Count subarrays with same even and odd elements
Last Updated :
11 Jul, 2025
Given an array of N integers, count number of even-odd subarrays. An even - odd subarray is a subarray that contains the same number of even as well as odd integers.
Examples :
Input : arr[] = {2, 5, 7, 8}
Output : 3
Explanation : There are total 3 even-odd subarrays.
1) {2, 5}
2) {7, 8}
3) {2, 5, 7, 8}
Input : arr[] = {3, 4, 6, 8, 1, 10}
Output : 3
Explanation : In this case, 3 even-odd subarrays are:
1) {3, 4}
2) {8, 1}
3) {1, 10}
This problem is mainly a variation of count subarrays with equal number of 0s and 1s.
A naive approach would be to check for all possible subarrays using two loops, whether they are even-odd subarrays or not. This approach will take O(N^2) time.
An Efficient approach solves the problem in O(N) time and it is based on following ideas:
- Even-odd subarrays will always be of even length.
- Maintaining track of the difference between the frequency of even and odd integers.
- Hashing of this difference of frequencies is useful in finding number of even-odd subarrays.
The basic idea is to use the difference between the frequency of odd and even numbers to obtain an optimal solution.
We will maintain two integer hash arrays for the positive and negative value of the difference.
-> Example to understand in better way :
-> Consider difference = freq(odd) - freq(even)
-> To calculate this difference, increment the value of 'difference' when there is
an odd integer and decrement it when there is an even integer. (initially, difference = 0)
arr[] = {3, 4, 6, 8, 1, 10}
index 0 1 2 3 4 5 6
array 3 4 6 8 1 10
difference 0 1 0 -1 -2 -1 -2
-> Observe that whenever a value 'k' repeats in the 'difference' array, there exists an
even-odd subarray for each previous occurrence of that value i.e. subarray exists from
index i + 1 to j where difference[i] = k and difference[j] = k.
-> Value '0' is repeated in 'difference' array at index 2 and hence subarray exists for
(0, 2] indexes. Similarly, for repetition of values '-1' (at indexes 3 and 5) and '-2' (at
indexes 4 and 6), subarray exists for (3, 5] and (4, 6] indexes.
Below is the implementation of the O(N) solution described above.
C++
/*C++ program to find total number of
even-odd subarrays present in given array*/
#include <bits/stdc++.h>
using namespace std;
// function that returns the count of subarrays that
// contain equal number of odd as well as even numbers
int countSubarrays(int arr[], int n)
{
// initialize difference and answer with 0
int difference = 0;
int ans = 0;
// create two auxiliary hash arrays to count frequency
// of difference, one array for non-negative difference
// and other array for negative difference. Size of these
// two auxiliary arrays is 'n+1' because difference can
// reach maximum value 'n' as well as minimum value '-n'
int hash_positive[n + 1], hash_negative[n + 1];
// initialize these auxiliary arrays with 0
fill_n(hash_positive, n + 1, 0);
fill_n(hash_negative, n + 1, 0);
// since the difference is initially 0, we have to
// initialize hash_positive[0] with 1
hash_positive[0] = 1;
// for loop to iterate through whole
// array (zero-based indexing is used)
for (int i = 0; i < n ; i++)
{
// incrementing or decrementing difference based on
// arr[i] being even or odd, check if arr[i] is odd
if (arr[i] & 1 == 1)
difference++;
else
difference--;
// adding hash value of 'difference' to our answer
// as all the previous occurrences of the same
// difference value will make even-odd subarray
// ending at index 'i'. After that, we will increment
// hash array for that 'difference' value for
// its occurrence at index 'i'. if difference is
// negative then use hash_negative
if (difference < 0)
{
ans += hash_negative[-difference];
hash_negative[-difference]++;
}
// else use hash_positive
else
{
ans += hash_positive[difference];
hash_positive[difference]++;
}
}
// return total number of even-odd subarrays
return ans;
}
// Driver code
int main()
{
int arr[] = {3, 4, 6, 8, 1, 10, 5, 7};
int n = sizeof(arr) / sizeof(arr[0]);
// Printing total number of even-odd subarrays
cout << "Total Number of Even-Odd subarrays"
" are " << countSubarrays(arr,n);
return 0;
}
// This code is contributed by Aditya Kumar (adityakumar129)
C
/*C program to find total number of
even-odd subarrays present in given array*/
#include <stdio.h>
// function that returns the count of subarrays that
// contain equal number of odd as well as even numbers
int countSubarrays(int arr[], int n)
{
// initialize difference and answer with 0
int difference = 0;
int ans = 0;
// create two auxiliary hash arrays to count frequency
// of difference, one array for non-negative difference
// and other array for negative difference. Size of
