#578105 (C++17) No.1303 Inconvenient Kingdom

提出ソース

結果

問題	No.1303 Inconvenient Kingdom
ユーザー	nok0
提出日時	2020-11-09 22:58:57
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,431 ms / 3,000 ms
コード長	15,099 bytes
コンパイル時間	3,282 ms
コンパイル使用メモリ	254,628 KB
実行使用メモリ	12,160 KB
最終ジャッジ日時	2024-07-22 16:23:37
合計ジャッジ時間	24,875 ms
ジャッジサーバーID （参考情報）	judge4 / judge2

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 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	1 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	AC	3 ms 5,376 KB
testcase_07	AC	4 ms 5,376 KB
testcase_08	AC	4 ms 5,376 KB
testcase_09	AC	1,180 ms 12,032 KB
testcase_10	AC	1,175 ms 12,032 KB
testcase_11	AC	1,253 ms 12,032 KB
testcase_12	AC	1,299 ms 12,160 KB
testcase_13	AC	1,390 ms 12,032 KB
testcase_14	AC	1,410 ms 11,904 KB
testcase_15	AC	1,428 ms 11,904 KB
testcase_16	AC	1,394 ms 11,904 KB
testcase_17	AC	1,431 ms 12,160 KB
testcase_18	AC	917 ms 12,032 KB
testcase_19	AC	912 ms 12,160 KB
testcase_20	AC	902 ms 12,032 KB
testcase_21	AC	558 ms 11,904 KB
testcase_22	AC	1,084 ms 12,032 KB
testcase_23	AC	1,290 ms 11,904 KB
testcase_24	AC	1,314 ms 11,904 KB
testcase_25	AC	1,315 ms 12,032 KB
testcase_26	AC	3 ms 5,376 KB
testcase_27	AC	2 ms 5,376 KB
testcase_28	AC	3 ms 5,376 KB
testcase_29	AC	2 ms 5,376 KB
testcase_30	AC	2 ms 5,376 KB
testcase_31	AC	1 ms 5,376 KB
testcase_32	AC	1 ms 5,376 KB
testcase_33	AC	1 ms 5,376 KB
testcase_34	AC	2 ms 5,376 KB
testcase_35	AC	2 ms 5,376 KB
testcase_36	AC	2 ms 5,376 KB
testcase_37	AC	2 ms 5,376 KB

