Sort a string according to the frequency of characters
Last Updated :
07 Aug, 2025
Given a string s consisting of lowercase and/or uppercase English letters, return a new string where the characters are sorted in increasing order of their frequency. If two characters have the same frequency, they should be sorted in lexicographical order (i.e., based on ASCII value).
Each character should appear in the output string exactly as many times as it appears in the input.
Examples:
Input: s = "geeksforgeeks"
Output: "forggkksseeee"
Explanation: Frequencies: e=4, g=2, k=2, s=2, f=1, o=1, r=1. Characters are sorted by increasing frequency, and lexicographically if equal.
Input: s = "abc"
Output: "abc"
Explanation: All characters occur once, so they are returned in lexicographical order.
[Naive Approach] Sorting the Pair of character and frequency - O(n^2) Time and O(n) Space
The idea is to sort the characters of the string based on how frequently they appear. For each character, we count its total frequency in the string and pair it with the character. These (frequency, character) pairs are then sorted in increasing order of frequency. Finally, we rebuild the string using the sorted characters to get the desired output.
Step-By-Step Approach:
- Traverse the string: For each character s[i], count how many times it appears in the entire string using a helper function countFrequency.
- Store pairs: Store each character with its frequency in an array of structs or a list of pairs.
- Sort by frequency: Use a sorting function (like sort() in C++/Java/Python or qsort() in C) to sort the array/list based on the frequency value.
- Build result: Concatenate characters from the sorted list to form the final output string.
C++
#include <iostream>
#include <algorithm>
#include <vector>
using namespace std;
// returns count of a character in the string
int countFrequency(string &s, char ch) {
int count = 0;
for (int i = 0; i < s.length(); i++) {
// check if current character matches ch
if (s[i] == ch)
++count;
}
return count;
}
// function to sort the string according to frequency
string frequencySort(string &s) {
int n = s.length();
// vector to store frequency with corresponding character
vector<pair<int, char>> vp;
// insert frequency and character into the vector
for (int i = 0; i < n; i++) {
vp.push_back(make_pair(countFrequency(s, s[i]), s[i]));
}
// sort the vector by frequency (pair first value)
sort(vp.begin(), vp.end());
// build the final answer string
string ans = "";
for (int i = 0; i < vp.size(); i++)
ans += vp[i].second;
return ans;
}
int main() {
string s = "geeksforgeeks";
string ans = frequencySort(s);
cout << ans << endl;
return 0;
}
C
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
// structure to hold frequency and character
typedef struct {
int freq;
char ch;
} CharFreq;
// returns count of a character in the string
int countFrequency(char s[], char ch) {
int count = 0;
int len = strlen(s);
for (int i = 0; i < len; i++) {
// check if current character matches ch
if (s[i] == ch)
++count;
}
return count;
}
// comparator function for qsort
int compare(const void *a, const void *b) {
CharFreq *x = (CharFreq *)a;
CharFreq *y = (CharFreq *)b;
return x->freq - y->freq;
}
// function to sort the string according to frequency
void frequencySort(char s[], char ans[]) {
int n = strlen(s);
// array to store frequency and corresponding character
CharFreq arr[100]; // assume max length <= 100
// insert frequency and character into the array
for (int i = 0; i < n; i++) {
arr[i].freq = countFrequency(s, s[i]);
arr[i].ch = s[i];
}
// sort the array by frequency
qsort(arr, n, sizeof(CharFreq), compare);
// build the final answer string
for (int i = 0; i < n; i++) {
ans[i] = arr[i].ch;
}
ans[n] = '\0'; // null-terminate the result
}
int main() {
char s[] = "geeksforgeeks";
char ans[100];
frequencySort(s, ans);
printf("%s\n", ans);
return 0;
}
Java
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
class GfG {
