#620946 (C++17) No.1392 Don't be together

提出ソース

結果

問題	No.1392 Don't be together
ユーザー	kaage
提出日時	2021-02-21 16:54:04
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	464 ms / 2,000 ms
コード長	11,405 bytes
コンパイル時間	2,422 ms
コンパイル使用メモリ	169,656 KB
実行使用メモリ	199,296 KB
最終ジャッジ日時	2024-09-19 14:52:37
合計ジャッジ時間	8,073 ms
ジャッジサーバーID （参考情報）	judge4 / judge5

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 6,812 KB
testcase_01	AC	1 ms 6,944 KB
testcase_02	AC	1 ms 6,940 KB
testcase_03	AC	1 ms 6,940 KB
testcase_04	AC	1 ms 6,940 KB
testcase_05	AC	1 ms 6,940 KB
testcase_06	AC	204 ms 83,712 KB
testcase_07	AC	345 ms 160,896 KB
testcase_08	AC	316 ms 141,952 KB
testcase_09	AC	464 ms 199,296 KB
testcase_10	AC	203 ms 97,664 KB
testcase_11	AC	325 ms 152,576 KB
testcase_12	AC	190 ms 91,392 KB
testcase_13	AC	273 ms 127,360 KB
testcase_14	AC	299 ms 141,428 KB
testcase_15	AC	200 ms 96,128 KB
testcase_16	AC	317 ms 154,112 KB
testcase_17	AC	211 ms 102,912 KB
testcase_18	AC	288 ms 138,240 KB
testcase_19	AC	258 ms 122,880 KB
testcase_20	AC	106 ms 78,244 KB
testcase_21	AC	40 ms 52,548 KB
testcase_22	AC	168 ms 96,096 KB
testcase_23	AC	114 ms 74,852 KB
testcase_24	AC	69 ms 45,768 KB
testcase_25	AC	124 ms 79,552 KB
testcase_26	AC	34 ms 39,672 KB
testcase_27	AC	45 ms 38,760 KB
testcase_28	AC	140 ms 92,788 KB
testcase_29	AC	69 ms 65,244 KB

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ソースコード

raw source code

#line 2 "library/other/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#ifdef ONLINE_JUDGE
#pragma GCC target("avx512f")
#elif defined EVAL
#else
#pragma GCC target("avx2")
#endif
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <string.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define rep(i, n) for (int i = 0; i < (n); i++)
#define REP(i, n) for (int i = 1; i <= (n); i++)
#define all(V) V.begin(), V.end()

using i128 = __int128_t;
using u128 = __uint128_t;
using uint = unsigned int;
using lint = long long;
using ulint = unsigned long long;
using IP = std::pair<int, int>;
using LP = std::pair<lint, lint>;

constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = DBL_EPSILON;
constexpr double PI = 3.141592653589793238462643383279;

template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {
};
template <class F>
inline constexpr decltype(auto) lambda_fix(F&& f) {
	return [f = std::forward<F>(f)](auto&&... args) {
		return f(f, std::forward<decltype(args)>(args)...);
	};
}
template <class T>
constexpr std::vector<T> make_vec(size_t n) {
	return std::vector<T>(n);
}
template <class T, class... Args>
constexpr auto make_vec(size_t n, Args&&... args) {
	return std::vector<decltype(make_vec<T>(args...))>(
		n, make_vec<T>(std::forward<Args>(args)...));
}
template <class T, class U>
constexpr inline bool chmax(T& lhs, const U& rhs) {
	if (lhs < rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
template <class T, class U>
constexpr inline bool chmin(T& lhs, const U& rhs) {
	if (lhs > rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
constexpr inline lint gcd(lint a, lint b) {
	while (b) {
		lint c = a;
		a = b;
		b = c % b;
	}
	return a;
}
inline lint lcm(lint a, lint b) { return a / gcd(a, b) * b; }
constexpr bool isprime(lint n) {
	if (n == 1) return false;
	for (int i = 2; i * i <= n; i++) {
		if (n % i == 0) return false;
	}
	return true;
}
template <class T>
constexpr T mypow(T a, lint b) {
	T res(1);
	while (true) {
		if (b & 1) res *= a;
		b >>= 1;
		if (!b) break;
		a *= a;
	}
	return res;
}
constexpr lint modpow(lint a, lint b, lint m) {
	a %= m;
	lint res(1);
	while (b) {
		if (b & 1) {
			res *= a;
			res %= m;
		}
		a *= a;
		a %= m;
		b >>= 1;
	}
	return res;
}
template <class T>
constexpr void printArray(const std::vector<T>& vec, char split = ' ') {
	rep(i, vec.size()) {
		std::cout << vec[i];
		std::cout << (i == (int)vec.size() - 1 ? '\n' : split);
	}
}
template <class InputIter>
constexpr void printArray(InputIter l, InputIter r, char split = ' ') {
	auto rprev = std::prev(r);
	for (auto i = l; i != r; i++) {
		std::cout << *i;
		std::cout << (i == rprev ? '\n' : split);
	}
}
LP extGcd(lint a, lint b) {
	if (b == 0) return {1, 0};
	LP s = extGcd(b, a % b);
	std::swap(s.first, s.second);
	s.second -= a / b * s.first;
	return s;
}
LP ChineseRem(const lint& b1, const lint& m1, const lint& b2, const lint& m2) {
	lint p = extGcd(m1, m2).first;
	lint tmp = (b2 - b1) * p % m2;
	lint r = (b1 + m1 * tmp + m1 * m2) % (m1 * m2);
	return {r, m1 * m2};
}
int LCS(const std::string& a, const std::string& b) {
	auto dp = make_vec<int>(a.size() + 1, b.size() + 1);
	rep(i, a.size()) {
		rep(j, b.size()) {
			chmax(dp[i + 1][j], dp[i][j]);
			chmax(dp[i][j + 1], dp[i][j]);
			if (a[i] == b[j]) chmax(dp[i + 1][j + 1], dp[i][j] + 1);
		}
		chmax(dp[i + 1][b.size()], dp[i][b.size()]);
	}
	rep(j, b.size()) chmax(dp[a.size()][j + 1], dp[a.size()][j]);
	return dp[a.size()][b.size()];
}
template <class T, std::enable_if_t<std::is_convertible<int, T>::value,
									std::nullptr_t> = nullptr>
void compress(std::vector<T>& vec) {
	auto tmp = vec;
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (T& i : vec) i = std::lower_bound(all(tmp), i) - tmp.begin();
}
template <class T>
void compress(T* l, T* r) {
	std::vector<T> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
template <class InputIter>
void compress(InputIter l, InputIter r) {
	std::vector<typename InputIter::value_type> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
#line 3 "library/other/type_traits.hpp"

