The 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 article, we will explore the insertion and search operations and prefix searches in Trie Data Structure.
Trie Data Structure
Representation of Trie Node
- Trie data structure consists of nodes connected by edges.
- Each node represents a character or a part of a string.
- The root node acts as a starting point and does not store any character.
C++
class TrieNode {
public:
// pointer array for child nodes of each node
TrieNode* children[26];
// Used for indicating ending of string
bool isLeaf;
TrieNode() {
// initialize the wordEnd variable with false
// initialize every index of childNode array with NULL
isLeaf = false;
for (int i = 0; i < 26; i++) {
children[i] = nullptr;
}
}
};
public class TrieNode {
// Array for child nodes of each node
TrieNode[] children;
// Used for indicating the end of a string
boolean isEndOfWord;
// Constructor
public TrieNode() {
// Initialize the wordEnd
// variable with false
isEndOfWord = false;
// Initialize every index of
// the child array with null
// In Java, we do not have to
// explicitely assign null as
// the values are by default
// assigned as null
children = new TrieNode[26];
}
}
class TrieNode:
def __init__(self):
self.children = [None] * 26
self.isEndOfWord = False
class TrieNode
{
public TrieNode[] children = new TrieNode[26];
public bool isLeaf = false;
}
class TrieNode {
constructor() {
// Initialize the child Node
// array with 26 nulls
this.children = Array(26).fill(null);
// Initialize wordEnd to the false
// indicating that no word ends here yet
this.isEndOfWord = false;
}
}
Insertion in Trie Data Structure - O(n) Time and O(n) Space
Insert Operation in Trie Data StructureInserting "and" in Trie data structure:
- Start at the root node: The root node has no character associated with it and its wordEnd value is 0, indicating no complete word ends at this point.
- First character "a": Calculate the index using 'a' - 'a' = 0. Check if the child[0] is null. Since it is, create a new TrieNode with the character "a", wordEnd set to 0, and an empty array of pointers. Move to this new node.
- Second character "n": Calculate the index using 'n' - 'a' = 13. Check if child[13] is null. It is, so create a new TrieNode with the character "n", wordEnd set to 0, and an empty array of pointers. Move to this new node.
- Third character "d": Calculate the index using 'd' - 'a' = 3. Check if child[3] is null. It is, so create a new TrieNode with the character "d", wordEnd set to 1 (indicating the word "and" ends here).
Inserting "ant" in Trie data structure:
- Start at the root node: Root node doesn't contain any data but it keep track of every first character of every string that has been inserted.
- First character "a": Calculate the index using 'a' - 'a' = 0. Check if the child[0] is null. We already have the "a" node created from the previous insertion. so move to the existing "a" node.
- First character "n": Calculate the index using 'n' - 'a' = 13. Check if child[13] is null. It's not, so move to the existing "n" node.
- Second character "t": Calculate the index using 't' - 'a' = 19. Check if child[19] is null. It is, so create a new TrieNode with the character "t", wordEnd set to 1 (indicating the word "ant" ends here).
