From ec1fae253d4d6cdf7be74b1d4b2f9f9030e3a1c3 Mon Sep 17 00:00:00 2001
From: Philippe Zwietering <philippe.zwietering@gmail.com>
Date: Sun, 14 Nov 2021 21:24:24 +0100
Subject: [PATCH] Finished 69 (nice), wasn't too hard but my solution is pretty
 slow for some reason (19 s)

---
 projecteuler/069/main.cpp | 101 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 101 insertions(+)
 create mode 100644 projecteuler/069/main.cpp

diff --git a/projecteuler/069/main.cpp b/projecteuler/069/main.cpp
new file mode 100644
index 0000000..206cd81
--- /dev/null
+++ b/projecteuler/069/main.cpp
@@ -0,0 +1,101 @@
+/* Totient maximum
+
+Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of numbers less than 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.
+
+It can be seen that n=6 produces a maximum n/φ(n) for n ≤ 10.
+
+Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.
+
+*/
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+const int MAX = 1000000;
+
+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> primes = vector<int>()){
+    if(primes.empty()){
+        primes = sieve(n);
+    }
+
+    vector<int> result;
+
+    for(int p : primes){
+        if(p > n){
+            break;
+        }
+
+        if(n % p == 0){
+            result.push_back(p);
+
+            while(n % p == 0){
+                n /= p;
+            }
+        }
+    }
+
+    return result;
+}
+
+int main(){
+
+    cout << "Hello this is Patrick" << endl;
+    auto start = chrono::high_resolution_clock::now();
+
+    vector<float> n_phi(MAX + 1, 0);
+    auto primes = sieve(MAX);
+
+    for(auto p : primes){
+        n_phi[p] = 1 + 1 / ((float)p - 1);
+    }
+
+    int n_max = 0;
+    float n_phi_max = 0;
+
+    for(size_t i = 2; i < n_phi.size(); ++i){
+        if(n_phi[i] == 0){
+            auto terms = prime_terms(i, primes);
+            float acc = 1;
+
+            for(int t : terms){
+                acc *= n_phi[t];
+            }
+            n_phi[i] = acc;
+
+            if(n_phi_max < acc){
+                n_max = i;
+                n_phi_max = acc;
+            }
+        }
+
+        // cout << i << " " << n_phi[i] << endl;
+    }
+
+    cout << n_max << endl;
+
+    auto duration = chrono::duration_cast<chrono::milliseconds>(chrono::high_resolution_clock::now() - start);
+    cout << (float)duration.count()/1000 << endl;
+    return 0;
+}