Added factorization, modular exponentiation, and sieve of eratosthenes

Author: prince776

Algorithms/Mathematical/factorization.cpp

@@ -0,0 +1,43 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+void printFactors(int n) 
+{ 
+    for (int i=1; i * i<=n; i++) 
+    { 
+        if (n%i == 0) 
+        { 
+            if (n/i == i) 
+                cout << i << " "; 
+  
+            else 
+                cout << i << " " << n/i << " "; 
+        } 
+    }
+    cout << "\n";
+} 
+
+void printPrimeFactors(int n)
+{
+	set<int> f;
+	for (int i = 2; i*i <= n; i++)
+	{
+		while (n % i == 0)
+		{
+			f.insert(i);
+			n /= i;
+		}
+	}
+	for (auto &i : f)
+	{
+		cout << i << " ";
+	}
+	cout << "\n";
+}
+
+int main()
+{
+	printFactors(100);
+	printPrimeFactors(100);
+	return 0;
+}

Algorithms/Mathematical/modular_exponentiation.cpp

@@ -0,0 +1,20 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+// To calculate (x^n) % m
+
+int modpow(int x, int n, int m)
+{
+	if (n == 0) return 1 % m;
+	long long u = modpow(x, n / 2, m);
+	u = (u * u) % m;
+	if (n % 2 == 1)
+		u = (u * x) % m;
+	return u;	
+}
+
+int main()
+{
+	cout << modpow(10, 50, 3) << "\n";
+	return 0;
+}

Algorithms/Mathematical/sieve_of_Eratosthenes.cpp

@@ -0,0 +1,33 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+void SieveOfEatosthenes(int n)
+{
+
+	bool prime[n+1];
+	memset(prime, true, sizeof(prime));
+
+	for (int p = 2; p * p <= n; p++)
+	{
+		if (prime[p])
+		{
+			for (int i = p * p; i <= n; i += p)
+				prime[i] = false;
+		}
+	}
+
+	// Print all prime numbers
+	for (int p = 2; p <= n; p++)
+	{
+		if (prime[p])
+			cout << p << " ";
+	}
+	cout << "\n";
+}
+
+int main()
+{
+	int n = 30;
+	SieveOfEatosthenes(n);
+	return 0;
+}