C++
// Method to insert a key into the Trie
void insert(TrieNode* root, const string& key) {
// Initialize the curr pointer with the root node
TrieNode* curr = root;
// Iterate across the length of the string
for (char c : key) {
// Check if the node exists for the
// current character in the Trie
if (curr->children[c - 'a'] == nullptr) {
// If node for current character does
// not exist then make a new node
TrieNode* newNode = new TrieNode();
// Keep the reference for the newly
// created node
curr->children[c - 'a'] = newNode;
}
// Move the curr pointer to the
// newly created node
curr = curr->children[c - 'a'];
}
// Mark the end of the word
curr->isLeaf = true;
}
// Function to insert a key into the Trie
void insert(struct TrieNode* root, const char* key) {
struct TrieNode* curr = root;
while (*key) {
int index = *key - 'a';
if (!curr->children[index]) {
curr->children[index] = getNode();
}
curr = curr->children[index];
key++;
}
curr->isEndOfWord = true;
}
// Method to insert a key into the Trie
static void insert(TrieNode root, String key) {
// Initialize the curr pointer with the root node
TrieNode curr = root;
// Iterate across the length of the string
for (char c : key.toCharArray()) {
// Check if the node exists for the
// current character in the Trie
if (curr.children[c - 'a'] == null) {
// If node for current character does
// not exist then make a new node
TrieNode newNode = new TrieNode();
// Keep the reference for the newly
// created node
curr.children[c - 'a'] = newNode;
}
// Move the curr pointer to the
// newly created node
curr = curr.children[c - 'a'];
}
// Mark the end of the word
curr.isEndOfWord = true;
}
# Method to insert a key into the Trie
def insert(root, key):
# Initialize the curr pointer with the root node
curr = root
# Iterate across the length of the string
for c in key:
# Check if the node exists for the
# current character in the Trie
index = ord(c) - ord('a')
if curr.children[index] is None:
# If node for current character does
# not exist then make a new node
new_node = TrieNode()
# Keep the reference for the newly
# created node
curr.children[index] = new_node
# Move the curr pointer to the
# newly created node
curr = curr.children[index]
# Mark the end of the word
curr.isEndOfWord = True
// Method to insert a key into the Trie
public static void Insert(TrieNode root, string key) {
// Initialize the curr pointer with the root node
TrieNode curr = root;
// Iterate across the length of the string
foreach(char c in key) {
// Check if the node exists for the current
// character in the Trie
if (curr.children[c - 'a'] == null) {
// If node for current character does
// not exist then make a new node
TrieNode newNode = new TrieNode();
// Keep the reference for the newly created node
curr.children[c - 'a'] = newNode;
}
// Move the curr pointer to the newly created node
curr = curr.children[c - 'a'];
}
// Mark the end of the word
curr.isLeaf = true;
}
// Method to insert a key into the Trie
function insert(root, key) {
// Initialize the curr pointer with the root node
let curr = root;
// Iterate across the length of the string
for (let c of key) {
// Check if the node exists for the
// current character in the Trie
let index = c.charCodeAt(0) - 'a'.charCodeAt(0);
if (curr.children[index] === null) {
// If node for current character does
// not exist then make a new node
let newNode = new TrieNode();
// Keep the reference for the newly
// created node
curr.children[index] = newNode;
}
// Move the curr pointer to the
// newly created node
curr = curr.children[index];
}
// Mark the end of the word
curr.isEndOfWord = true;
}
Time Complexity: O(n), where n is the length of the word to insert.
Auxiliary Space: O(n)
Searching in Trie Data Structure - O(n) Time and O(1) Space
Searching for a key in Trie data structure is similar to its insert operation. However, It only compares the characters and moves down. The search can terminate due to the end of a string or lack of key in the trie.
Here's a visual representation of searching word "dad" in Trie data structure:
Let's assume that we have successfully inserted the words "and", "ant", and "dad" into our Trie, and we have to search for specific words within the Trie data structure. Let's try searching for the word "dad":
Search Operation in Trie Data Structure
Here's a visual representation of searching word "dad" in Trie data structure:
Let's assume that we have successfully inserted the words "and", "ant", and "dad" into our Trie, and we have to search for specific words within the Trie data structure. Let's try searching for the word "dad":
- We start at the root node.
- We follow the branch corresponding to the character 'd'.
- We follow the branch corresponding to the character 'a'.
- We follow the branch corresponding to the character 'd'.
- We reach the end of the word and wordEnd flag is 1.
- This means that "dad" is present in the Trie.