// these two auxiliary arrays is 'n+1' because
// difference can reach maximum value 'n' as well as
// minimum value '-n'
int hash_positive[n + 1], hash_negative[n + 1];
// initialize these auxiliary arrays with 0
for (int i = 0; i < n + 1; i++)
hash_positive[i] = 0;
for (int i = 0; i < n + 1; i++)
hash_negative[i] = 0;
// since the difference is initially 0, we have to
// initialize hash_positive[0] with 1
hash_positive[0] = 1;
// for loop to iterate through whole
// array (zero-based indexing is used)
for (int i = 0; i < n; i++) {
// incrementing or decrementing difference based on
// arr[i] being even or odd, check if arr[i] is odd
if (arr[i] & 1 == 1)
difference++;
else
difference--;
// adding hash value of 'difference' to our answer
// as all the previous occurrences of the same
// difference value will make even-odd subarray
// ending at index 'i'. After that, we will
// increment hash array for that 'difference' value
// for its occurrence at index 'i'. if difference is
// negative then use hash_negative
if (difference < 0) {
ans += hash_negative[-difference];
hash_negative[-difference]++;
}
// else use hash_positive
else {
ans += hash_positive[difference];
hash_positive[difference]++;
}
}
// return total number of even-odd subarrays
return ans;
}
// Driver code
int main()
{
int arr[] = { 3, 4, 6, 8, 1, 10, 5, 7 };
int n = sizeof(arr) / sizeof(arr[0]);
// Printing total number of even-odd subarrays
printf("Total Number of Even-Odd subarrays are %d ",
countSubarrays(arr, n));
return 0;
}
// This code is contributed by Aditya Kumar (adityakumar129)
Java
// Java program to find total number of even-odd subarrays
// present in given array
class GFG {
// function that returns the count of subarrays that
// contain equal number of odd as well as even numbers
static int countSubarrays(int[] arr, int n)
{
// initialize difference and answer with 0
int difference = 0;
int ans = 0;
// create two auxiliary hash arrays to count
// frequency of difference, one array for
// non-negative difference and other array for
// negative difference. Size of these two auxiliary
// arrays is 'n+1' because difference can reach
// maximum value 'n' as well as minimum value '-n'
// initialize these auxiliary arrays with 0
int[] hash_positive = new int[n + 1];
int[] hash_negative = new int[n + 1];
// since the difference is initially 0, we have to
// initialize hash_positive[0] with 1
hash_positive[0] = 1;
// for loop to iterate through whole array
// (zero-based indexing is used)
for (int i = 0; i < n; i++) {
// incrementing or decrementing difference based
// on arr[i] being even or odd, check if arr[i]
// is odd
if ((arr[i] & 1) == 1)
difference++;
else
difference--;
// adding hash value of 'difference' to our
// answer as all the previous occurrences of the
// same difference value will make even-odd
// subarray ending at index 'i'. After that, we
// will increment hash array for that
// 'difference' value for its occurrence at
// index 'i'. if difference is negative then use
// hash_negative
if (difference < 0) {
ans += hash_negative[-difference];
hash_negative[-difference]++;
} // else use hash_positive
else {
ans += hash_positive[difference];
hash_positive[difference]++;
}
}
// return total number of even-odd subarrays
return ans;
}
// Driver code
public static void main(String[] args)
{
int[] arr = new int[] { 3, 4, 6, 8, 1, 10, 5, 7 };
int n = arr.length;
// Printing total number of even-odd subarrays
System.out.println(
"Total Number of Even-Odd subarrays are "
+ countSubarrays(arr, n));
}
}
// This code is contributed by Aditya Kumar (adityakumar129)
Python3
# Python3 program to find total
# number of even-odd subarrays
# present in given array
# function that returns the count
# of subarrays that contain equal
# number of odd as well as even numbers
def countSubarrays(arr, n):
# initialize difference and
# answer with 0
difference = 0
ans = 0
# create two auxiliary hash
# arrays to count frequency
# of difference, one array
# for non-negative difference
# and other array for negative
# difference. Size of these two
# auxiliary arrays is 'n+1'
# because difference can reach
# maximum value 'n' as well as
# minimum value '-n'
hash_positive = [0] * (n + 1)
hash_negative = [0] * (n + 1)
# since the difference is
# initially 0, we have to
# initialize hash_positive[0] with 1
hash_positive[0] = 1
# for loop to iterate through
# whole array (zero-based
# indexing is used)
for i in range(n):
# incrementing or decrementing
# difference based on arr[i]
# being even or odd, check if
# arr[i] is odd
if (arr[i] & 1 == 1):
difference = difference + 1
else:
difference = difference - 1