// returns count of a character in the string
static int countFrequency(String s, char ch) {
int count = 0;
for (int i = 0; i < s.length(); i++) {
// check if current character matches ch
if (s.charAt(i) == ch)
++count;
}
return count;
}
// function to sort the string according to frequency
static String frequencySort(String s) {
int n = s.length();
// list to store frequency with corresponding character (as ASCII)
List<List<Integer>> vp = new ArrayList<>();
// insert frequency and character into the list
for (int i = 0; i < n; i++) {
List<Integer> temp = new ArrayList<>();
temp.add(countFrequency(s, s.charAt(i))); // frequency
temp.add((int) s.charAt(i)); // character ASCII
vp.add(temp);
}
// sort the list by frequency (first value)
Collections.sort(vp, new Comparator<List<Integer>>() {
public int compare(List<Integer> a, List<Integer> b) {
return a.get(0) - b.get(0);
}
});
// build the final answer string
StringBuilder ans = new StringBuilder();
for (List<Integer> entry : vp) {
ans.append((char)(int) entry.get(1));
}
return ans.toString();
}
public static void main(String[] args) {
String s = "geeksforgeeks";
String ans = frequencySort(s);
System.out.println(ans);
}
}
Python
# returns count of a character in the string
def countFrequency(s, ch):
count = 0
for i in range(len(s)):
# check if current character matches ch
if s[i] == ch:
count += 1
return count
# function to sort the string according to frequency
def frequencySort(s):
n = len(s)
# list to store frequency with corresponding character
vp = []
# insert frequency and character into the list
for i in range(n):
vp.append((countFrequency(s, s[i]), s[i]))
# sort the list by frequency (pair first value)
vp.sort()
# build the final answer string
ans = ""
for freq, ch in vp:
ans += ch
return ans
if __name__ == "__main__":
s = "geeksforgeeks"
ans = frequencySort(s)
print(ans)
C#
using System;
using System.Collections.Generic;
class GfG {
// returns count of a character in the string
static int countFrequency(string s, char ch) {
int count = 0;
for (int i = 0; i < s.Length; i++) {
// check if current character matches ch
if (s[i] == ch)
++count;
}
return count;
}
// function to sort the string according to frequency
static string frequencySort(string s) {
int n = s.Length;
// list to store frequency with corresponding character
List<(int, char)> vp = new List<(int, char)>();
// insert frequency and character into the list
for (int i = 0; i < n; i++) {
vp.Add((countFrequency(s, s[i]), s[i]));
}
// sort the list by frequency (pair first value)
vp.Sort((a, b) => a.Item1.CompareTo(b.Item1));
// build the final answer string
string ans = "";
foreach (var p in vp)
ans += p.Item2;
return ans;
}
static void Main(string[] args) {
string s = "geeksforgeeks";
string ans = frequencySort(s);
Console.WriteLine(ans);
}
}
JavaScript
// returns count of a character in the string
function countFrequency(s, ch) {
let count = 0;
for (let i = 0; i < s.length; i++) {
// check if current character matches ch
if (s[i] === ch)
count++;
}
return count;
}
// function to sort the string according to frequency
function frequencySort(s) {
let n = s.length;
// array to store frequency with corresponding character
let vp = [];
// insert frequency and character into the array
for (let i = 0; i < n; i++) {
vp.push([countFrequency(s, s[i]), s[i]]);
}
// sort the array by frequency (pair first value)
vp.sort((a, b) => a[0] - b[0]);
// build the final answer string
let ans = "";
for (let i = 0; i < vp.length; i++)
ans += vp[i][1];
return ans;
}
// Driver Code
let s = "geeksforgeeks";
let ans = frequencySort(s);
console.log(ans);
[Expected Approach 1] Frequency Counting + Custom Sorting
The idea is to first count the frequency of each character using a fixed-size array (since we assume lowercase letters only). We then create a vector of (frequency, character) pairs and sort it in increasing order of frequency. Finally, we rebuild the original string by placing each character according to its frequency in the sorted order.