C++
// Method to search a key in the Trie
bool search(TrieNode* root, const string& key) {
// Initialize the curr pointer with the root node
TrieNode* curr = root;
// Iterate across the length of the string
for (char c : key) {
// Check if the node exists for the
// current character in the Trie
if (curr->children[c - 'a'] == nullptr)
return false;
// Move the curr pointer to the
// already existing node for the
// current character
curr = curr->children[c - 'a'];
}
// Return true if the word exists
// and is marked as ending
return curr->isLeaf;
}
// Function to search a key in the Trie
bool search(struct TrieNode* root, const char* key) {
struct TrieNode* curr = root;
while (*key) {
int index = *key - 'a';
if (!curr->children[index]) {
return false;
}
curr = curr->children[index];
key++;
}
return (curr != NULL && curr->isEndOfWord);
}
// Method to search a key in the Trie
static boolean search(TrieNode root, String key)
{
// Initialize the curr pointer with the root node
TrieNode curr = root;
// Iterate across the length of the string
for (char c : key.toCharArray()) {
// Check if the node exists for the
// current character in the Trie
if (curr.children[c - 'a'] == null)
return false;
// Move the curr pointer to the
// already existing node for the
// current character
curr = curr.children[c - 'a'];
}
// Return true if the word exists
// and is marked as ending
return curr.isEndOfWord;
}
# Method to search a key in the Trie
def search(root, key):
# Initialize the curr pointer with the root node
curr = root
# Iterate across the length of the string
for c in key:
# Check if the node exists for the
# current character in the Trie
index = ord(c) - ord('a')
if curr.children[index] is None:
return False
# Move the curr pointer to the
# already existing node for the
# current character
curr = curr.children[index]
# Return true if the word exists
# and is marked as ending
return curr.isEndOfWord
// Method to search a key in the Trie
public static bool Search(TrieNode root, string key)
{
// Initialize the curr pointer with the root node
TrieNode curr = root;
// Iterate across the length of the string
foreach(char c in key)
{
// Check if the node exists for the current
// character in the Trie
if (curr.children[c - 'a'] == null)
return false;
// Move the curr pointer to the already
// existing node for the current character
curr = curr.children[c - 'a'];
}
// Return true if the word exists and
// is marked as ending
return curr.isLeaf;
}
// Method to search a key in the Trie
function search(root, key) {
// Initialize the curr pointer with the root node
let curr = root;
// Iterate across the length of the string
for (let c of key) {
// Check if the node exists for the
// current character in the Trie
let index = c.charCodeAt(0) - 'a'.charCodeAt(0);
if (curr.children[index] === null)
return false;
// Move the curr pointer to the
// already existing node for the
// current character
curr = curr.children[index];
}
// Return true if the word exists
// and is marked as ending
return curr.isEndOfWord;
}
Time Complexity: O(n), where n is the length of the word to search.
Auxiliary Space: O(1)
Prefix Searching in Trie Data Structure - O(n) Time and O(1) Space
Searching for a prefix in a Trie data structure is similar to searching for a key, but the search does not need to reach the end of the word. Instead, we stop as soon as we reach the end of the prefix or if any character in the prefix doesn't exist in the Trie.
Here's a visual representation of prefix searching for the word 'da' in the Trie data structure:
Let's assume that we have successfully inserted the words 'and', 'ant', and 'dad' into our Trie. Now, let's search for the prefix 'da' within the Trie data structure.
- We start at the root node.
- We follow the branch corresponding to the character 'd'.
- We move to the node corresponding to the character 'a'.
- We reach the end of the prefix "da". Since we haven't encountered any missing characters along the way, we return
true.
C++
// Method to Seach Prefix key in Trie
bool isPrefix(TrieNode *root, string &key)
{
TrieNode *current = root;
for (char c : key)
{
int index = c - 'a';
// If character doesn't exist, return false
if (current->children[index] == nullptr)
{
return false;
}
current = current->children[index];
}
return true;
}
boolean isPrefix(TrieNode root, String key)
{
TrieNode current = root;
for (char c : key.toCharArray()) {
int index = c - 'a';
// If character doesn't exist, return false
if (current.children[index] == null) {
return false;
}
current = current.children[index];
}
return true;
}
def is_prefix(root, key):
current = root
for c in key:
index = ord(c) - ord('a')
# If character doesn't exist, return false
if current.children[index] is None:
return False
current = current.children[index]
return True
bool IsPrefix(TrieNode root, string key)
{
TrieNode current = root;
foreach(char c in key)
{
int index = c - 'a';
// If character doesn't exist, return false
if (current.Children[index] == null) {
return false;
}
current = current.Children[index];
}
return true;
}
function isPrefix(root, key)
{
let current = root;
for (let c of key) {
let index = c.charCodeAt(0) - "a".charCodeAt(0);
// If character doesn't exist, return false
if (current.children[index] === null) {
return false;
}
current = current.children[index];
}
return true;
}
Time Complexity: O(n), where n is the length of the word to search.
