From 529fc1843edf7059993a1397e49456365ab3f38e Mon Sep 17 00:00:00 2001
From: akhem301 <akhem301@gmail.com>
Date: Sat, 28 Oct 2017 02:01:19 +0530
Subject: [PATCH] Prime Factorization of a number

---
 Math/Prime_Factorization/README.md            | 10 +++
 .../primefactorization.cpp                    | 71 +++++++++++++++++++
 2 files changed, 81 insertions(+)
 create mode 100644 Math/Prime_Factorization/README.md
 create mode 100644 Math/Prime_Factorization/primefactorization.cpp

diff --git a/Math/Prime_Factorization/README.md b/Math/Prime_Factorization/README.md
new file mode 100644
index 000000000..9d9cd83a4
--- /dev/null
+++ b/Math/Prime_Factorization/README.md
@@ -0,0 +1,10 @@
+Prime Factorization is a very important and useful technique to factorize any number into its prime factors. It has various applications in the field of number theory.
+
+The method of prime factorization involves two function calls.
+First: Calculating all the prime number up till a certain range using the standard
+       Sieve of Eratosthenes.
+
+Second: Using the prime numbers to reduce the the given number and thus find all its prime factors.
+
+The complexity of the solution involves approx. O(n logn) in calculating sieve of eratosthenes
+O(log n) in calculating the prime factors of the number. So in total approx. O(n logn).
diff --git a/Math/Prime_Factorization/primefactorization.cpp b/Math/Prime_Factorization/primefactorization.cpp
new file mode 100644
index 000000000..8a17badd7
--- /dev/null
+++ b/Math/Prime_Factorization/primefactorization.cpp
@@ -0,0 +1,71 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+// Declaring variables for maintaing prime numbers and to check whether a number is prime or not
+bool isprime[1000006];
+vector<int> prime_numbers;
+vector<pair<int,int> > factors;
+
+// Calculating prime number upto a given range
+void SieveOfEratosthenes(int N)
+{
+	memset(isprime, true, sizeof isprime);
+	
+	for(int i=2; i<=N ;i++)
+	{
+		if(isprime[i])
+		{
+			for(int j=2*i; j<=N; j+=i)
+			isprime[j]=false;
+		}
+	}
+	
+	for(int i=2;i<=N;i++)
+	{
+		if(isprime[i])
+		prime_numbers.push_back(i);
+	}
+	
+	return;
+}
+
+// Prime factorization of a number
+void prime_factorization(int num)
+{
+	for(int i=0; prime_numbers[i]<=num; i++)
+	{
+		int count=0;
+		
+		while(num%prime_numbers[i] == 0)
+		{
+			count++;
+			num = num/prime_numbers[i];
+		}
+		
+		if(count)
+		factors.push_back(make_pair(prime_numbers[i],count));
+	}
+	
+	if(num>2)
+	factors.push_back(make_pair(num,1));
+	
+	return;
+}
+
+int main()
+{
+	int num;
+	cin>>num;
+	
+	SieveOfEratosthenes(num);
+	
+	prime_factorization(num);
+	
+	// Prime factors with their powers in the given number in new line
+	for(auto it: factors)
+	{
+		cout<<it.first<<" "<<it.second<<endl;
+	}
+	
+	return 0;
+}