権限があれば一括ダウンロードができます

ソースコード

raw source code

/**
 *	author: nok0
 *	created: 2020.10.05 18:09:46
**/
#ifdef LOCAL
#define _GLIBCXX_DEBUG
#endif
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
#define FOR(i, l, r) for(int i = (l); i < (r); ++i)
#define REP(i, n) FOR(i, 0, n)
#define REPS(i, n) FOR(i, 1, n + 1)
#define RFOR(i, l, r) for(int i = (l); i >= (r); --i)
#define RREP(i, n) RFOR(i, n - 1, 0)
#define RREPS(i, n) RFOR(i, n, 1)
#define pb push_back
#define eb emplace_back
#define SZ(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
template <class T = int>
using V = vector<T>;
template <class T = int>
using VV = V<V<T>>;
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
#define VEC(type, name, size) \
	V<type> name(size);       \
	IN(name)
#define VVEC(type, name, h, w)    \
	VV<type> name(h, V<type>(w)); \
	IN(name)
#define INT(...)     \
	int __VA_ARGS__; \
	IN(__VA_ARGS__)
#define LL(...)     \
	ll __VA_ARGS__; \
	IN(__VA_ARGS__)
#define STR(...)        \
	string __VA_ARGS__; \
	IN(__VA_ARGS__)
#define CHAR(...)     \
	char __VA_ARGS__; \
	IN(__VA_ARGS__)
#define DOUBLE(...)     \
	DOUBLE __VA_ARGS__; \
	IN(__VA_ARGS__)
#define LD(...)     \
	LD __VA_ARGS__; \
	IN(__VA_ARGS__)
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(long double &a) { cin >> a; }
void scan(char a[]) { scanf("%s", a); }
void scan(string &a) { cin >> a; }
template <class T>
void scan(V<T> &);
template <class T, class L>
void scan(pair<T, L> &);
template <class T>
void scan(V<T> &a) {
	for(auto &i : a) scan(i);
}
template <class T, class L>
void scan(pair<T, L> &p) {
	scan(p.first);
	scan(p.second);
}
template <class T>
void scan(T &a) { cin >> a; }
void IN() {}
template <class Head, class... Tail>
void IN(Head &head, Tail &... tail) {
	scan(head);
	IN(tail...);
}
template <class T>
inline void print(T x) { cout << x << '\n'; }
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
	is >> p.first >> p.second;
	return is;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
	os << p.first << " " << p.second;
	return os;
}
template <class T>
ostream &operator<<(ostream &os, const V<T> &v) {
	REP(i, SZ(v)) {
		if(i) os << " ";
		os << v[i];
	}
	return os;
}
//debug
template <typename T>
void view(const V<T> &v) {
	cerr << "{ ";
	for(const auto &e : v) {
		cerr << e << ", ";
	}
	cerr << "\b\b }";
}
template <typename T>
void view(const VV<T> &vv) {
	cerr << "{\n";
	for(const auto &v : vv) {
		cerr << "\t";
		view(v);
		cerr << "\n";
	}
	cerr << "}";
}
template <typename T, typename U>
void view(const V<pair<T, U>> &v) {
	cerr << "{\n";
	for(const auto &c : v) cerr << "\t(" << c.first << ", " << c.second << ")\n";
	cerr << "}";
}
template <typename T, typename U>
void view(const map<T, U> &m) {
	cerr << "{\n";
	for(auto &t : m) cerr << "\t[" << t.first << "] : " << t.second << "\n";
	cerr << "}";
}
template <typename T, typename U>
void view(const pair<T, U> &p) { cerr << "(" << p.first << ", " << p.second << ")"; }
template <typename T>
void view(const set<T> &s) {
	cerr << "{ ";
	for(auto &t : s) {
		view(t);
		cerr << ", ";
	}
	cerr << "\b\b }";
}
template <typename T>
void view(T e) { cerr << e; }
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
	view(H);
	cerr << ", ";
	debug_out(T...);
}
#define debug(...)                                           \
	do {                                                     \
		cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
		debug_out(__VA_ARGS__);                              \
		cerr << "\b\b]\n";                                   \
	} while(0)
#else
#define debug(...) (void(0))
#endif
template <class T>
V<T> press(V<T> &x) {
	V<T> res = x;
	sort(all(res));
	res.erase(unique(all(res)), res.end());
	REP(i, SZ(x)) {
		x[i] = lower_bound(all(res), x[i]) - res.begin();
	}
	return res;
}
template <class T>
inline bool chmin(T &a, T b) {
	if(a > b) {
		a = b;
		return true;
	}
	return false;
}
template <class T>
inline bool chmax(T &a, T b) {
	if(a < b) {
		a = b;
		return true;
	}
	return false;
}
inline void Yes(bool b = true) { cout << (b ? "Yes" : "No") << '\n'; }
inline void YES(bool b = true) { cout << (b ? "YES" : "NO") << '\n'; }
inline void err(bool b = true) {
	if(b) {
		cout << -1 << '\n';
		exit(0);
	}
}
template <class T>
inline void fin(bool b = true, T e = 0) {
	if(b) {
		cout << e << '\n';
		exit(0);
	}
}
template <class T>
T divup(T x, T y) { return (x + (y - 1)) / y; }
template <typename T>
T pow(T a, long long n, T e = 1) {
	T ret = e;
	while(n) {
		if(n & 1) ret *= a;
		a *= a;
		n >>= 1;
	}
	return ret;
}
struct iofast {
	iofast() {
		ios::sync_with_stdio(false);
		cin.tie(nullptr);
		cout << fixed << setprecision(15);
	}
} iofast_;
const int inf = 1e9;
const ll INF = 1e18;
#pragma endregion

struct UnionFind {
private:
	std::vector<int> par;

public:
	UnionFind() = default;

	UnionFind(size_t n)
	  : par(n, -1) {}

	int root(int x) {
		if(par[x] < 0) return x;
		return par[x] = root(par[x]);
	}

	bool same(int x, int y) { return root(x) == root(y); }

	bool unite(int x, int y) {
		x = root(x);
		y = root(y);
		if(x == y) return false;
		if(par[x] > par[y]) std::swap(x, y);
		par[x] += par[y];
		par[y] = x;
		return true;
	}

	size_t size(int x) { return -par[root(x)]; }

	size_t size() const { return par.size(); }
};

template <class T>
struct Matrix {
private:
	std::vector<std::vector<T>> A;

	static Matrix I(size_t n) {
		Matrix mat(n);
		for(int i = 0; i < n; i++) mat[i][i] = 1;
		return mat;
	}

public:
	Matrix() = default;

