結果

問題 No.1978 Permutation Repetition
ユーザー ForestedForested
提出日時 2022-06-10 23:16:58
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 10,948 bytes
コンパイル時間 1,637 ms
コンパイル使用メモリ 139,948 KB
最終ジャッジ日時 2025-01-29 20:18:12
ジャッジサーバーID
(参考情報)
judge3 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 32 WA * 12
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ソースコード

diff #
プレゼンテーションモードにする

#ifndef LOCAL
#define FAST_IO
#endif
// ===== template.hpp =====
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i)
#define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = __uint128_t;
using i32 = signed int;
using i64 = signed long long;
using i128 = __int128_t;
using f64 = double;
using f80 = long double;
template <typename T>
using Vec = vector<T>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
istream &operator>>(istream &is, i128 &x) {
i64 v;
is >> v;
x = v;
return is;
}
ostream &operator<<(ostream &os, i128 x) {
os << (i64) x;
return os;
}
istream &operator>>(istream &is, u128 &x) {
u64 v;
is >> v;
x = v;
return is;
}
ostream &operator<<(ostream &os, u128 x) {
os << (u64) x;
return os;
}
template <typename F, typename Comp = less<>>
Vec<i32> sort_index(i32 n, F f, Comp comp = Comp()) {
Vec<i32> idx(n);
iota(ALL(idx), 0);
sort(ALL(idx), [&](i32 i, i32 j) -> bool {
return comp(f(i), f(j));
});
return idx;
}
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
#ifdef FAST_IO
__attribute__((constructor)) void fast_io() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(10);
}
#endif
// ===== template.hpp =====
#ifdef DEBUGF
#include "cpl/template/debug.hpp"
#else
#define DBG(x) (void) 0
#endif
// ===== mod_int.hpp =====
#include <cassert>
#include <iostream>
#include <type_traits>
// ===== utils.hpp =====
constexpr bool is_prime(unsigned n) {
if (n == 0 || n == 1) {
return false;
}
for (unsigned i = 2; i * i <= n; ++i) {
if (n % i == 0) {
return false;
}
}
return true;
}
constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
unsigned ret = 1, self = x;
while (y != 0) {
if (y & 1) {
ret = static_cast<unsigned>(static_cast<unsigned long long>(ret) * self % mod);
}
self = static_cast<unsigned>(static_cast<unsigned long long>(self) * self % mod);
y /= 2;
}
return ret;
}
template <unsigned mod>
constexpr unsigned primitive_root() {
static_assert(is_prime(mod), "`mod` must be a prime number.");
if (mod == 2) {
return 1;
}
unsigned primes[32] = {};
int it = 0;
{
unsigned m = mod - 1;
for (unsigned i = 2; i * i <= m; ++i) {
if (m % i == 0) {
primes[it++] = i;
while (m % i == 0) {
m /= i;
}
}
}
if (m != 1) {
primes[it++] = m;
}
}
for (unsigned i = 2; i < mod; ++i) {
bool ok = true;
for (int j = 0; j < it; ++j) {
if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
ok = false;
break;
}
}
if (ok)
return i;
}
return 0;
}
// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
x %= y;
if (x < 0) {
x += y;
}
return x;
}
// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return x / y;
} else {
return -((-x + y - 1) / y);
}
}
// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return (x + y - 1) / y;
} else {
return -(-x / y);
}
}
// ===== utils.hpp =====
template <unsigned mod>
class ModInt {
static_assert(mod != 0, "`mod` must not be equal to 0.");
static_assert(
mod < (1u << 31),
"`mod` must be less than (1u << 31) = 2147483648.");
unsigned val;
public:
constexpr ModInt() : val(0) {}
template <typename T>
constexpr ModInt(T x) : val(static_cast<unsigned>(safe_mod(x, static_cast<T>(mod)))) {}
static constexpr ModInt raw(unsigned x) {
ModInt<mod> ret;
ret.val = x;
return ret;
}
constexpr unsigned get_val() const {
return val;
}
constexpr ModInt operator+() const {
return *this;
}
constexpr ModInt operator-() const {
return ModInt<mod>(0u) - *this;
}
constexpr ModInt &operator+=(const ModInt &rhs) {
val += rhs.val;
if (val >= mod)
val -= mod;
return *this;
}
constexpr ModInt &operator-=(const ModInt &rhs) {
