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subcrip 2024-03-30 11:52:59 +08:00
parent 89481b2877
commit ff3cf8618c
Signed by: subcrip
SSH Key Fingerprint: SHA256:dFPFi68d8C87YkFkEBU4TkcrYRySWpekRR1hbnDWUCw
1 changed files with 88 additions and 0 deletions

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number/pollard_rho.cc Normal file
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vector<tuple<int, int, ll>> decompose(ll x) {
vector<tuple<int, int, ll>> res;
for (int i = 2; i * i <= x; i++) {
if (x % i == 0) {
int cnt = 0;
ll pw = 1;
while (x % i == 0) ++cnt, x /= i, pw *= i;
res.emplace_back(i, cnt, pw);
}
}
if (x != 1) {
res.emplace_back(x, 1, x);
}
return res;
}
struct pollard_rho {
ll max_factor;
pollard_rho() : max_factor(0) { srand(time(NULL)); }
ll quick_pow(ll x, ll p, ll mod) {
ll ans = 1;
while (p) {
if (p & 1) ans = (__int128)ans * x % mod;
x = (__int128)x * x % mod;
p >>= 1;
}
return ans;
}
bool Miller_Rabin(ll p) {
if (p < 2) return 0;
if (p == 2) return 1;
if (p == 3) return 1;
ll d = p - 1, r = 0;
while (!(d & 1)) ++r, d >>= 1;
for (ll k = 0; k < 10; ++k) {
ll a = rand() % (p - 2) + 2;
ll x = quick_pow(a, d, p);
if (x == 1 || x == p - 1) continue;
for (int i = 0; i < r - 1; ++i) {
x = (__int128)x * x % p;
if (x == p - 1) break;
}
if (x != p - 1) return 0;
}
return 1;
}
ll Pollard_Rho(ll x) {
ll s = 0, t = 0;
ll c = (ll)rand() % (x - 1) + 1;
int step = 0, goal = 1;
ll val = 1;
for (goal = 1;; goal *= 2, s = t, val = 1) {
for (step = 1; step <= goal; ++step) {
t = ((__int128)t * t + c) % x;
val = (__int128)val * abs(t - s) % x;
if ((step % 127) == 0) {
ll d = gcd(val, x);
if (d > 1) return d;
}
}
ll d = gcd(val, x);
if (d > 1) return d;
}
}
void fac(ll x) {
if (x <= max_factor || x < 2) return;
if (Miller_Rabin(x)) {
max_factor = max(max_factor, x);
return;
}
ll p = x;
while (p >= x) p = Pollard_Rho(x);
while ((x % p) == 0) x /= p;
fac(x), fac(p);
}
// find greatest prime factor of `x`
ll solve(ll x) {
max_factor = 0;
fac(x);
return max_factor;
}
};