class ModInt__Base {};
class StaticModInt__Base : ModInt__Base {};
class DynamicModInt__Base : ModInt__Base {};

template <class T>
class is_ModInt : public std::is_base_of<ModInt__Base, T> {};
template <class T>
constexpr bool is_ModInt_v = is_ModInt<T>::value;

template <class T>
class is_StaticModInt : public std::is_base_of<StaticModInt__Base, T> {};
template <class T>
constexpr bool is_StaticModInt_v = is_StaticModInt<T>::value;

template <class T>
class is_DynamicModInt : public std::is_base_of<DynamicModInt__Base, T> {};
template <class T>
constexpr bool is_DynamicModInt_v = is_DynamicModInt<T>::value;
#line 4 "library/algebraic/StaticModInt.hpp"
template <uint modulo>
class StaticModInt : StaticModInt__Base {
	std::conditional_t<(modulo > INT_MAX >> 1), lint, int> value;

  public:
	static constexpr uint mod_value = modulo;
	constexpr StaticModInt() : value(0) {}
	template <class T,
			  std::enable_if_t<!std::is_convertible<T, StaticModInt>::value,
							   std::nullptr_t> = nullptr>
	constexpr StaticModInt(T value = 0) : value(value) {
		this->value =
			(value < 0 ? -(-value % modulo) + modulo : lint(value)) % modulo;
	}
	inline constexpr StaticModInt inv() const {
		return mypow(*this, modulo - 2);
	}
	inline constexpr operator int() const { return value; }
	inline constexpr StaticModInt& operator+=(const StaticModInt& x) {
		value = value + x.value;
		if (value >= modulo) value -= modulo;
		return *this;
	}
	inline constexpr StaticModInt& operator++() {
		if (value == modulo - 1)
			value = 0;
		else
			value++;
		return *this;
	}
	inline constexpr StaticModInt operator++(int) {
		StaticModInt res = *this;
		++*this;
		return res;
	}
	inline constexpr StaticModInt operator-() const {
		return StaticModInt(0) -= *this;
	}
	inline constexpr StaticModInt& operator-=(const StaticModInt& x) {
		value -= x.value;
		if (value < 0) value += modulo;
		return *this;
	}
	inline constexpr StaticModInt& operator--() {
		if (value == 0)
			value = modulo - 1;
		else
			value--;
		return *this;
	}
	inline constexpr StaticModInt operator--(int) {
		StaticModInt res = *this;
		--*this;
		return res;
	}
	inline constexpr StaticModInt& operator*=(const StaticModInt& x) {
		value = (lint)value * x.value % modulo;
		return *this;
	}
	inline constexpr StaticModInt& operator/=(const StaticModInt& rhs) {
		return *this *= rhs.inv();
	}
	template <class T>
	constexpr StaticModInt operator+(const T& rhs) const {
		return StaticModInt(*this) += rhs;
	}
	template <class T>
	constexpr StaticModInt& operator+=(const T& rhs) {
		return operator+=(StaticModInt(rhs));
	}
	template <class T>
	constexpr StaticModInt operator-(const T& rhs) const {
		return StaticModInt(*this) -= rhs;
	}
	template <class T>
	constexpr StaticModInt& operator-=(const T& rhs) {
		return operator-=(StaticModInt(rhs));
	}
	template <class T>
	constexpr StaticModInt operator*(const T& rhs) const {
		return StaticModInt(*this) *= rhs;
	}
	template <class T>
	constexpr StaticModInt& operator*=(const T& rhs) {
		return operator*=(StaticModInt(rhs));
	}
	template <class T>
	constexpr StaticModInt operator/(const T& rhs) const {
		return StaticModInt(*this) /= rhs;
	}
	template <class T>
	constexpr StaticModInt& operator/=(const T& rhs) {
		return operator/=(StaticModInt(rhs));
	}
	static int primitive_root() {
		static int p = 0;
		static std::random_device rd;
		static std::mt19937 mt(rd());
		static std::uniform_int_distribution<> uid(1, modulo - 1);
		if (p) return 0;

