結果

問題 No.1364 [Renaming] Road to Cherry from Zelkova
コンテスト
ユーザー kaikey
提出日時 2021-01-23 00:26:14
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 216 ms / 2,500 ms
コード長 8,825 bytes
コンパイル時間 3,925 ms
コンパイル使用メモリ 235,164 KB
最終ジャッジ日時 2025-01-18 06:55:11
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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ファイルパターン 結果
sample AC * 3
other AC * 45
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

diff # 

#include <bits/stdc++.h>
#include <random>
using namespace std; typedef unsigned long long _ulong; typedef long long int lint; typedef pair<lint, lint> plint; typedef pair<double long, double long> pld;
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((lint)(x).size())
#define FOR(i, begin, end) for(lint i=(begin),i##_end_=(end);i<i##_end_;++i)
#define IFOR(i, begin, end) for(lint i=(end)-1,i##_begin_=(begin);i>=i##_begin_;--i)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
#define endk '\n'
#define fi first
#define se second
struct fast_ios { fast_ios() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
template<class T> auto add = [](T a, T b) -> T { return a + b; };
template<class T> auto f_max = [](T a, T b) -> T { return max(a, b); };
template<class T> auto f_min = [](T a, T b) -> T { return min(a, b); };
template<class T> using V = vector<T>;
using Vl = V<lint>; using VVl = V<Vl>;
template< typename T > ostream& operator<<(ostream& os, const vector< T >& v) {
	for (int i = 0; i < (int)v.size(); i++) os << v[i] << (i + 1 != v.size() ? " " : "");
	return os;
}
template< typename T >istream& operator>>(istream& is, vector< T >& v) {
	for (T& in : v) is >> in;
	return is;
}
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; }
lint gcd(lint a, lint b) { if (b == 0) return a; else return gcd(b, a % b); }
lint ceil(lint a, lint b) { return (a + b - 1) / b; }
lint digit(lint a) { return (lint)log10(a); }
lint e_dist(plint a, plint b) { return abs(a.fi - b.fi) * abs(a.fi - b.fi) + abs(a.se - b.se) * abs(a.se - b.se); }
lint m_dist(plint a, plint b) { return abs(a.fi - b.fi) + abs(a.se - b.se); }
void Worshall_Floyd(VVl& g) { REP(k, SZ(g)) REP(i, SZ(g)) REP(j, SZ(g)) chmin(g[i][j], g[i][k] + g[k][j]); }
const lint MOD = 1e9 + 7, INF = 1e9 + 1;
lint dx[8] = { 1, 0, -1, 0, 1, -1, 1, -1 }, dy[8] = { 0, 1, 0, -1, -1, -1, 1, 1 };
bool YN(bool flag) { cout << (flag ? "YES" : "NO") << endk; return flag; } bool yn(bool flag) { cout << (flag ? "Yes" : "No") << endk; return flag; }
struct Edge {
	lint from, to;
	lint cost;
	Edge(lint u, lint v, lint c) {
		cost = c;
		from = u;
		to = v;
	}
	bool operator<(const Edge& e) const {
		return cost < e.cost;
	}
};
struct WeightedEdge {
	lint to;
	lint cost;
	WeightedEdge(lint v, lint c = 1) {
		to = v;
		cost = c;
	}
	bool operator<(const WeightedEdge& e) const {
		return cost < e.cost;
	}
};
using WeightedGraph = V<V<WeightedEdge>>;
typedef pair<lint, plint> tlint;
typedef pair<plint, plint> qlint;
typedef pair<string, lint> valstring;


template <std::int_fast64_t Modulus>
class modint
{
	using u64 = std::int_fast64_t;

public:
	u64 a;
	constexpr modint(const u64 x = 0) noexcept : a(x% Modulus) {}
	constexpr u64& value() noexcept { return a; }
	constexpr const u64& value() const noexcept { return a; }
	constexpr modint operator+(const modint rhs) const noexcept
	{
		return modint(*this) += rhs;
	}
	constexpr modint operator-(const modint rhs) const noexcept
	{
		return modint(*this) -= rhs;
	}
	constexpr modint operator*(const modint rhs) const noexcept
	{
		return modint(*this) *= rhs;
	}
	constexpr modint operator/(const modint rhs) const noexcept
	{
		return modint(*this) /= rhs;
	}
	constexpr modint& operator+=(const modint rhs) noexcept
	{
		a += rhs.a;
		if (a >= Modulus)
		{
			a -= Modulus;
		}
		return *this;
	}
	constexpr modint& operator-=(const modint rhs) noexcept
	{
		if (a < rhs.a)
		{
			a += Modulus;
		}
		a -= rhs.a;
		return *this;
	}
	constexpr modint& operator*=(const modint rhs) noexcept
	{
		a = a * rhs.a % Modulus;
		return *this;
	}
	constexpr modint& operator/=(modint rhs) noexcept
	{
		u64 exp = Modulus - 2;
		while (exp)
		{
			if (exp % 2)
			{
				*this *= rhs;
			}
			rhs *= rhs;
			exp /= 2;
		}
		return *this;
	}
};
typedef modint<MOD> ModInt;

ModInt mod_pow(ModInt x, lint n) {
	ModInt ret = 1;
	while (n > 0) {
		if (n & 1) (ret *= x);
		(x *= x);
		n >>= 1;
	}
	return ret;
}

ModInt func[200000];
void funcinit(int N)
{
	func[0] = 1;
	for (int i = 1; i <= N; i++)
	{
		func[i] = func[i - 1] * i;
	}
}
ModInt comb(ModInt n, ModInt r)
{
	if (n.a <= 0 || n.a < r.a)
	{
		return 1;
	}
	return func[n.a] / (func[r.a] * func[(n - r).a]);
}

struct Topological_Sort {
public:

