結果

問題 No.1301 Strange Graph Shortest Path
ユーザー nok0nok0
提出日時 2020-10-29 22:53:50
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,155 ms / 3,000 ms
コード長 11,633 bytes
コンパイル時間 3,018 ms
コンパイル使用メモリ 229,756 KB
実行使用メモリ 86,724 KB
最終ジャッジ日時 2024-09-13 00:19:47
合計ジャッジ時間 20,499 ms
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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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 2 ms
6,816 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 564 ms
73,828 KB
testcase_03 AC 514 ms
65,484 KB
testcase_04 AC 458 ms
75,692 KB
testcase_05 AC 628 ms
76,484 KB
testcase_06 AC 426 ms
69,896 KB
testcase_07 AC 473 ms
72,592 KB
testcase_08 AC 495 ms
65,948 KB
testcase_09 AC 322 ms
66,468 KB
testcase_10 AC 507 ms
66,088 KB
testcase_11 AC 377 ms
71,764 KB
testcase_12 AC 375 ms
72,100 KB
testcase_13 AC 611 ms
73,856 KB
testcase_14 AC 468 ms
66,252 KB
testcase_15 AC 336 ms
67,248 KB
testcase_16 AC 435 ms
75,640 KB
testcase_17 AC 380 ms
76,872 KB
testcase_18 AC 410 ms
70,256 KB
testcase_19 AC 345 ms
70,420 KB
testcase_20 AC 391 ms
69,508 KB
testcase_21 AC 375 ms
74,164 KB
testcase_22 AC 442 ms
70,740 KB
testcase_23 AC 318 ms
74,696 KB
testcase_24 AC 422 ms
71,172 KB
testcase_25 AC 542 ms
75,276 KB
testcase_26 AC 403 ms
72,272 KB
testcase_27 AC 442 ms
71,636 KB
testcase_28 AC 661 ms
72,468 KB
testcase_29 AC 513 ms
74,976 KB
testcase_30 AC 376 ms
74,692 KB
testcase_31 AC 417 ms
74,352 KB
testcase_32 AC 2 ms
6,944 KB
testcase_33 AC 248 ms
77,720 KB
testcase_34 AC 1,155 ms
86,724 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

diff # 

/**
 *	author: nok0
 *	created: 2020.10.29 19:10:49
**/
#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);       \
	INPUT(name)
#define VVEC(type, name, h, w)    \
	VV<type> name(h, V<type>(w)); \
	INPUT(name)
#define INT(...)     \
	int __VA_ARGS__; \
	INPUT(__VA_ARGS__)
#define LL(...)     \
	ll __VA_ARGS__; \
	INPUT(__VA_ARGS__)
#define STR(...)        \
	string __VA_ARGS__; \
	INPUT(__VA_ARGS__)
#define CHAR(...)     \
	char __VA_ARGS__; \
	INPUT(__VA_ARGS__)
#define DOUBLE(...)     \
	DOUBLE __VA_ARGS__; \
	INPUT(__VA_ARGS__)
#define LD(...)     \
	LD __VA_ARGS__; \
	INPUT(__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 INPUT() {}
template <class Head, class... Tail>
void INPUT(Head &head, Tail &... tail) {
	scan(head);
	INPUT(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 <typename T>
istream &operator>>(istream &is, vector<T> &v) {
	for(T &in : v) is >> in;
	return is;
}
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

enum Objective {
	MINIMIZE = 1,
	MAXIMIZE = -1,
};
enum class Status {
	OPTIMAL,
	INFEASIBLE,
};

template <class Flow, class Cost, Objective objective = Objective::MINIMIZE, Flow SCALING_FACTOR = 2>
struct MinCostFlow {
private:
	using V_id = uint32_t;
	using E_id = uint32_t;

	struct Edge {
		friend struct MinCostFlow;

	private:
		V_id src, dst;
		Flow flow, cap;
		Cost cost;
		E_id rev;

	public:
		Edge() = default;

