prev = nextNode;
// Update swapped
swapped = true;
}
else {
// Move to the next pair of nodes
curr = curr.next;
}
}
// Update the last sorted element
last = curr;
} while (swapped);
return head;
}
static void PrintList(Node node) {
Node curr = node;
while (curr != null) {
Console.Write(curr.Data + " ");
curr = curr.next;
}
Console.WriteLine();
}
static void Main(string[] args) {
// Create a hard-coded linked list:
// 5 <-> 3 <-> 4 <-> 1 <-> 2
Node head = new Node(5);
head.next = new Node(3);
head.next.prev = head;
head.next.next = new Node(4);
head.next.next.prev = head.next;
head.next.next.next = new Node(1);
head.next.next.next.prev = head.next.next;
head.next.next.next.next = new Node(2);
head.next.next.next.next.prev
= head.next.next.next;
head = BubbleSort(head);
PrintList(head);
}
}
// Javascript program to sort a doubly linked list
// using bubble sort by interchanging links
class Node {
constructor(data) {
this.data = data;
this.next = null;
this.prev = null;
}
}
function bubbleSort(head) {
if (head === null) return head;
let swapped;
let last = null;
// Keep going until no swaps occur in a pass
do {
swapped = false;
let curr = head;
// Traverse through the list and swap adjacent
// nodes if they are in the wrong order
while (curr.next !== last) {
if (curr.data > curr.next.data) {
// Nodes to be swapped
let nextNode = curr.next;
// Perform the swap
if (curr.prev === null) {
// Swapping the head node with next node
head = nextNode;
}
else {
// Linking previous node to next node
curr.prev.next = nextNode;
}
if (nextNode.next !== null) {
nextNode.next.prev = curr;
}
// Re-linking nodes to complete swap
curr.next = nextNode.next;
nextNode.prev = curr.prev;
nextNode.next = curr;
curr.prev = nextNode;
// Update swapped
swapped = true;
}
else {
// Move to the next pair of nodes
curr = curr.next;
}
}
// Update the last sorted element
last = curr;
} while (swapped);
return head;
}
function printList(node) {
let curr = node;
while (curr !== null) {
console.log(curr.data + " ");
curr = curr.next;
}
console.log();
}
// Create a hard-coded linked list:
// 5 <-> 3 <-> 4 <-> 1 <-> 2
let head = new Node(5);
head.next = new Node(3);
head.next.prev = head;
head.next.next = new Node(4);
head.next.next.prev = head.next;
head.next.next.next = new Node(1);
head.next.next.next.prev = head.next.next;
head.next.next.next.next = new Node(2);
head.next.next.next.next.prev = head.next.next.next;
head = bubbleSort(head);
printList(head);
Time Complexity: O(n^2), as we are using nested loops for sorting, where n is the number of nodes in the linked list.
Auxiliary Space: O(1)
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
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
2 min read
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
2 min read
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:
2 min read
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
2 min read
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
2 min read
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
4 min read
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
3 min read
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
15+ min read
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
Interview Preparation
Practice Problem