# adding hash value of 'difference'
# to our answer as all the previous
# occurrences of the same difference
# value will make even-odd subarray
# ending at index 'i'. After that,
# we will increment hash array for
# that 'difference' value for
# its occurrence at index 'i'. if
# difference is negative then use
# hash_negative
if (difference < 0):
ans += hash_negative[-difference]
hash_negative[-difference] = hash_negative[-difference] + 1
# else use hash_positive
else:
ans += hash_positive[difference]
hash_positive[difference] = hash_positive[difference] + 1
# return total number of
# even-odd subarrays
return ans
# Driver code
arr = [3, 4, 6, 8, 1, 10, 5, 7]
n = len(arr)
# Printing total number
# of even-odd subarrays
print("Total Number of Even-Odd subarrays are " +
str(countSubarrays(arr, n)))
# This code is contributed
# by Yatin Gupta
C#
// C# program to find total
// number of even-odd subarrays
// present in given array
using System;
class GFG
{
// function that returns the
// count of subarrays that
// contain equal number of
// odd as well as even numbers
static int countSubarrays(int []arr,
int n)
{
// initialize difference
// and answer with 0
int difference = 0;
int ans = 0;
// create two auxiliary hash
// arrays to count frequency
// of difference, one array
// for non-negative difference
// and other array for negative
// difference. Size of these
// two auxiliary arrays is 'n+1'
// because difference can
// reach maximum value 'n' as
// well as minimum value '-n'
int []hash_positive = new int[n + 1];
int []hash_negative = new int[n + 1];
// initialize these
// auxiliary arrays with 0
Array.Clear(hash_positive, 0, n + 1);
Array.Clear(hash_negative, 0, n + 1);
// since the difference is
// initially 0, we have to
// initialize hash_positive[0] with 1
hash_positive[0] = 1;
// for loop to iterate
// through whole array
// (zero-based indexing is used)
for (int i = 0; i < n ; i++)
{
// incrementing or decrementing
// difference based on
// arr[i] being even or odd,
// check if arr[i] is odd
if ((arr[i] & 1) == 1)
difference++;
else
difference--;
// adding hash value of 'difference'
// to our answer as all the previous
// occurrences of the same difference
// value will make even-odd subarray
// ending at index 'i'. After that,
// we will increment hash array for
// that 'difference' value for its
// occurrence at index 'i'. if
// difference is negative then use
// hash_negative
if (difference < 0)
{
ans += hash_negative[-difference];
hash_negative[-difference]++;
}
// else use hash_positive
else
{
ans += hash_positive[difference];
hash_positive[difference]++;
}
}
// return total number
// of even-odd subarrays
return ans;
}
// Driver code
static void Main()
{
int []arr = new int[]{3, 4, 6, 8,
1, 10, 5, 7};
int n = arr.Length;
// Printing total number
// of even-odd subarrays
Console.Write("Total Number of Even-Odd" +
" subarrays are " +
countSubarrays(arr,n));
}
}
// This code is contributed by
// Manish Shaw(manishshaw1)
PHP
<?php
// PHP program to find total number of
// even-odd subarrays present in given array
// function that returns the count of subarrays
// that contain equal number of odd as well
// as even numbers
function countSubarrays(&$arr, $n)
{
// initialize difference and
// answer with 0
$difference = 0;
$ans = 0;
// create two auxiliary hash arrays to count
// frequency of difference, one array for
// non-negative difference and other array
// for negative difference. Size of these
// two auxiliary arrays is 'n+1' because
// difference can reach maximum value 'n'
// as well as minimum value '-n'
$hash_positive = array_fill(0, $n + 1, NULL);
$hash_negative = array_fill(0, $n + 1, NULL);
// since the difference is initially 0, we
// have to initialize hash_positive[0] with 1
$hash_positive[0] = 1;
// for loop to iterate through whole
// array (zero-based indexing is used)
for ($i = 0; $i < $n ; $i++)
{
// incrementing or decrementing difference
// based on arr[i] being even or odd, check
// if arr[i] is odd
if ($arr[$i] & 1 == 1)
$difference++;
else
$difference--;
// adding hash value of 'difference' to our
// answer as all the previous occurrences of
// the same difference value will make even-odd
// subarray ending at index 'i'. After that, we
// will increment hash array for that 'difference'
// value for its occurrence at index 'i'. if
// difference is negative then use hash_negative
if ($difference < 0)
{
$ans += $hash_negative[-$difference];
$hash_negative[-$difference]++;
}
// else use hash_positive
else
{
$ans += $hash_positive[$difference];
$hash_positive[$difference]++;
}
}
// return total number of even-odd
// subarrays
return $ans;
}
// Driver code
$arr = array(3, 4, 6, 8, 1, 10, 5, 7);
$n = sizeof($arr);
// Printing total number of even-odd
// subarrays
echo "Total Number of Even-Odd subarrays".