C++
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
class Solution {
public:
// function to sort the string according to frequency
string frequencySort(string &s) {
int n = s.size();
// array to store frequency of lowercase letters
vector<int> fre(26, 0);
for (int i = 0; i < n; i++) {
fre[s[i] - 'a']++;
}
// vector to store (frequency, character) pairs
vector<pair<int, char>> vec;
for (int i = 0; i < 26; i++) {
if (fre[i] != 0)
vec.push_back({fre[i], i + 'a'});
}
// sort the vector by frequency (ascending)
sort(vec.begin(), vec.end());
// rebuild the string
int idx = 0;
for (auto it : vec) {
int cnt = it.first;
while (cnt--) {
s[idx++] = it.second;
}
}
return s;
}
};
int main() {
string s = "geeksforgeeks";
Solution obj;
string ans = obj.frequencySort(s);
cout << ans << endl;
return 0;
}
C
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
// structure to hold frequency and character
typedef struct {
int freq;
char ch;
} CharFreq;
// comparator for sorting by frequency
int compare(const void* a, const void* b) {
CharFreq* x = (CharFreq*)a;
CharFreq* y = (CharFreq*)b;
return x->freq - y->freq;
}
// function to sort the string according to frequency
void frequencySort(char s[]) {
int n = strlen(s);
// array to store frequency of lowercase letters
int fre[26] = {0};
for (int i = 0; i < n; i++) {
fre[s[i] - 'a']++;
}
// create frequency-character array
CharFreq vec[26];
int size = 0;
for (int i = 0; i < 26; i++) {
if (fre[i] > 0) {
vec[size].freq = fre[i];
vec[size].ch = i + 'a';
size++;
}
}
// sort the array by frequency
qsort(vec, size, sizeof(CharFreq), compare);
// rebuild the string
int idx = 0;
for (int i = 0; i < size; i++) {
for (int j = 0; j < vec[i].freq; j++) {
s[idx++] = vec[i].ch;
}
}
s[idx] = '\0'; // null-terminate
}
int main() {
char s[] = "geeksforgeeks";
frequencySort(s);
printf("%s\n", s);
return 0;
}
Java
import java.util.Collections;
import java.util.ArrayList;
import java.util.List;
class GfG {
// function to sort the string according to frequency
static String frequencySort(String s) {
int n = s.length();
// array to store frequency of lowercase letters
int[] fre = new int[26];
for (int i = 0; i < n; i++) {
fre[s.charAt(i) - 'a']++;
}
// list to store (frequency, character)
List<int[]> vec = new ArrayList<>();
for (int i = 0; i < 26; i++) {
if (fre[i] > 0) {
vec.add(new int[]{fre[i], i});
}
}
// sort the list by frequency
Collections.sort(vec, (a, b) -> a[0] - b[0]);
// rebuild the string
StringBuilder ans = new StringBuilder();
for (int[] pair : vec) {
for (int i = 0; i < pair[0]; i++) {
ans.append((char) (pair[1] + 'a'));
}
}
return ans.toString();
}
public static void main(String[] args) {
String s = "geeksforgeeks";
String ans = frequencySort(s);
System.out.println(ans);
}
}
Python
# function to sort the string according to frequency
def frequencySort(s):
n = len(s)
# array to store frequency of lowercase letters
fre = [0] * 26
for ch in s:
fre[ord(ch) - ord('a')] += 1
# list to store (frequency, character)
vec = []
for i in range(26):
if fre[i] > 0:
vec.append((fre[i], chr(i + ord('a'))))
# sort the list by frequency
vec.sort()
# rebuild the string
ans = ""
for freq, ch in vec:
ans += ch * freq
return ans