if (val < rhs.val)
val += mod;
val -= rhs.val;
return *this;
}
constexpr ModInt &operator*=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.val % mod;
return *this;
}
constexpr ModInt &operator/=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.inv().val % mod;
return *this;
}
friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) += rhs;
}
friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) -= rhs;
}
friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) *= rhs;
}
friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) /= rhs;
}
constexpr ModInt pow(unsigned long long x) const {
ModInt<mod> ret = ModInt<mod>::raw(1);
ModInt<mod> self = *this;
while (x != 0) {
if (x & 1)
ret *= self;
self *= self;
x >>= 1;
}
return ret;
}
constexpr ModInt inv() const {
static_assert(is_prime(mod), "`mod` must be a prime number.");
assert(val != 0);
return this->pow(mod - 2);
}
friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
is >> x.val;
x.val %= mod;
return is;
}
friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
os << x.val;
return os;
}
friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
return lhs.val != rhs.val;
}
};
[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;
// ===== mod_int.hpp =====
using Mint = ModInt<mod1000000007>;
// ===== factorial_table.hpp =====
#include <vector>
#include <cassert>
template <typename T>
class FactorialTable {
std::vector<T> fac;
std::vector<T> ifac;
public:
FactorialTable() : fac(1, T(1)), ifac(1, T(1)) {}
FactorialTable(int n) : fac(n + 1), ifac(n + 1) {
assert(n >= 0);
fac[0] = T(1);
for (int i = 1; i <= n; ++i) {
fac[i] = fac[i - 1] * T(i);
}
ifac[n] = T(1) / T(fac[n]);
for (int i = n; i > 0; --i) {
ifac[i - 1] = ifac[i] * T(i);
}
}
void resize(int n) {
int old = n_max();
if (n <= old) {
return;
}
fac.resize(n + 1);
for (int i = old + 1; i <= n; ++i) {
fac[i] = fac[i - 1] * T(i);
}
ifac.resize(n + 1);
ifac[n] = T(1) / T(fac[n]);
for (int i = n; i > old; --i) {
ifac[i - 1] = ifac[i] * T(i);
}
}
inline int n_max() const {
return static_cast<int>(fac.size() - 1);
}
inline T fact(int n) const {
assert(n >= 0 && n <= n_max());
return fac[n];
}
inline T inv_fact(int n) const {
assert(n >= 0 && n <= n_max());
return ifac[n];
}
inline T choose(int n, int k) const {
assert(k <= n_max() && n <= n_max());
if (k > n || k < 0) {
return T(0);
}
return fac[n] * ifac[k] * ifac[n - k];
}
inline T multi_choose(int n, int k) const {
assert(n >= 1 && k >= 0 && k + n - 1 <= n_max());
return choose(k + n - 1, k);
}
inline T n_terms_sum_k(int n, int k) const {
assert(n >= 0);
if (k < 0) {
return T(0);
}
if (n == 0) {
return k == 0 ? T(1) : T(0);
}
return choose(n + k - 1, n - 1);
}
};
// ===== factorial_table.hpp =====
int main() {
i32 n, m;
cin >> n >> m;
Vec<i32> a(n);
REP(i, n) {
cin >> a[i];
--a[i];
}
FactorialTable<Mint> table(n);
Vec<i32> cycle_cnt(n + 1, 0);
{
Vec<bool> checked(n, false);
REP(i, n) {
if (checked[i]) {
continue;
}
i32 cur = i, cnt = 0;
while (!checked[cur]) {
checked[cur] = true;
++cnt;
cur = a[cur];
}
++cycle_cnt[cnt];
}
}
DBG(cycle_cnt);
Vec<Vec<pair<i32, Mint>>> gens(n + 1);
REP(i, 1, n + 1) {
i32 gc = gcd(i, m);
gens[i / gc].emplace_back(gc, Mint(i / gc).pow(gc - 1));
}
DBG(gens);
Mint ans(1);
REP(i, 1, n + 1) {
Vec<Mint> dp(cycle_cnt[i] + 1);
dp[0] = Mint(1);
for (auto [cnt, wgt] : gens[i]) {
Vec<Mint> ndp(cycle_cnt[i] + 1);
REP(j, cycle_cnt[i] + 1) {
for (i32 k = 0; j + k * cnt <= cycle_cnt[i]; ++k) {
ndp[j + k * cnt] += dp[j] * table.choose(cycle_cnt[i] - j, k * cnt) * table.fact(k * cnt) * table.inv_fact(cnt).pow(k) * table
                        .inv_fact(k) * wgt.pow(k);
}
}
/*REP(j, cycle_cnt[i] - cnt + 1) {
dp[j + cnt] += dp[j] * wgt * table.inv_fact(cnt);
}*/
dp = ndp;
DBG(dp);
}
DBG(dp);
ans *= dp[cycle_cnt[i]];
//ans *= dp[cycle_cnt[i]] * table.fact(cycle_cnt[i]);
}
cout << ans << '\n';
}
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