" are " . countSubarrays($arr, $n);
// This code is contributed by ita_c
?>
JavaScript
<script>
// Javascript program to find total
// number of even-odd subarrays
// present in given array
// function that returns the
// count of subarrays that
// contain equal number of
// odd as well as even numbers
function countSubarrays(arr, n)
{
// initialize difference
// and answer with 0
let difference = 0;
let ans = 0;
// create two auxiliary hash
// arrays to count frequency
// of difference, one array
// for non-negative difference
// and other array for negative
// difference. Size of these
// two auxiliary arrays is 'n+1'
// because difference can
// reach maximum value 'n' as
// well as minimum value '-n'
// initialize these
// auxiliary arrays with 0
let hash_positive = new Array(n + 1);
let hash_negative = new Array(n + 1);
for(let i=0;i<n+1;i++)
{
hash_positive[i] = 0;
hash_negative[i] = 0;
}
// since the difference is
// initially 0, we have to
// initialize hash_positive[0] with 1
hash_positive[0] = 1;
// for loop to iterate
// through whole array
// (zero-based indexing is used)
for (let i = 0; i < n; i++)
{
// incrementing or decrementing
// difference based on
// arr[i] being even or odd,
// check if arr[i] is odd
if ((arr[i] & 1) == 1)
{
difference++;
}
else
{
difference--;
}
// adding hash value of 'difference'
// to our answer as all the previous
// occurrences of the same difference
// value will make even-odd subarray
// ending at index 'i'. After that,
// we will increment hash array for
// that 'difference' value for its
// occurrence at index 'i'. if
// difference is negative then use
// hash_negative
if (difference < 0)
{
ans += hash_negative[-difference];
hash_negative[-difference]++;
}
// else use hash_positive
else
{
ans += hash_positive[difference];
hash_positive[difference]++;
}
}
// return total number
// of even-odd subarrays
return ans;
}
// Driver code
let arr = [3, 4, 6, 8,
1, 10, 5, 7];
let n = arr.length;
// Printing total number
// of even-odd subarrays
document.write("Total Number of Even-Odd"
+ " subarrays are "
+ countSubarrays(arr, n));
// This code is contributed by avanitrachhadiya2155
</script>
OutputTotal Number of Even-Odd subarrays are 7
Complexity Analysis:
- Time Complexity: O(N), where N is the number of integers.
- Auxiliary Space: O(2N), where N is the number of integers.