		// use naive factorize due to file size limit
		std::vector<int> vec;
		int tmp = modulo - 1;
		for (int i = 2; i * i <= tmp; i++) {
			if (tmp % i == 0) {
				vec.emplace_back(i);
				do {
					tmp /= i;
				} while (tmp % i == 0);
			}
		}
		if (tmp != 1) vec.emplace_back(tmp);

		vec.erase(std::unique(all(vec)), vec.end());
		while (true) {
			p = uid(mt);
			bool f = true;
			for (const auto& i : vec) {
				if (mypow(StaticModInt(p), (modulo - 1) / i) == 1) {
					f = false;
					break;
				}
			}
			if (f) return p;
		}
	}
};
template <uint modulo>
std::istream& operator>>(std::istream& ist, StaticModInt<modulo>& x) {
	lint a;
	ist >> a;
	x = a;
	return ist;
}

/**
 * @title StaticModInt
 */
#line 5 "library/algebraic/Combinatorics.hpp"
template <typename T>
class Combinatorics {
  protected:
	std::vector<T> factorial;
	void append(int n) noexcept {
		while (factorial.size() <= n) {
			factorial.emplace_back(factorial.back() * factorial.size());
		}
	}

  public:
	Combinatorics() noexcept : factorial(1, 1) {}
	Combinatorics(int n) noexcept : factorial(1, 1) { append(n); }
	virtual T get_comb(int a, int b) noexcept {
		append(a);
		return factorial[a] / factorial[a - b] / factorial[b];
	}
	virtual T get_dcomb(int a, int b) noexcept { return get_comb(a + b - 1, b); }
};
template <typename T, typename std::enable_if_t<is_ModInt<T>::value,
												std::nullptr_t> = nullptr>
class ModCombinatorics : Combinatorics<T> {
	using Combinatorics<T>::factorial;
	std::vector<T> inv;
	void append(int n) noexcept {
		int tmp = factorial.size();
		if (n < tmp) return;
		Combinatorics<T>::append(n);
		inv.resize(n + 1);
		inv[n] = T(1) / factorial.back();
		for (int i = n; i > tmp; i--) inv[i - 1] = inv[i] * i;
	}

  public:
	ModCombinatorics() noexcept : Combinatorics<T>(), inv(1, 1) {}
	ModCombinatorics(int n) noexcept : Combinatorics<T>(n), inv(1, 1) {
		append(n);
	}
	T get_comb(int a, int b) noexcept override {
		append(a);
		return factorial[a] * inv[a - b] * inv[b];
	}
	T get_dcomb(int a, int b) noexcept override {
		return get_comb(a + b - 1, b);
	}
	T perm(int a, int b) noexcept {
		append(a);
		return factorial[a] * inv[a - b];
	}
};

/**
 * @title Combinatorics/ModCombinatorics
 */
#line 4 "main.cpp"
using ModInt = StaticModInt<998244353>;
int N, M, P[5010];
ModInt dp[5010][5010][2];
std::vector<int> vec;
bool done[5010];
int main() {
	std::cin >> N >> M;
	REP(i, N) std::cin >> P[i];
	REP(i, N) {
		if (!done[i]) {
			int now = i, cnt = 0;
			do {
				done[now] = true;
				now = P[now];
				cnt++;
			} while (now != i);
			vec.emplace_back(cnt);
		}
	}
	REP(i, M) {
		dp[i][1][0] = 0, dp[i][1][1] = i;
		REP(j, N - 1) {
			dp[i][j + 1][0] += dp[i][j][0] * (i - 2);
			dp[i][j + 1][1] += dp[i][j][0];
			dp[i][j + 1][0] += dp[i][j][1] * (i - 1);
		}
	}
	ModCombinatorics<ModInt> comb;
	ModInt ans = 0;
	rep(i, M) {
		ModInt cnt = 1;
		for (const auto& j : vec) cnt *= dp[M - i][j][0];
		ans += cnt * comb.get_comb(M, i) * (i % 2 ? -1 : 1);
	}
	REP(i, M) ans /= i;
	std::cout << ans << std::endl;
	return 0;
}

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結果

テストケース

ソースコード