	Matrix(std::vector<std::vector<T>> &vvec) { A = vvec; }

	Matrix(size_t n, size_t m) : A(n, std::vector<T>(m, 0)) {}

	Matrix(size_t n, size_t m, T init) : A(n, std::vector<T>(m, init)) {}

	Matrix(size_t n, std::vector<T> &vec) : A(n, vec) {}

	Matrix(size_t n) : A(n, std::vector<T>(n, 0)) {}

	size_t height() const { return A.size(); }

	size_t width() const { return A[0].size(); }

	inline const std::vector<T> &operator[](int k) const {
		return A[k];
	}

	inline std::vector<T> &operator[](int k) {
		return A[k];
	}

	Matrix &operator+=(const Matrix &B) {
		size_t n = height(), m = width();
		assert(n == B.height() and m == B.width());
		for(int i = 0; i < n; i++)
			for(int j = 0; j < m; j++)
				(*this)[i][j] += B[i][j];
		return *this;
	}

	Matrix &operator-=(const Matrix &B) {
		size_t n = height(), m = width();
		assert(n == B.height() and m == B.width());
		for(int i = 0; i < n; i++)
			for(int j = 0; j < m; j++)
				(*this)[i][j] -= B[i][j];
		return *this;
	}

	Matrix &operator*=(const Matrix &B) {
		size_t n = height(), m = B.width(), p = width();
		assert(p == B.height());
		std::vector<std::vector<T>> C(n, std::vector<T>(m, 0));
		for(int i = 0; i < n; i++)
			for(int j = 0; j < m; j++)
				for(int k = 0; k < p; k++)
					C[i][j] += (*this)[i][k] * B[k][j];
		A.swap(C);
		return *this;
	}

	Matrix &operator^=(long long k) {
		Matrix B = Matrix::I(height());
		while(k > 0) {
			if(k & 1) B *= (*this);
			*this *= *this;
			k >>= 1ll;
		}
		A.swap(B.A);
		return *this;
	}

	bool operator==(const Matrix &B) {
		size_t n = height(), m = width();
		if(n != B.height() or m != B.width()) return false;
		for(int i = 0; i < n; i++)
			for(int j = 0; j < m; j++)
				if((*this)[i][j] != B[i][j]) return false;
		return true;
	}

	Matrix operator+(const Matrix &B) const {
		return (Matrix(*this) += B);
	}

	Matrix operator-(const Matrix &B) const {
		return (Matrix(*this) -= B);
	}

	Matrix operator*(const Matrix &B) const {
		return (Matrix(*this) *= B);
	}

	Matrix operator^(const long long &k) const {
		return (Matrix(*this) ^= k);
	}

	Matrix &operator+=(const T &t) {
		int n = height(), m = width();
		for(int i = 0; i < n; i++)
			for(int j = 0; j < m; j++)
				(*this)[i][j] += t;
		return *this;
	}

	Matrix &operator-=(const T &t) {
		int n = height(), m = width();
		for(int i = 0; i < n; i++)
			for(int j = 0; j < m; j++)
				(*this)[i][j] -= t;
		return *this;
	}

	Matrix &operator*=(const T &t) {
		int n = height(), m = width();
		for(int i = 0; i < n; i++)
			for(int j = 0; j < m; j++)
				(*this)[i][j] *= t;
		return *this;
	}

	Matrix &operator/=(const T &t) {
		int n = height(), m = width();
		for(int i = 0; i < n; i++)
			for(int j = 0; j < m; j++)
				(*this)[i][j] /= t;
		return *this;
	}

	Matrix operator+(const T &t) const {
		return (Matrix(*this) += t);
	}

	Matrix operator-(const T &t) const {
		return (Matrix(*this) -= t);
	}

	Matrix operator*(const T &t) const {
		return (Matrix(*this) *= t);
	}

	Matrix operator/(const T &t) const {
		return (Matrix(*this) /= t);
	}

	friend std::ostream &operator<<(std::ostream &os, Matrix &p) {
		size_t n = p.height(), m = p.width();
		for(int i = 0; i < n; i++) {
			os << '[';
			for(int j = 0; j < m; j++)
				os << p[i][j] << (j == m - 1 ? "]\n" : ",");
		}
		return (os);
	}

