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#include "../util.h"
#define ll lll
#include <math/modPowIterativ.cpp>
#undef ll
#include <math/millerRabin.cpp>
#include <math/rho.cpp>
ll phi(ll pk, ll p, ll /*k*/) {return pk - pk / p;}
ll phi(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 *= phi(pk, p, k);
}}
if (n > 1) res *= phi(n, n, 1);
return res;
}
#include <math/primitiveRoot.cpp>
bool naiveIsPrimitive(ll g, ll n) {
if (gcd(g, n) != 1) return false;
vector<bool> seen(n);
ll c = g;
for (ll i = 0; i < n; i++) {
seen[c] = true;
c = (c * g) % n;
}
ll res = 0;
for (bool x : seen) if (x) res++;
return res == phi(n);
}
void stress_test() {
int queries = 0;
for (int tries = 0; tries < 20'000; tries++) {
ll a = Random::integer<ll>(1, 3);
ll p = Random::prime<ll>(0, 1000);
ll k = p == 2 ? 1 : Random::integer<ll>(1, log(100'000) / log(p) + 1);
ll x = a;
for (int i = 0; i < k; i++) x *= p;
ll got = findPrimitive(x);
if (got < 0 || got >= x) cerr << "error: out of range" << FAIL;
if (!naiveIsPrimitive(got, x)) cerr << "error: wrong" << got << " " << x << FAIL;
queries++;
}
cerr << "tested random queries: " << queries << endl;
}
void stress_test2() {
int queries = 0;
for (int x = 2; x < 5'000; x++) {
map<ll, int> facts;
factor(x, facts);
if (x % 2 == 0) facts.erase(facts.find(2));
bool expected = ssize(facts) == 1;
if (x % 4 == 0) expected = false;
if (x == 2 || x == 4) expected = true;
bool got = findPrimitive(x) >= 0;
if (got != expected) cerr << "error" << FAIL;
queries++;
}
cerr << "tested random queries: " << queries << endl;
}
int main() {
stress_test();
stress_test2();
}
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