		Edge(const V_id src, const V_id dst, const Flow cap, const Cost cost,
		     const E_id rev)
		  : src(src), dst(dst), flow(0), cap(cap), cost(cost), rev(rev) {}

		[[nodiscard]] Flow residual_cap() const { return cap - flow; }
	};

public:
	struct EdgePtr {
		friend struct MinCostFlow;

	private:
		const MinCostFlow *instance;
		const V_id v;
		const E_id e;

		EdgePtr(const MinCostFlow *instance, const V_id v, const E_id e)
		  : instance(instance), v(v), e(e) {}

		[[nodiscard]] const Edge &edge() const { return instance->g[v][e]; }

		[[nodiscard]] const Edge &rev() const {
			const Edge &e = edge();
			return instance->g[e.dst][e.rev];
		}

	public:
		[[nodiscard]] V_id src() const { return rev().dst; }

		[[nodiscard]] V_id dst() const { return edge().dst; }

		[[nodiscard]] Flow flow() const { return edge().flow; }

		[[nodiscard]] Flow lower() const { return -rev().cap; }

		[[nodiscard]] Flow upper() const { return edge().cap; }

		[[nodiscard]] Cost cost() const { return edge().cost; }

		[[nodiscard]] Cost gain() const { return -edge().cost; }
	};

private:
	V_id n;
	std::vector<std::vector<Edge>> g;
	std::vector<Flow> b;

public:
	MinCostFlow() : n(0) {}

	V_id add_vertex() {
		++n;
		g.resize(n);
		b.resize(n);
		return n - 1;
	}

	std::vector<V_id> add_vertices(const size_t size) {
		std::vector<V_id> ret;
		for(V_id i = 0; i < size; ++i) ret.emplace_back(n + i);
		n += size;
		g.resize(n);
		b.resize(n);
		return ret;
	}

	EdgePtr add_edge(const V_id src, const V_id dst, const Flow lower, const Flow upper, const Cost cost) {
		const E_id e = g[src].size(), re = src == dst ? e + 1 : g[dst].size();
		assert(lower <= upper);
		g[src].emplace_back(Edge{src, dst, upper, cost * objective, re});
		g[dst].emplace_back(Edge{dst, src, -lower, -cost * objective, e});
		return EdgePtr{this, src, e};
	}

	void add_supply(const V_id v, const Flow amount) { b[v] += amount; }

	void add_demand(const V_id v, const Flow amount) { b[v] -= amount; }

private:
	static Cost constexpr unreachable = std::numeric_limits<Cost>::max();
	Cost farthest;
	std::vector<Cost> potential;
	std::vector<Cost> dist;
	std::vector<Edge *> parent;
	std::priority_queue<std::pair<Cost, int>, std::vector<std::pair<Cost, int>>, std::greater<>> pq;
	std::vector<V_id> excess_vs, deficit_vs;

	Edge &rev(const Edge &e) { return g[e.dst][e.rev]; }

	void push(Edge &e, const Flow amount) {
		e.flow += amount;
		g[e.dst][e.rev].flow -= amount;
	}

	Cost residual_cost(const V_id src, const V_id dst, const Edge &e) {
		return e.cost + potential[src] - potential[dst];
	}

	bool dual(const Flow delta) {
		dist.assign(n, unreachable);
		parent.assign(n, nullptr);
		excess_vs.erase(std::remove_if(std::begin(excess_vs), std::end(excess_vs), [&](const V_id v) { return b[v] < delta; }), std::end(excess_vs));
		deficit_vs.erase(std::remove_if(std::begin(deficit_vs), std::end(deficit_vs), [&](const V_id v) { return b[v] > -delta; }), std::end(deficit_vs));
		for(const auto v : excess_vs) pq.emplace(dist[v] = 0, v);
		farthest = 0;
		std::size_t deficit_count = 0;
		while(!pq.empty()) {
			const auto [d, u] = pq.top();
			pq.pop();
			if(dist[u] < d) continue;
			farthest = d;
			if(b[u] <= -delta) ++deficit_count;
			if(deficit_count >= deficit_vs.size()) break;
			for(auto &e : g[u]) {
				if(e.residual_cap() < delta) continue;
				const auto v = e.dst;
				const auto new_dist = d + residual_cost(u, v, e);
				if(new_dist >= dist[v]) continue;
				pq.emplace(dist[v] = new_dist, v);
				parent[v] = &e;
			}
		}
		pq = decltype(pq)();
		for(V_id v = 0; v < n; ++v) {
			potential[v] += std::min(dist[v], farthest);
		}
		return deficit_count > 0;
	}

