From 673b908d162caf211e7019d57966fcd30dbe2876 Mon Sep 17 00:00:00 2001
From: Philippe Zwietering <philippe.zwietering@gmail.com>
Date: Sun, 14 Nov 2021 22:20:56 +0100
Subject: [PATCH] Edited the prime factorization function of 69 so it is quick
 now

---
 projecteuler/069/main.cpp | 30 +++++++++++++++++-------------
 1 file changed, 17 insertions(+), 13 deletions(-)

diff --git a/projecteuler/069/main.cpp b/projecteuler/069/main.cpp
index 206cd81..ab75815 100644
--- a/projecteuler/069/main.cpp
+++ b/projecteuler/069/main.cpp
@@ -35,27 +35,31 @@ vector<int> sieve(int n){
     return result;
 }
 
-vector<int> prime_terms(int n, vector<int> primes = vector<int>()){
-    if(primes.empty()){
-        primes = sieve(n);
-    }
-
+vector<int> prime_terms(int n){
     vector<int> result;
 
-    for(int p : primes){
-        if(p > n){
-            break;
+    if(n % 2 == 0){
+        result.push_back(2);
+
+        while(n % 2 == 0){
+            n /= 2;
         }
+    }
 
-        if(n % p == 0){
-            result.push_back(p);
+    for(int i = 3; i <= sqrt(n); i += 2){
+        if(n % i == 0){
+            result.push_back(i);
 
-            while(n % p == 0){
-                n /= p;
+            while(n % i == 0){
+                n /= i;
             }
         }
     }
 
+    if(n > 2){
+        result.push_back(n);
+    }
+
     return result;
 }
 
@@ -76,7 +80,7 @@ int main(){
 
     for(size_t i = 2; i < n_phi.size(); ++i){
         if(n_phi[i] == 0){
-            auto terms = prime_terms(i, primes);
+            auto terms = prime_terms(i);
             float acc = 1;
 
             for(int t : terms){