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Mathematics/SieveOfEratosthenes.cpp

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+
+	// Sieve of Eratosthenes is one of the most efficient algorithms to find all prime
+	// numbers less than a given 'n'
+
+	// #ALgorithm:
+	// 	1. Create a list of n+1 elements and initialize them to True.
+	// 	2. Initialize a variable, lets say 'p' to 2, the first prime number.
+	// 	3. Starting from 'p' check every element until 'n',if it is 'True' in list, modify the element at positions of multiples of'p' to 'False'
+
+	// #Time Complexity:
+	// 	O(nloglogn)
+
+	// #Space Complexity: 
+	// 	O(n)
+	// 
+
+#include<bits/stdc++.h>
+using namespace std;
+
+//Sieve Of Eratosthenes Function:
+void soe(int n)
+{
+	bool isprime[n+1];
+	memset(isprime, true, sizeof(isprime)); //Memset is used to assign values to a list
+
+	for(int p=2;p*p<=n;++p)
+	{
+		if(isprime[p]==true)
+		{
+			//Update all multiples of p to False
+			for(int i=p*p;i<=n;i+=p)
+				isprime[i]=false;
+		}
+	}
+
+	//Print all Prime Numbers
+	for(int p=2;p<=n;++p)
+	{
+		if(isprime[p]==true)
+			cout<<p<<" ";
+	}
+}
+
+int main()
+{
+	int n;
+	cout<<"Enter Number: ";
+	cin>>n;
+
+	cout<<"\n Prime Numbers less than "<<n<<" are: \n";
+	soe(n);
+	cout<<"\n";
+}