1 files changed, 50 insertions, 0 deletions
diff --git a/content/math/linearSieve.cpp b/content/math/linearSieve.cpp
new file mode 100644
index 0000000..64440dd
--- /dev/null
+++ b/content/math/linearSieve.cpp
@@ -0,0 +1,50 @@
+constexpr ll N = 10'000'000;
+ll small[N], power[N], sieved[N];
+vector<ll> primes;
+
+//wird aufgerufen mit (p^k, p, k) für prime p und k > 0
+ll mu(ll pk, ll p, ll k) {return -(k == 1);}
+ll phi(ll pk, ll p, ll k) {return pk - pk / p;}
+ll div(ll pk, ll p, ll k) {return k+1;}
+ll divSum(ll pk, ll p, ll k) {return (pk*p-1) / (p - 1);}
+ll square(ll pk, ll p, ll k) {return k % 2 ? pk / p : pk;}
+ll squareFree(ll pk, ll p, ll k) {return p;}
+
+void sieve() { // O(N)
+	small[1] = power[1] = sieved[1] = 1;
+	for (ll i = 2; i < N; i++) {
+		if (small[i] == 0) {
+			primes.push_back(i);
+			for (ll pk = i, k = 1; pk < N; pk *= i, k++) {
+				small[pk] = i;
+				power[pk] = pk;
+				sieved[pk] = mu(pk, i, k); // Aufruf ändern!
+		}}
+		for (ll j=0; i*primes[j] < N && primes[j] < small[i]; j++) {
+			ll k = i * primes[j];
+			small[k] = power[k] = primes[j];
+			sieved[k] = sieved[i] * sieved[primes[j]];
+		}
+		if (i * small[i] < N && power[i] != i) {
+			ll k = i * small[i];
+			small[k] = small[i];
+			power[k] = power[i] * small[i];
+			sieved[k] = sieved[power[k]] * sieved[k / power[k]];
+}}}
+
+ll naive(ll n) { // O(sqrt(n))
+	ll res = 1;
+	for (ll p = 2; p * p <= n; p++) {
+		if (n % p == 0) {
+			ll pk = 1;
+			ll k = 0;
+			do {
+				n /= p;
+				pk *= p;
+				k++;
+			} while (n % p == 0);
+			res *= mu(pk, p, k); // Aufruf ändern!
+	}}
+	if (n > 1) res *= mu(n, n, 1);
+	return res;
+}