Auxiliary Space: O(1)
Implementation of Insert, Search and Prefix Searching Operations in Trie Data Structure
Now that we've learned how to insert words into a Trie, search for complete words, and perform prefix searches, let's do some hands-on practice.
We'll start by inserting the following words into the Trie: ["and", "ant", "do", "dad"].
Then, we'll search for the presence of these words: ["do", "gee", "bat"].
Finally, we'll check for the following prefixes: ["ge", "ba", "do", "de"].
Steps-by-step approach:
- Create a root node with the help of TrieNode() constructor.
- Store a collection of strings that have to be inserted in the Trie in a vector of strings say, arr.
- Inserting all strings in Trie with the help of the insertKey() function,
- Search strings with the help of searchKey() function.
- Prefix searching with the help of isPrefix() function.
C++
#include <bits/stdc++.h>
using namespace std;
class TrieNode
{
public:
// Array for children nodes of each node
TrieNode *children[26];
// for end of word
bool isLeaf;
TrieNode()
{
isLeaf = false;
for (int i = 0; i < 26; i++)
{
children[i] = nullptr;
}
}
};
// Method to insert a key into the Trie
void insert(TrieNode *root, const string &key)
{
// Initialize the curr pointer with the root node
TrieNode *curr = root;
// Iterate across the length of the string
for (char c : key)
{
// Check if the node exists for the
// current character in the Trie
if (curr->children[c - 'a'] == nullptr)
{
// If node for current character does
// not exist then make a new node
TrieNode *newNode = new TrieNode();
// Keep the reference for the newly
// created node
curr->children[c - 'a'] = newNode;
}
// Move the curr pointer to the
// newly created node
curr = curr->children[c - 'a'];
}
// Mark the end of the word
curr->isLeaf = true;
}
// Method to search a key in the Trie
bool search(TrieNode *root, const string &key)
{
if (root == nullptr)
{
return false;
}
// Initialize the curr pointer with the root node
TrieNode *curr = root;
// Iterate across the length of the string
for (char c : key)
{
// Check if the node exists for the
// current character in the Trie
if (curr->children[c - 'a'] == nullptr)
return false;
// Move the curr pointer to the
// already existing node for the
// current character
curr = curr->children[c - 'a'];
}
// Return true if the word exists
// and is marked as ending
return curr->isLeaf;
}
// Method to check if a prefix exists in the Trie
bool isPrefix(TrieNode *root, const string &prefix)
{
// Initialize the curr pointer with the root node
TrieNode *curr = root;
// Iterate across the length of the prefix string
for (char c : prefix)
{
// Check if the node exists for the current character in the Trie
if (curr->children[c - 'a'] == nullptr)
return false;
// Move the curr pointer to the already existing node
// for the current character
curr = curr->children[c - 'a'];
}
// If we reach here, the prefix exists in the Trie
return true;
}
int main()
{
// Create am example Trie
TrieNode *root = new TrieNode();
vector<string> arr = {"and", "ant", "do", "dad"};
for (const string &s : arr)
{
insert(root, s);
}
// One by one search strings
vector<string> searchKeys = {"do", "gee", "bat"};
for (string &s : searchKeys){
if(search(root, s))
cout << "true ";
else
cout << "false ";
}
cout<<"\n";
// One by one search for prefixes
vector<string> prefixKeys = {"ge", "ba", "do", "de"};
for (string &s : prefixKeys){
if (isPrefix(root, s))
cout << "true ";
else
cout << "false ";
}
return 0;
}
class TrieNode {
TrieNode[] children;
boolean isLeaf;
TrieNode()
{
children = new TrieNode[26];
isLeaf = false;
}
}
public class Trie {
TrieNode root;