	T determinant() {
		Matrix B(*this);
		size_t n = height(), m = width();
		assert(n == m);
		T ret = 1;
		for(int i = 0; i < n; i++) {
			int idx = -1;
			for(int j = i; j < n; j++)
				if(B[j][i] != 0) idx = j;
			if(idx == -1) return 0;
			if(i != idx) {
				ret *= -1;
				swap(B[i], B[idx]);
			}
			ret *= B[i][i];
			T vv = B[i][i];
			for(int j = 0; j < n; j++) B[i][j] /= vv;
			for(int j = i + 1; j < n; j++) {
				T a = B[j][i];
				for(int k = 0; k < n; k++) {
					B[j][k] -= B[i][k] * a;
				}
			}
		}
		return ret;
	}

	Matrix inv() {
		int n = height();
		if(determinant() == T(0)) return Matrix(0);
		Matrix a(*(this)), l = I(n), u(n);
		for(int j = 0; j < n; j++) u[0][j] = a[0][j];
		for(int j = 1; j < n; j++) l[j][0] = a[j][0] / u[0][0];
		for(int k = 1; k < n; k++) {
			for(int j = k; j < n; j++)
				for(int i = 0; i < k; i++) a[j][k] -= l[j][i] * u[i][k];
			u[k][k] = a[k][k];
			for(int j = k + 1; j < n; j++) {
				u[k][j] = a[k][j];
				for(int i = 0; i < k; i++)
					u[k][j] -= l[k][i] * u[i][j];
			}
			for(int j = k + 1; j < n; j++) l[j][k] = a[j][k] / u[k][k];
		}
		Matrix x(n), y = I(n);
		for(int i = 0; i < n; i++)
			for(int j = 0; j < n; j++) {
				for(int k = 0; k < j; k++) y[j][i] -= l[j][k] * y[k][i];
			}
		T sigma;
		for(int h = 0; h < n; h++)
			for(int i = n - 1; i >= 0; i--) {
				sigma = y[i][h];
				for(int j = i + 1; j < n; j++) {
					sigma -= u[i][j] * x[j][h];
				}
				x[i][h] = sigma / u[i][i];
			}
		return move(x);
	}
};

//ModInt
template <const int &mod>
struct ModInt {
private:
	long long x;

	long long ext_gcd(long long a, long long b, long long &x, long long &y) {
		if(b == 0) {
			x = 1, y = 0;
			return a;
		}
		long long q = a / b;
		long long g = ext_gcd(b, a - q * b, x, y);
		long long z = x - q * y;
		x = y, y = z;
		return g;
	}

public:
	ModInt() : x(0) {}

	ModInt(long long x_) {
		if((x = x_ % mod + mod) >= mod) x -= mod;
	}

	constexpr ModInt &operator+=(ModInt rhs) {
		if((x += rhs.x) >= mod) x -= mod;
		return *this;
	}

	constexpr ModInt &operator-=(ModInt rhs) {
		if((x -= rhs.x) < 0) x += mod;
		return *this;
	}

	constexpr ModInt &operator*=(ModInt rhs) {
		x = (unsigned long long)x * rhs.x % mod;
		return *this;
	}

	constexpr ModInt &operator/=(ModInt rhs) {
		x = (unsigned long long)x * rhs.inv().x % mod;
		return *this;
	}

	constexpr ModInt operator-() const noexcept { return -x < 0 ? mod - x : -x; }

	constexpr ModInt operator+(ModInt rhs) const noexcept { return ModInt(*this) += rhs; }

	constexpr ModInt operator-(ModInt rhs) const noexcept { return ModInt(*this) -= rhs; }

	constexpr ModInt operator*(ModInt rhs) const noexcept { return ModInt(*this) *= rhs; }

	constexpr ModInt operator/(ModInt rhs) const noexcept { return ModInt(*this) /= rhs; }

