Added algo sieve of eranthoses

Domains/CompetitiveProgramming/Programs/C++/sieveoferanthoses.cpp

@@ -0,0 +1,66 @@
+/*
+Algorithm: Sieve of Eratosthenes
+Category: Number Theory
+Difficulty: Easy
+Link: https://cp-algorithms.com/algebra/sieve-of-eratosthenes.html
+
+Problem Statement:
+Given an integer n, find all prime numbers less than or equal to n.
+
+The Sieve of Eratosthenes efficiently finds all primes up to n by marking
+multiples of each prime starting from 2, the smallest prime number.
+
+Input:
+A single integer n (2 ≤ n ≤ 10^6)
+
+Output:
+All prime numbers ≤ n.
+
+Example:
+Input:
+10
+
+Output:
+2 3 5 7
+
+Explanation:
+Starting from 2, we mark all multiples of 2 as non-prime (4, 6, 8, 10),
+then move to the next unmarked number (3), and mark its multiples.
+Remaining unmarked numbers are primes.
+
+Approach:
+1. Create a boolean array `isPrime` initialized as true for all numbers ≥ 2.
+2. For each i from 2 to √n:
+   - If `isPrime[i]` is true, mark all multiples of i as false.
+3. Print all numbers i where `isPrime[i]` is true.
+
+Time Complexity: O(n log log n)
+Space Complexity: O(n)
+
+Contributor: SampleContributor
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+typedef long long ll;
+int main()
+{
+   ll n;
+   cin>>n;
+   vector<ll> isPrime(n+1,true);
+   for(ll i=2;(i*i)<=n;i++){
+    if(isPrime[i]){
+             for(ll j=i*i;(j)<=n;j+=i){
+          isPrime[j]=false;
+       }
+    }
+
+   }
+   cout<<"Prime numbers ";
+   for(ll i=2;i<=n;i++){
+          if(isPrime[i]){
+              cout<<i<<endl;
+          }
+   }
+    return 0;
+}

Domains/CompetitiveProgramming/Programs/README.md

@@ -75,6 +75,11 @@ Pick the language folder you're most comfortable with or want to learn:
    - Time: O(n log n), Space: O(n)
    - Link: https://www.codechef.com/problems/TSORT
 
+4. **Sieve of Eranthoses** (`sieveoferanthoses.cpp`)
+   - Topics: Number Theory
+   - Time: O(n log log n), Space: O(n)
+   - Link: Link: https://cp-algorithms.com/algebra/sieve-of-eratosthenes.html
+
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