if __name__ == "__main__":
s = "geeksforgeeks"
ans = frequencySort(s)
print(ans)
C#
using System;
using System.Collections.Generic;
class GfG {
// function to sort the string according to frequency
static string frequencySort(string s) {
int n = s.Length;
// array to store frequency of lowercase letters
int[] fre = new int[26];
for (int i = 0; i < n; i++) {
fre[s[i] - 'a']++;
}
// list to store (frequency, character index)
List<(int, int)> vec = new List<(int, int)>();
for (int i = 0; i < 26; i++) {
if (fre[i] > 0) {
vec.Add((fre[i], i));
}
}
// sort the list by frequency
vec.Sort((a, b) => a.Item1.CompareTo(b.Item1));
// rebuild the string
string ans = "";
foreach (var pair in vec) {
ans += new string((char)(pair.Item2 + 'a'), pair.Item1);
}
return ans;
}
static void Main(string[] args) {
string s = "geeksforgeeks";
string ans = frequencySort(s);
Console.WriteLine(ans);
}
}
JavaScript
// function to sort the string according to frequency
function frequencySort(s) {
let n = s.length;
// array to store frequency of lowercase letters
let fre = new Array(26).fill(0);
for (let i = 0; i < n; i++) {
fre[s.charCodeAt(i) - 97]++;
}
// array to store (frequency, character index)
let vec = [];
for (let i = 0; i < 26; i++) {
if (fre[i] > 0) {
vec.push([fre[i], i]);
}
}
// sort the array by frequency
vec.sort((a, b) => a[0] - b[0]);
// rebuild the string
let ans = "";
for (let [freq, idx] of vec) {
ans += String.fromCharCode(idx + 97).repeat(freq);
}
return ans;
}
// Driver Code
let s = "geeksforgeeks";
let ans = frequencySort(s);
console.log(ans);
Time Complexity: O(n + k log k), the frequency of each character is counted in O(n) time, where n is the length of the string. After that, we sort at most k = 26 unique lowercase letters based on their frequency, which takes O(k log k) time. Since k is constant (26), the overall complexity simplifies to O(n) in practice.
Auxiliary Space: O(k), an extra array of size 26 is used to store the frequency of lowercase letters, and a temporary list or array of up to 26 elements is created for sorting. Therefore, the auxiliary space is O(k), which is O(1) in practice because the alphabet size is fixed.
[Expected Approach 2] Using Mean Heap
The idea is to count the frequency of each character in the given string using a hash map. Then, insert each character along with its frequency into a min-heap (priority queue or sorted structure) so that characters with lower frequency come first. After building the heap, we repeatedly extract the minimum frequency character and append it to the result string as many times as its frequency. This results in sorting characters based on their frequency in ascending order.
Step-By-Step Approach:
- First, we iterate through the string and count the frequency of each character using a hash map or dictionary.
- Then, for each character-frequency pair, we push it into a min-heap where the element with the lowest frequency comes at the top. If two characters have the same frequency, the one with the lower ASCII value is prioritized.
- Finally, we repeatedly extract the top of the heap and append the character to the result string as many times as its frequency, until the heap is empty.