public Trie() { root = new TrieNode(); }
// Method to insert a key into the Trie
public void insert(String key)
{
TrieNode curr = root;
for (char c : key.toCharArray()) {
if (curr.children[c - 'a'] == null) {
curr.children[c - 'a'] = new TrieNode();
}
curr = curr.children[c - 'a'];
}
curr.isLeaf = true;
}
// Method to search a key in the Trie
public boolean search(String key)
{
TrieNode curr = root;
for (char c : key.toCharArray()) {
if (curr.children[c - 'a'] == null) {
return false;
}
curr = curr.children[c - 'a'];
}
return curr.isLeaf;
}
// Method to check if a prefix exists in the Trie
public boolean isPrefix(String prefix)
{
TrieNode curr = root;
for (char c : prefix.toCharArray()) {
if (curr.children[c - 'a'] == null) {
return false;
}
curr = curr.children[c - 'a'];
}
return true;
}
public static void main(String[] args)
{
Trie trie = new Trie();
String[] arr
= {"and", "ant", "do", "dad"};
for (String s : arr) {
trie.insert(s);
}
String[] searchKeys = { "do", "gee", "bat" };
for (String s : searchKeys) {
if (trie.search(s))
System.out.print("true ");
else
System.out.print("false ");
}
System.out.println();
String[] prefixKeys = { "ge", "ba", "do", "de" };
for (String s : prefixKeys) {
if (trie.isPrefix(s))
System.out.print("true ");
else
System.out.print("false ");
}
}
}
class TrieNode:
def __init__(self):
self.children = [None] * 26
self.isLeaf = False
class Trie:
def __init__(self):
self.root = TrieNode()
# Method to insert a key into the Trie
def insert(self, key):
curr = self.root
for c in key:
index = ord(c) - ord('a')
if curr.children[index] is None:
curr.children[index] = TrieNode()
curr = curr.children[index]
curr.isLeaf = True
# Method to search a key in the Trie
def search(self, key):
curr = self.root
for c in key:
index = ord(c) - ord('a')
if curr.children[index] is None:
return False
curr = curr.children[index]
return curr.isLeaf
# Method to check if a prefix exists in the Trie
def isPrefix(self, prefix):
curr = self.root
for c in prefix:
index = ord(c) - ord('a')
if curr.children[index] is None:
return False
curr = curr.children[index]
return True
if __name__ == '__main__':
trie = Trie()
arr = ["and", "ant", "do", "dad"]
for s in arr:
trie.insert(s)
searchKeys = ["do", "gee", "bat"]
for s in searchKeys:
if trie.search(s):
print("true", end= " ")
else:
print("false", end=" ")
print()
prefixKeys = ["ge", "ba", "do", "de"]
for s in prefixKeys:
if trie.isPrefix(s):
print("true", end = " ")
else:
print("false", end = " ")
// Using System.Collections.Generic;
using System;
class TrieNode {
public TrieNode[] children = new TrieNode[26];
public bool isLeaf;
public TrieNode()
{
isLeaf = false;
for (int i = 0; i < 26; i++) {
children[i] = null;
}
}
}
class Trie {
private TrieNode root;
public Trie() { root = new TrieNode(); }
// Method to insert a key into the Trie
public void Insert(string key)
{
TrieNode curr = root;
foreach(char c in key)
{
if (curr.children[c - 'a'] == null) {
curr.children[c - 'a'] = new TrieNode();
}
curr = curr.children[c - 'a'];
}
curr.isLeaf = true;
}
// Method to search a key in the Trie
public bool Search(string key)
{
TrieNode curr = root;
foreach(char c in key)
{
if (curr.children[c - 'a'] == null)
return false;
curr = curr.children[c - 'a'];
}
return curr.isLeaf;
}
// Method to check if a prefix exists in the Trie
public bool isPrefix(string prefix)
{
TrieNode curr = root;
foreach(char c in prefix)
{
if (curr.children[c - 'a'] == null)
return false;
curr = curr.children[c - 'a'];
}
return true;
}
}
class GfG{
static void Main()
{
Trie trie = new Trie();
string[] arr
= { "and", "ant", "do", "dad"};
foreach(string s in arr) { trie.Insert(s); }
// One by one search strings