	constexpr ModInt &operator++() {
		*this += 1;
		return *this;
	}

	constexpr ModInt operator++(int) {
		*this += 1;
		return *this - 1;
	}

	constexpr ModInt &operator--() {
		*this -= 1;
		return *this;
	}

	constexpr ModInt operator--(int) {
		*this -= 1;
		return *this + 1;
	}

	bool operator==(ModInt rhs) const { return x == rhs.x; }

	bool operator!=(ModInt rhs) const { return x != rhs.x; }

	bool operator<=(ModInt rhs) const { return x <= rhs.x; }

	bool operator>=(ModInt rhs) const { return x >= rhs.x; }

	bool operator<(ModInt rhs) const { return x < rhs.x; }

	bool operator>(ModInt rhs) const { return x > rhs.x; }

	ModInt inv() {
		long long x, y;
		ext_gcd(this->x, mod, x, y);
		return (ModInt)x;
	}

	friend std::ostream &operator<<(std::ostream &s, ModInt<mod> a) {
		s << a.x;
		return s;
	}

	friend std::istream &operator>>(std::istream &s, ModInt<mod> &a) {
		s >> a.x;
		return s;
	}
};

//Modulo Calculation
static int MOD = 998244353;
using mint = ModInt<MOD>;

int main() {
	INT(n, m);
	int connect = n, inconv = 0;
	mint pat = 1;
	UnionFind uf(n);
	V<> a(m), b(m);
	V<> h(n, 0);
	REP(i, m) {
		INT(x, y);
		x--, y--;
		if(x > y) swap(x, y);
		a[i] = x, b[i] = y;
		h[x]++, h[y]++;
		if(!uf.same(x, y)) connect--;
		uf.unite(x, y);
	}
	V<bool> used(n, 0);
	V<int> siz;
	REP(i, n) {
		if(used[uf.root(i)]) continue;
		used[uf.root(i)] = 1;
		siz.pb(uf.size(i));
	}
	if(connect == 1) {
		inconv = 0;
		Matrix<mint> mat(n), nm(n - 1);
		REP(i, n)
		mat[i][i] = h[i];
		REP(i, m) {
			mat[a[i]][b[i]]--;
			mat[b[i]][a[i]]--;
		}
		REP(i, n - 1)
		REP(j, n - 1)
		nm[i][j] = mat[i][j];
		pat = nm.determinant();
		V<Matrix<mint>> vec(n);
		REP(k, n) {
			Matrix<mint> nmat(n - 1);
			int icnt = -1;
			REP(i, n) {
				if(i == k) continue;
				icnt++;
				int jcnt = -1;
				REP(j, n) {
					if(j == k) continue;
					jcnt++;
					nmat[icnt][jcnt] = mat[i][j];
				}
			}
			vec[k] = nmat.inv() * nmat.determinant();
		}
		REP(i, n)
		debug(vec[i]);
		for(int i = 0; i < n - 1; i++)
			for(int j = i + 1; j < n; j++) {
				if(mat[i][j] != 0) continue;
				pat += vec[i][j - 1][j - 1];
			}
	} else {
		sort(rall(siz));
		int fircount = 0, seccount = 0;
		int fir = siz[0], sec = siz[1];
		inconv += (n - (siz[0] + siz[1])) * (siz[0] + siz[1]);
		for(int i = 2; i < siz.size(); i++) {
			inconv += (n - siz[i]) * siz[i];
		}
		REP(i, SZ(siz)) {
			if(siz[i] == fir) fircount++;
			if(siz[i] == sec) seccount++;
		}
		map<int, pair<V<>, V<pii>>> mp;
		REP(i, m) {
			int r = uf.root(a[i]);
			mp[r].first.pb(a[i]);
			mp[r].first.pb(b[i]);
			mp[r].second.eb(a[i], b[i]);
		}
		for(auto v : mp) {
			auto &tyo = v.second.first;
			auto &hen = v.second.second;
			V<> res = press(tyo);
			int sz = SZ(res);
			map<int, int> changer;
			REP(i, sz)
			changer[res[i]] = i;
			Matrix<mint> mat(sz), nmat(sz - 1);
			REP(i, SZ(hen)) {
				auto [a, b] = hen[i];
				a = changer[a], b = changer[b];
				mat[a][a]++, mat[b][b]++, mat[a][b]--, mat[b][a]--;
			}
			REP(i, sz - 1)
			REP(j, sz - 1)
			nmat[i][j] = mat[i][j];
			mint nowp = nmat.determinant();
			pat *= nowp;
		}
		if(fir != sec) {
			pat *= fir * sec * seccount;
		} else {
			pat *= fir * fir * fircount * (fircount - 1) / 2;
		}
	}
	print(inconv);
	print(pat);
}

yukicoder

結果

テストケース

ソースコード