C++
#include <iostream>
#include <vector>
#include <queue>
#include <unordered_map>
#include <string>
using namespace std;
// Custom comparator for min-heap
class Compare {
public:
bool operator()(vector<int>& below, vector<int>& above) {
// if frequency is the same, compare by character
if (below[0] == above[0]) {
return below[1] > above[1];
}
// else compare by frequency
return below[0] > above[0];
}
};
// function to sort characters by frequency (ascending)
string frequencySort(string &s) {
// map to store frequency of each character
unordered_map<char, int> freqMap;
for (char ch : s) {
freqMap[ch]++;
}
// min-heap to store {frequency, character ASCII}
priority_queue<vector<int>, vector<vector<int>>, Compare> minHeap;
for (auto it : freqMap) {
minHeap.push({it.second, (int)it.first});
}
// build the final answer string
string ans = "";
while (!minHeap.empty()) {
int freq = minHeap.top()[0];
char ch = (char)minHeap.top()[1];
// append character freq number of times
ans.append(freq, ch);
minHeap.pop();
}
return ans;
}
int main() {
string s = "geeksforgeeks";
cout << frequencySort(s) << "\n";
return 0;
}
C
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define MAX_CHAR 256
// structure to store frequency and character ASCII
typedef struct {
int freq;
int ch;
} CharFreq;
// function to swap two CharFreq elements
void swap(CharFreq* a, CharFreq* b) {
CharFreq temp = *a;
*a = *b;
*b = temp;
}
// function to maintain min-heap property
void heapify(CharFreq heap[], int n, int i) {
int smallest = i;
int l = 2*i + 1;
int r = 2*i + 2;
// if frequency is same, use ASCII comparison
if (l < n && (heap[l].freq < heap[smallest].freq ||
(heap[l].freq == heap[smallest].freq && heap[l].ch < heap[smallest].ch))) {
smallest = l;
}
if (r < n && (heap[r].freq < heap[smallest].freq ||
(heap[r].freq == heap[smallest].freq && heap[r].ch < heap[smallest].ch))) {
smallest = r;
}
if (smallest != i) {
swap(&heap[i], &heap[smallest]);
heapify(heap, n, smallest);
}
}
// function to build a min-heap
void buildMinHeap(CharFreq heap[], int n) {
for (int i = n/2 - 1; i >= 0; i--) {
heapify(heap, n, i);
}
}
// function to extract the min element from heap
CharFreq extractMin(CharFreq heap[], int* heapSize) {
CharFreq min = heap[0];
heap[0] = heap[*heapSize - 1];
(*heapSize)--;
heapify(heap, *heapSize, 0);
return min;
}
// function to sort characters by frequency (ascending)
char* frequencySort(char* s) {
int freqMap[MAX_CHAR] = {0};
// count frequency
for (int i = 0; s[i]; i++) {
freqMap[(int)s[i]]++;
}
CharFreq heap[MAX_CHAR];
int heapSize = 0;
// fill heap array with non-zero frequency characters
for (int i = 0; i < MAX_CHAR; i++) {
if (freqMap[i]) {
heap[heapSize].freq = freqMap[i];
heap[heapSize].ch = i;
heapSize++;
}
}
// build the min-heap
buildMinHeap(heap, heapSize);
// create result string
char* ans = (char*)malloc(strlen(s) + 1);
int idx = 0;
while (heapSize > 0) {
CharFreq curr = extractMin(heap, &heapSize);
for (int i = 0; i < curr.freq; i++) {
ans[idx++] = (char)curr.ch;
}
}
ans[idx] = '\0';
return ans;
}
int main() {
char s[] = "geeksforgeeks";
char* res = frequencySort(s);
printf("%s\n", res);
free(res);
return 0;
}
Java
import java.util.PriorityQueue;
import java.util.HashMap;
import java.util.Map;
import java.util.Comparator;
class GfG {
// class to represent [frequency, character ASCII]
static class CharFreq {
int freq;
int ch;
CharFreq(int freq, int ch) {
this.freq = freq;
this.ch = ch;
}
}
// Custom comparator for PriorityQueue
static class Compare implements Comparator<CharFreq> {
public int compare(CharFreq a, CharFreq b) {
// if frequency is the same, compare by character
if (a.freq == b.freq) {
return a.ch - b.ch;
}
// else compare by frequency
return a.freq - b.freq;
}
}
// function to sort characters by frequency (ascending)
static String frequencySort(String s) {
Map<Character, Integer> freqMap = new HashMap<>();