	void primal(const Flow delta) {
		for(const auto t : deficit_vs) {
			if(dist[t] > farthest) continue;
			Flow f = -b[t];
			V_id v;
			for(v = t; parent[v] != nullptr && f >= delta; v = parent[v]->src) {
				f = std::min(f, parent[v]->residual_cap());
			}
			f = std::min(f, b[v]);
			if(f < delta) continue;
			for(v = t; parent[v] != nullptr;) {
				auto &e = *parent[v];
				push(e, f);
				const size_t u = parent[v]->src;
				parent[v] = nullptr;
				v = u;
			}
			b[t] += f;
			b[v] -= f;
		}
	}

	void saturate_negative(const Flow delta) {
		excess_vs.clear();
		deficit_vs.clear();
		for(auto &es : g)
			for(auto &e : es) {
				const Flow rcap = e.residual_cap();
				const Cost rcost = residual_cost(e.src, e.dst, e);
				if(rcost < 0 && rcap >= delta) {
					push(e, rcap);
					b[e.src] -= rcap;
					b[e.dst] += rcap;
				}
			}
		for(V_id v = 0; v < n; ++v)
			if(b[v] != 0) {
				(b[v] > 0 ? excess_vs : deficit_vs).emplace_back(v);
			}
	}

public:
	std::pair<Status, Cost> solve() {
		potential.resize(n);
		for(auto &es : g)
			for(auto &e : es) {
				const Flow rcap = e.residual_cap();
				if(rcap < 0) {
					push(e, rcap);
					b[e.src] -= rcap;
					b[e.dst] += rcap;
				}
			}

		Flow inf_flow = 1;
		for(const auto &es : g)
			for(const auto &e : es) inf_flow = std::max(inf_flow, e.residual_cap());
		Flow delta = 1;
		while(delta <= inf_flow) delta *= SCALING_FACTOR;

		for(delta /= SCALING_FACTOR; delta; delta /= SCALING_FACTOR) {
			saturate_negative(delta);
			while(dual(delta)) primal(delta);
		}

		Cost value = 0;
		for(const auto &es : g)
			for(const auto &e : es) {
				value += e.flow * e.cost;
			}
		value /= 2;

		if(excess_vs.empty() && deficit_vs.empty()) {
			return {Status::OPTIMAL, value / objective};
		} else {
			return {Status::INFEASIBLE, value / objective};
		}
	}
};

template <class Flow, class Cost>
using MaxGainFlow = MinCostFlow<Flow, Cost, Objective::MAXIMIZE>;

int u, v;
ll c, d;
int main() {
	INT(n, m);

	MinCostFlow<int, ll> MCF;
	MCF.add_vertices(n);
	MCF.add_supply(0, 2);
	MCF.add_demand(n - 1, 2);

	auto add = [&](int u, int v) {
		auto w = MCF.add_vertex();
		MCF.add_edge(u, w, 0, 2, c);
		MCF.add_edge(w, v, 0, 1, 0);
		MCF.add_edge(w, v, 0, 1, d - c);
	};

	REP(i, m) {
		cin >> u >> v >> c >> d;
		u--, v--;
		add(u, v);
		add(v, u);
	}

	auto p = MCF.solve();

	print(p.second);
}
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