	Topological_Sort(int _n) : G(_n, Vl()), indegree(_n, 0), N(_n) {}

	void add_edge(int u, int v) {
		G[u].push_back(v);
		indegree[v]++;
	}

	Vl get() {
		Vl sorted_vertices;
		Vl tmp_indegree = indegree;
		queue<int> que;
		REP(i, N) {
			if (tmp_indegree[i] == 0) que.push(i);
		}

		while (!que.empty()) {
			int v = que.front(); que.pop();
			REP(i, SZ(G[v])) {
				int u = G[v][i];
				tmp_indegree[u]--;
				if (tmp_indegree[u] == 0) que.push(u);
			}
			sorted_vertices.push_back(v);
		}

		return sorted_vertices;
	}
private:
	VVl G;
	Vl indegree;
	int N;
};

struct UnionFind {
public:
	UnionFind() : _n(0) {}
	UnionFind(int n) : _n(n), parent_or_size(n, -1) {}

	int merge(int a, int b) {
		assert(0 <= a && a < _n);
		assert(0 <= b && b < _n);
		int x = leader(a), y = leader(b);
		if (x == y) return x;
		if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
		if (used_count) {
			if (count_in_set[x].size() < count_in_set[y].size()) {
				std::swap(count_in_set[x], count_in_set[y]);
			}
			for (auto p : count_in_set[y]) {
				count_in_set[x][p.first] += p.second;
			}
		}
		if (set_operate) {
			root_values[x] = f(root_values[y], root_values[x]);
		}
		parent_or_size[x] += parent_or_size[y];
		parent_or_size[y] = x;

		return x;
	}

	bool same(int a, int b) {
		assert(0 <= a && a < _n);
		assert(0 <= b && b < _n);
		return leader(a) == leader(b);
	}

	int leader(int a) {
		assert(0 <= a && a < _n);
		if (parent_or_size[a] < 0) return a;
		return parent_or_size[a] = leader(parent_or_size[a]);
	}

	int size(int a) {
		assert(0 <= a && a < _n);
		return -parent_or_size[leader(a)];
	}

	std::vector<std::vector<int>> groups() {
		std::vector<int> leader_buf(_n), group_size(_n);
		for (int i = 0; i < _n; i++) {
			leader_buf[i] = leader(i);
			group_size[leader_buf[i]]++;
		}
		std::vector<std::vector<int>> result(_n);
		for (int i = 0; i < _n; i++) {
			result[i].reserve(group_size[i]);
		}
		for (int i = 0; i < _n; i++) {
			result[leader_buf[i]].push_back(i);
		}
		result.erase(
			std::remove_if(result.begin(), result.end(),
				[&](const std::vector<int>& v) { return v.empty(); }),
			result.end());
		return result;
	}
	//update root calc
	//set by set operations
	void set_operate_and_value(std::vector<lint> array, function<lint(lint, lint)> _f) {
		f = _f;
		root_values = array;
		set_operate = true;
	}
	lint get_set_value(int a) {
		return root_values[leader(a)];
	}

	//regist count
	void regist_count(int a, int label) {
		if (!used_count) {
			used_count = true;
			count_in_set.assign(_n, std::map<int, int>());
		}
		count_in_set[leader(a)][label]++;
	}

	int get_count(int a, int label) {
		if (!used_count) return -1;
		return count_in_set[leader(a)][label];
	}

private:
	int _n;
	std::vector<int> parent_or_size;
	std::vector<std::map<int, int>> count_in_set;
	bool used_count = false;
	std::vector<lint> root_values;
	function<lint(lint, lint)> f;
	bool set_operate = false;
};


lint N, M, u, v, l, a;
int main() {
	cin >> N >> M;
	V<V<tlint>> rev(N + 1, V<tlint>());
	VVl to(N + 1, Vl());
	Topological_Sort topo(N + 1);
	V<plint> edges;
	UnionFind tree(N + 1);
	REP(i, M) {
		cin >> u >> v >> l >> a;
		rev[v].push_back({ u, {l, a} });
		edges.push_back({ u, v });
		tree.merge(u, v);
		to[u].push_back(v);
	}
	queue<lint> que;
	deque<bool> visited(N + 1, false), _visited(N + 1, false);
	que.push(0);
	visited[0] = true;
	while (!que.empty()) {
		lint curr = que.front(); que.pop();
		for (lint nxt : to[curr]) {
			if (visited[nxt]) continue;
			visited[nxt] = true;
			que.push(nxt);
		}
	}
	que.push(N);
	_visited[N] = true;
	while (!que.empty()) {
		lint curr = que.front(); que.pop();
		for (auto v : rev[curr]) {
			lint nxt = v.first;
			if (_visited[nxt]) continue;
			_visited[nxt] = true;
			que.push(nxt);
		}
	}
	REP(i, M) {
		if (visited[edges[i].first] && _visited[edges[i].second]) {
			topo.add_edge(edges[i].first, edges[i].second);
		}
	}
	auto vec = topo.get();
	if (!tree.same(0, N) || !visited[N]) {
		cout << 0 << endk;
	}else if (SZ(vec) != N + 1) {
		cout << "INF" << endk;
	}
	else {
		reverse(ALL(vec));
		V<ModInt> dp(N + 1);
		V<ModInt> cnt(N + 1, 0);
		cnt[N] = 1;
		for (lint v : vec) {
			for (auto nxt : rev[v]) {
				dp[nxt.first] += dp[v] * nxt.second.second + (cnt[v] * nxt.second.second) * nxt.second.first;
				cnt[nxt.first] += cnt[v] * nxt.second.second;
			}
		}
		ModInt ans = 0;
		cout << dp[0].a << endk;
	}
}
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