for (char ch : s.toCharArray()) {
freqMap.put(ch, freqMap.getOrDefault(ch, 0) + 1);
}
PriorityQueue<CharFreq> minHeap = new PriorityQueue<>(new Compare());
for (Map.Entry<Character, Integer> entry : freqMap.entrySet()) {
minHeap.add(new CharFreq(entry.getValue(), (int) entry.getKey()));
}
StringBuilder ans = new StringBuilder();
while (!minHeap.isEmpty()) {
CharFreq top = minHeap.poll();
for (int i = 0; i < top.freq; i++) {
ans.append((char) top.ch);
}
}
return ans.toString();
}
public static void main(String[] args) {
String s = "geeksforgeeks";
System.out.println(frequencySort(s));
}
}
Python
import heapq
# function to sort characters by frequency
def frequencySort(s):
freq = [0] * 128
for ch in s:
freq[ord(ch)] += 1
minH = []
for i in range(128):
if freq[i] > 0:
heapq.heappush(minH, [freq[i], chr(i)])
ans = ""
while minH:
count, ch = heapq.heappop(minH)
ans += ch * count
return ans
if __name__ == "__main__":
s = "geeksforgeeks"
print(frequencySort(s))
C#
using System;
using System.Collections.Generic;
class Pair : IComparable<Pair> {
public int first; // frequency
public char second; // character
public Pair(int first, char second) {
this.first = first;
this.second = second;
}
// Custom comparator useful for SortedSet
public int CompareTo(Pair other) {
// If frequencies are same, compare characters
if (this.first == other.first) {
if (this.second == other.second)
return 0;
return this.second - other.second;
}
return this.first - other.first;
}
// Override Equals and GetHashCode for correctness in SortedSet
public override bool Equals(object obj) {
if (obj == null || GetType() != obj.GetType()) return false;
Pair p = (Pair)obj;
return this.first == p.first && this.second == p.second;
}
public override int GetHashCode() {
return first.GetHashCode() ^ second.GetHashCode();
}
}
class Program {
// function to sort characters by frequency (ascending)
public static string frequencySort(string s) {
// map to store frequency of each character
Dictionary<char, int> mpp = new Dictionary<char, int>();
// calculate frequency
foreach (char ch in s.ToCharArray()) {
if (mpp.ContainsKey(ch))
mpp[ch]++;
else
mpp[ch] = 1;
}
// min-heap using SortedSet
SortedSet<Pair> minHeap = new SortedSet<Pair>();
foreach (char ch in mpp.Keys) {
minHeap.Add(new Pair(mpp[ch], ch));
}
string ans = "";
// build final answer
while (minHeap.Count > 0) {
Pair top = minHeap.Min;
for (int i = 0; i < top.first; i++) {
ans += top.second;
}
minHeap.Remove(top);
}
return ans;
}
// Driver code
public static void Main(string[] args) {
string str = "geeksforgeeks";
Console.WriteLine(frequencySort(str));
}
}
JavaScript
// function to sort characters by frequency (ascending)
function frequencySort(s) {
// map to store frequency of each character
let freqMap = {};
for (let ch of s) {
freqMap[ch] = (freqMap[ch] || 0) + 1;
}
// create an array of [frequency, ASCII] pairs
let heap = [];
for (let ch in freqMap) {
heap.push([freqMap[ch], ch.charCodeAt(0)]);
}
// sort using custom comparator
heap.sort((a, b) => {
if (a[0] === b[0]) return a[1] - b[1];
return a[0] - b[0];
});
let ans = "";
for (let [freq, ascii] of heap) {
let ch = String.fromCharCode(ascii);
ans += ch.repeat(freq);
}
return ans;
}
// Driver Code
let s = "geeksforgeeks";
console.log(frequencySort(s));
Time Complexity: O(n × log k), Here, n is the length of the input string and k is the number of distinct characters. We first traverse the string in O(n) to build the frequency map. Then, we insert k elements into the min-heap, each taking O(log k) time. Lastly, extracting and appending also takes O(k log k) in total.
Auxiliary Space: O(k), We use extra space for the frequency map and the heap, both storing up to k entries where k is the number of distinct characters.
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. Hereâs 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