string[] searchKeys = { "do", "gee", "bat" };
foreach(string s in searchKeys){
if (trie.Search(s))
Console.Write("true ");
else
Console.Write("false ");
}
Console.WriteLine();
// One by one search for prefixes
string[] prefixKeys = { "ge", "ba", "do", "de" };
foreach(string s in prefixKeys){
if (trie.isPrefix(s))
Console.Write("true ");
else
Console.Write("false ");
}
}
}
// TrieNode class
class TrieNode {
constructor()
{
this.children = new Array(26).fill(null);
this.isLeaf = false;
}
}
// Trie class
class Trie {
constructor() { this.root = new TrieNode(); }
// Method to insert a key into the Trie
insert(key)
{
let curr = this.root;
for (let c of key) {
if (curr.children[c.charCodeAt(0)
- "a".charCodeAt(0)]
=== null) {
curr.children[c.charCodeAt(0)
- "a".charCodeAt(0)]
= new TrieNode();
}
curr = curr.children[c.charCodeAt(0)
- "a".charCodeAt(0)];
}
curr.isLeaf = true;
}
// Method to search a key in the Trie
search(key)
{
let curr = this.root;
for (let c of key) {
if (curr.children[c.charCodeAt(0)
- "a".charCodeAt(0)]
=== null)
return false;
curr = curr.children[c.charCodeAt(0)
- "a".charCodeAt(0)];
}
return curr.isLeaf;
}
// Method to check if a prefix exists in the Trie
isPrefix(prefix)
{
let curr = this.root;
for (let c of prefix) {
if (curr.children[c.charCodeAt(0)
- "a".charCodeAt(0)]
=== null)
return false;
curr = curr.children[c.charCodeAt(0)
- "a".charCodeAt(0)];
}
return true;
}
}
const trie = new Trie();
const arr = [ "and", "ant", "do", "dad"];
for (let s of arr) {
trie.insert(s);
}
// One by one search strings
const searchKeys = [ "do", "gee", "bat" ];
console.log(searchKeys.map(s => trie.search(s) ? "true" : "false").join(" "));
// One by one search for prefixes
const prefixKeys = [ "ge", "ba", "do", "de" ];
console.log(prefixKeys.map(s => trie.isPrefix(s) ? "true" : "false").join(" "));
Outputtrue false false
false false true false
Complexity Analysis of Trie Data Structure
| Operation | Time Complexity |
|---|
| Insertion | O(n) Here n is the length of the string inserted |
|---|
| Searching | O(n) Here n is the length of the string searched |
|---|
Prefix Searching | O(n) Here n is the length of the string searched |
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Introduction to Trie Data Structure
Trie (Representation, Search & Insert)
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DSA Tutorial - Learn Data Structures and Algorithms DSA (Data Structures and Algorithms) is the study of organizing data efficiently using data structures like arrays, stacks, and trees, paired with step-by-step procedures (or algorithms) to solve problems effectively. Data structures manage how data is stored and accessed, while algorithms focus on
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Basics & Prerequisites
Data Structures
Getting Started with Array Data StructureArray is a collection of items of the same variable type that are stored at contiguous memory locations. It is one of the most popular and simple data structures used in programming. Basic terminologies of ArrayArray Index: In an array, elements are identified by their indexes. Array index starts fr
14 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
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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
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:
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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
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
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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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