added seive

Algorithms/C++/prime_factorization_using_sieve.cpp

@@ -0,0 +1,50 @@
+/* 
+Prime Factors [1,n]
+while( num ! = 1 ):
+
+We keep on dividing it with its smallest prime factor.
+
+The smallest prime factor is pre-calculated using a slightly modified prime sieve.
+Since we start from 2 and go on, we mark the first multiple as the spf.
+Preprocessing for Sieve: O(n log log n)
+Time Complexity for factorization: O(log n)
+Space Complexity: O(n) 
+*/
+#include <bits/stdc++.h>
+using namespace std;
+
+void pfsieve(int n)
+{
+   int spf[n + 1];
+   for (int i = 2; i <= n; i++)
+   {
+      spf[i] = i;
+   }
+
+   for (int i = 2; i <= n; i++)
+   {
+      if (spf[i] == i)
+      {
+         for (int j = i * i; j <= n; j += i)
+         {
+            if (spf[j] == j)
+            {
+               spf[j] = i;
+            }
+         }
+      }
+   }
+   while (n != 1)
+   {
+      cout << spf[n] << " ";
+      n = n / spf[n];
+   }
+}
+
+int main()
+{
+   int n;
+   cin >> n;
+   pfsieve(n);
+   return 0;
+}