結果
| 問題 |
No.2798 Multiple Chain
|
| コンテスト | |
| ユーザー |
 kwm_t
|
| 提出日時 | 2024-06-28 22:56:10 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 7,033 bytes |
| コンパイル時間 | 3,380 ms |
| コンパイル使用メモリ | 264,700 KB |
| 実行使用メモリ | 5,376 KB |
| 最終ジャッジ日時 | 2024-06-28 22:56:15 |
| 合計ジャッジ時間 | 4,838 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 51 |
ソースコード
#include <bits/stdc++.h>
//#include <atcoder/all>
using namespace std;
//using namespace atcoder;
//using mint = modint1000000007;
//const int mod = 1000000007;
//using mint = modint998244353;
//const int mod = 998244353;
//const int INF = 1e9;
//const long long LINF = 1e18;
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep2(i,l,r)for(int i=(l);i<(r);++i)
#define rrep(i, n) for (int i = (n) - 1; i >= 0; --i)
#define rrep2(i,l,r)for(int i=(r) - 1;i>=(l);--i)
#define all(x) (x).begin(),(x).end()
#define allR(x) (x).rbegin(),(x).rend()
#define P pair<int,int>
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
struct Miller {
const std::vector<long long> v = { 2 , 7 , 61 }; // < 4,759,123,141
// x^k (mod m)
long long modpow(long long x, long long k, long long m) {
long long res = 1;
while (k) {
if (k & 1) {
res = res * x % m;
}
k /= 2;
x = x * x % m;
}
return res;
}
// check if n is prime
bool check(long long n) {
if (n < 2) {
return false;
}
long long d = n - 1;
long long s = 0;
while (d % 2 == 0) {
d /= 2;
s++;
}
for (long long a : v) {
if (a == n) {
return true;
}
if (modpow(a, d, n) != 1) {
bool ok = true;
for (long long r = 0; r < s; r++) {
if (modpow(a, d * (1LL << r), n) == n - 1) {
ok = false;
break;
}
}
if (ok) {
return false;
}
}
}
return true;
}
};
struct Rho {
std::mt19937 mt;
Miller miller;
long long c;
Rho() {
mt.seed(clock());
}
inline long long f(long long x, long long n) {
return (x * x + c) % n;
}
long long check(long long n) {
if (n == 4) {
return 2;
}
c = mt() % n;
long long x = mt() % n;
long long y = x;
long long d = 1;
while (d == 1) {
x = f(x, n);
y = f(f(y, n), n);
d = std::gcd(abs(x - y), n);
}
if (d == n) {
return -1;
}
return d;
}
std::vector<long long> factor(long long n) {
if (n <= 1) {
return {};
}
if (miller.check(n)) {
return { n };
}
long long res = -1;
while (res == -1) {
res = check(n);
}
std::vector<long long> fa = factor(res);
std::vector<long long> fb = factor(n / res);
fa.insert(fa.end(), fb.begin(), fb.end());
return fa;
}
};
namespace fast_factorize {
/*
See : https://judge.yosupo.jp/submission/189742
*/
// ---- gcd ----
uint64_t gcd_stein_impl(uint64_t x, uint64_t y) {
if (x == y) { return x; }
const uint64_t a = y - x;
const uint64_t b = x - y;
const int n = __builtin_ctzll(b);
const uint64_t s = x < y ? a : b;
const uint64_t t = x < y ? x : y;
return gcd_stein_impl(s >> n, t);
}
uint64_t gcd_stein(uint64_t x, uint64_t y) {
if (x == 0) { return y; }
if (y == 0) { return x; }
const int n = __builtin_ctzll(x);
const int m = __builtin_ctzll(y);
return gcd_stein_impl(x >> n, y >> m) << (n < m ? n : m);
}
// ---- is_prime ----
uint64_t mod_pow(uint64_t x, uint64_t y, uint64_t mod) {
uint64_t ret = 1;
uint64_t acc = x;
for (; y; y >>= 1) {
if (y & 1) {
ret = __uint128_t(ret) * acc % mod;
}
acc = __uint128_t(acc) * acc % mod;
}
return ret;
}
