Added wheel factorization

Author: fredbr

math/compute_wheel.cpp

@@ -0,0 +1,36 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+vector<int> compute_wheel(vector<int> const& v) {
+    int sz = 1;
+    for (auto x : v) sz *= x;
+
+    vector<int> primes;
+
+    vector<char> s(sz+1);
+    for (auto i : v)
+        for (int j = i; j <= sz; j += i)
+            s[j] = 1;
+
+    for (int i = v.back(); i <= sz; i++)
+        if (!s[i])
+            primes.push_back(i);
+
+    primes.push_back(sz+1);
+    primes.push_back(primes.front()+sz);
+    vector<int> inc(primes.size()-1);
+
+    for (int i = 0; i < int(inc.size()); i++)
+        inc[i] = primes[i+1]-primes[i];
+
+    return inc;
+}
+
+int main() {
+    auto x = compute_wheel({2, 3, 5});
+        
+    cout << "{ ";
+    for (auto i : x) cout << i << ", ";
+    cout << "}\n";
+}

math/wheel_factorization.cpp

@@ -0,0 +1,46 @@
+#include <bits/stdc++.h>
+
+#pragma GCC optimize("O3")
+
+using namespace std;
+
+using ll = uint64_t;
+
+template <typename T, int sz>
+int tam(T(&)[sz]) {
+    return sz;
+}
+
+vector<ll> factor(ll x) {
+    static const int primes[] = {2, 3, 5};
+    static const int inc[] = { 4, 2, 4, 2, 4, 6, 2, 6 };
+    // see compute_wheel.cpp to compute the wheel efficiently
+
+    vector<ll> factors;
+
+    for (auto p : primes) 
+        while (x%p == 0) x /= p, factors.push_back(p);
+
+    ll k = 7, i = 0;
+
+    while (k*k <= x) {
+        while (x%k == 0)
+            x /= k, factors.push_back(k);
+        k += inc[i++];
+        if (i == tam(inc)) i = 0;
+    }
+
+    factors.push_back(x);
+    sort(factors.begin(), factors.end());
+    return factors;
+}
+
+int main() {
+    ll x;
+    cin >> x;
+
+    auto ans = factor(x);
+
+    for (auto p : ans) cout << p << " ";
+    cout << "\n";
+}