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