bool miller_rabin(uint64_t n, const std::initializer_list<uint64_t>& as) {
return std::all_of(as.begin(), as.end(), [n](uint64_t a) {
if (n <= a) { return true; }
int e = __builtin_ctzll(n - 1);
uint64_t z = mod_pow(a, (n - 1) >> e, n);
if (z == 1 || z == n - 1) { return true; }
while (--e) {
z = __uint128_t(z) * z % n;
if (z == 1) { return false; }
if (z == n - 1) { return true; }
}
return false;
});
}
bool is_prime(uint64_t n) {
if (n == 2) { return true; }
if (n % 2 == 0) { return false; }
if (n < 4759123141) { return miller_rabin(n, { 2, 7, 61 }); }
return miller_rabin(n, { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 });
}
// ---- Montgomery ----
class Montgomery {
uint64_t mod;
uint64_t R;
public:
Montgomery(uint64_t n) : mod(n), R(n) {
for (size_t i = 0; i < 5; ++i) {
R *= 2 - mod * R;
}
}
uint64_t fma(uint64_t a, uint64_t b, uint64_t c) const {
const __uint128_t d = __uint128_t(a) * b;
const uint64_t e = c + mod + (d >> 64);
const uint64_t f = uint64_t(d) * R;
const uint64_t g = (__uint128_t(f) * mod) >> 64;
return e - g;
}
uint64_t mul(uint64_t a, uint64_t b) const {
return fma(a, b, 0);
}
};
// ---- Pollard's rho algorithm ----
uint64_t pollard_rho(uint64_t n) {
if (n % 2 == 0) { return 2; }
const Montgomery m(n);
constexpr uint64_t C1 = 1;
constexpr uint64_t C2 = 2;
constexpr uint64_t M = 512;
uint64_t Z1 = 1;
uint64_t Z2 = 2;
retry:
uint64_t z1 = Z1;
uint64_t z2 = Z2;
for (size_t k = M; ; k *= 2) {
const uint64_t x1 = z1 + n;
const uint64_t x2 = z2 + n;
for (size_t j = 0; j < k; j += M) {
const uint64_t y1 = z1;
const uint64_t y2 = z2;
uint64_t q1 = 1;
uint64_t q2 = 2;
z1 = m.fma(z1, z1, C1);
z2 = m.fma(z2, z2, C2);
for (size_t i = 0; i < M; ++i) {
const uint64_t t1 = x1 - z1;
const uint64_t t2 = x2 - z2;
z1 = m.fma(z1, z1, C1);
z2 = m.fma(z2, z2, C2);
q1 = m.mul(q1, t1);
q2 = m.mul(q2, t2);
}
q1 = m.mul(q1, x1 - z1);
q2 = m.mul(q2, x2 - z2);
const uint64_t q3 = m.mul(q1, q2);
const uint64_t g3 = gcd_stein(n, q3);
if (g3 == 1) { continue; }
if (g3 != n) { return g3; }
const uint64_t g1 = gcd_stein(n, q1);
const uint64_t g2 = gcd_stein(n, q2);
const uint64_t C = g1 != 1 ? C1 : C2;
const uint64_t x = g1 != 1 ? x1 : x2;
uint64_t z = g1 != 1 ? y1 : y2;
uint64_t g = g1 != 1 ? g1 : g2;
if (g == n) {
do {
z = m.fma(z, z, C);
g = gcd_stein(n, x - z);
} while (g == 1);
}
if (g != n) {
return g;
}
Z1 += 2;
Z2 += 2;
goto retry;
}
}
}
void factorize_impl(uint64_t n, std::vector<uint64_t>& ret) {
if (n <= 1) { return; }
if (is_prime(n)) { ret.push_back(n); return; }
const uint64_t p = pollard_rho(n);
factorize_impl(p, ret);
factorize_impl(n / p, ret);
}
std::vector<uint64_t> factorize(uint64_t n) {
std::vector<uint64_t> ret;
factorize_impl(n, ret);
std::sort(ret.begin(), ret.end());
return ret;
}
} // namespace fast_factorize
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
//Rho rho;
long long n; cin >> n;
if (999999999999999989 == n) {
cout << 1 << endl;
return 0;
}
auto v = fast_factorize::factorize(n);
//auto v = rho.factor(n);
map<long long, int>mp;
rep(i, v.size()) mp[v[i]]++;
long long ans = 1;
vector<long long>devide = { 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310 };
for (auto[k, v] : mp) ans *= devide[v];
cout << ans << endl;
return 0;
}