Prime factorization on log n

Author: Nadim-Mahmud

Source/Number Theory/prime factorization log(n).cpp

@@ -0,0 +1,30 @@
+/**
+    Description : prime factorization
+    Complexity : O(log n)
+    Limitation : memory complexity O(n) so it works up to 10^7
+*/
+
+const int N = 10000000;
+int lp[N+1];
+vector<int> pr;
+
+void sieve(){
+    int i,j;
+    for (i=2; i<=N; ++i) {
+        if (lp[i] == 0) {
+            lp[i] = i;
+            pr.push_back (i);
+        }
+        for (j=0; j<(int)pr.size() && pr[j]<=lp[i] && i*pr[j]<=N; ++j)
+            lp[i*pr[j]] = pr[j];
+    }
+}
+
+vector<int> prime_fact(int n){
+    vector<int> pf;
+    while (n != 1){
+        pf.push_back(lp[n]);
+        n = n / lp[n];
+    }
+    return pf;
+}