From 20237a22af46bf1a2190a57c1ac87af41496d838 Mon Sep 17 00:00:00 2001
From: Philippe Zwietering <philippe.zwietering@gmail.com>
Date: Sun, 14 Nov 2021 22:25:02 +0100
Subject: [PATCH] Finished 070, by using the way quicker prime factorization it
 is done in 18 seconds

---
 projecteuler/070/main.cpp | 103 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 103 insertions(+)
 create mode 100644 projecteuler/070/main.cpp

diff --git a/projecteuler/070/main.cpp b/projecteuler/070/main.cpp
new file mode 100644
index 0000000..c3877c9
--- /dev/null
+++ b/projecteuler/070/main.cpp
@@ -0,0 +1,103 @@
+/*
+
+Totient permutation
+
+Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of positive numbers less than or equal to n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6.
+The number 1 is considered to be relatively prime to every positive number, so φ(1)=1.
+
+Interestingly, φ(87109)=79180, and it can be seen that 87109 is a permutation of 79180.
+
+Find the value of n, 1 < n < 107, for which φ(n) is a permutation of n and the ratio n/φ(n) produces a minimum.
+
+*/
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+const int MAX = pow(10, 7);
+
+vector<int> sieve(int n){
+    vector<bool> numbers(n+1, true);
+    vector<int> result;
+
+    int i = 2;
+    while(i <= n){
+        if(numbers[i]){
+            result.push_back(i);
+
+            int j = 2 * i;
+            while(j <= n){
+                numbers[j] = false;
+                j += i;
+            }
+        }
+        ++i;
+    }
+
+    return result;
+}
+
+vector<int> prime_terms(int n){
+    vector<int> result;
+
+    if(n % 2 == 0){
+        result.push_back(2);
+
+        while(n % 2 == 0){
+            n /= 2;
+        }
+    }
+
+    for(int i = 3; i <= sqrt(n); i += 2){
+        if(n % i == 0){
+            result.push_back(i);
+
+            while(n % i == 0){
+                n /= i;
+            }
+        }
+    }
+
+    if(n > 2){
+        result.push_back(n);
+    }
+
+    return result;
+}
+
+int main(){
+
+    cout << "Hello this is Patrick" << endl;
+    auto start = chrono::high_resolution_clock::now();
+
+    int n_min = 0;
+    float min_ratio = 2;
+
+    for(int n = 2; n < MAX; ++n){
+        auto terms = prime_terms(n);
+
+        float phi = n;
+        for(float term : terms){
+            phi *= 1.0 - 1.0 / term;
+        }
+
+        int p = phi;
+        string s_phi = to_string(p), s_n = to_string(n);
+        sort(s_phi.begin(), s_phi.end());
+        sort(s_n.begin(), s_n.end());
+
+        if(s_phi == s_n){
+            if((float)n / phi < min_ratio){
+                min_ratio = (float)n / phi;
+                n_min = n;
+            }
+        }
+    }
+
+    cout << n_min << endl;
+
+    auto duration = chrono::duration_cast<chrono::milliseconds>(chrono::high_resolution_clock::now() - start);
+    cout << (float)duration.count()/1000 << endl;
+    return 0;
+}