Another approach:- This approach is much simpler and easy to understand. It can be solved easily by using the same concept of
Count subarrays with equal numbers of 1’s and 0’s. Change the odd elements to -1 and even elements to 1. And now count the ways to find sum=0;
Implementation:
C++
#include <bits/stdc++.h>
using namespace std;
// function to count the subarrays having equal number of
// even and odd
long long int countSubarrays(int arr[], int n)
{
long long int k = 0, currsum = 0, count = 0;
unordered_map<int, int> map;
for (int i = 0; i < n; i++) {
if (arr[i] % 2 == 0)
arr[i] = 1;
else if (arr[i] % 2 != 0)
arr[i] = -1;
currsum += arr[i];
if (currsum == k)
count++;
if (map.find(currsum - k) != map.end()) {
count += map[currsum - k];
}
map[currsum]++;
}
// return total number of even-odd subarrays
return count;
}
// Driver code
int main()
{
int arr[] = { 3, 4, 6, 8, 1, 10, 5, 7 };
int n = sizeof(arr) / sizeof(arr[0]);
// Printing total number of even-odd subarrays
cout << "Total Number of Even-Odd subarrays"
" are "
<< countSubarrays(arr, n);
}
// this code is contributed by naveen shah
Java
/*package whatever //do not write package name here */
import java.util.*;
class GFG {
// function to count the subarrays having equal number of
// even and odd
static long countSubarrays(int arr[], int n)
{
long k = 0, currsum = 0, count = 0;
HashMap<Long, Integer> map = new HashMap<>();
for (int i = 0; i < n; i++) {
if (arr[i] % 2 == 0)
arr[i] = 1;
else if (arr[i] % 2 != 0)
arr[i] = -1;
currsum += arr[i];
if (currsum == k)
count++;
if (map.containsKey(currsum - k)) {
count += map.get(currsum - k);
}
map.put(currsum,map.getOrDefault(currsum,0)+1);
}
// return total number of even-odd subarrays
return count;
}
public static void main (String[] args) {
int arr[] = { 3, 4, 6, 8, 1, 10, 5, 7 };
int n = arr.length;
// Printing total number of even-odd subarrays
System.out.println("Total Number of Even-Odd subarrays are " + countSubarrays(arr, n));
}
}
Python3
# function to count the subarrays having equal number of
# even and odd
def countSubarrays(arr, n):
k = 0
currsum = 0
count = 0
map = {}
for i in range(n):
if arr[i] % 2 == 0:
arr[i] = 1
else:
arr[i] = -1
currsum += arr[i]
if currsum == k:
count += 1
if currsum - k in map:
count += map[currsum - k]
if currsum not in map:
map[currsum] = 1
else:
map[currsum] += 1
# return total number of even-odd subarrays
return count
arr = [3, 4, 6, 8, 1, 10, 5, 7]
n = len(arr)
# Printing total number of even-odd subarrays
print("Total Number of Even-Odd subarrays are", countSubarrays(arr, n))
# this code is contributed by akashish__
C#
// Include namespace system
using System;
using System.Collections.Generic;
using System.Collections;
public class GFG
{
// function to count the subarrays having equal number of
// even and odd
public static long countSubarrays(int[] arr, int n)
{
var k = 0;
var currsum = 0;
var count = 0;
var map = new Dictionary<long, int>();
for (int i = 0; i < n; i++)
{
if (arr[i] % 2 == 0)
{
arr[i] = 1;
}
else if (arr[i] % 2 != 0)
{
arr[i] = -1;
}
currsum += arr[i];
if (currsum == k)
{
count++;
}
if (map.ContainsKey(currsum - k))
{
count += map[currsum - k];
}
map[currsum] = (map.ContainsKey(currsum) ? map[currsum] : 0) + 1;
}
// return total number of even-odd subarrays
return count;
}
public static void Main(String[] args)
{
int[] arr = {3, 4, 6, 8, 1, 10, 5, 7};
var n = arr.Length;
// Printing total number of even-odd subarrays
Console.WriteLine("Total Number of Even-Odd subarrays are " + GFG.countSubarrays(arr, n).ToString());
}
}
// This code is contributed by aadityaburujwale.
JavaScript
// JavaScript Code implementation
// function to count the subarrays having equal number of
// even and odd
function countSubarrays(arr, n){
var k = 0, currsum = 0, count = 0;
var map = new Map();
for(let i=0;i<n;i++){
if(arr[i]%2==0){
arr[i] = 1;
}
else if(arr[i]%2!=0){
arr[i] = -1;
}
currsum += arr[i];
if(currsum == k){
count++;
}
if(map.has(currsum-k)){
count += map.get(currsum-k);
}
var temp = (map.has(currsum) ? map.get(currsum) : 0) + 1;
map.set(currsum, temp);
}
// return total number of even-odd subarrays
return count;
}
var arr = [ 3, 4, 6, 8, 1, 10, 5, 7 ];
var n = arr.length;
// Printing total number of even-odd subarrays
console.log("Total Number of Even-Odd subarrays are " + countSubarrays(arr, n));
// This code is contributed by lokesh.
OutputTotal Number of Even-Odd subarrays are 7
Complexity Analysis:
- Time Complexity: O(N).
- Auxiliary Space: O(N).
Similar Reads
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
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