結果

問題 No.1301 Strange Graph Shortest Path
ユーザー nok0nok0
提出日時 2020-10-30 22:40:07
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 533 ms / 3,000 ms
コード長 4,636 bytes
コンパイル時間 2,615 ms
コンパイル使用メモリ 221,780 KB
実行使用メモリ 72,644 KB
最終ジャッジ日時 2024-09-13 00:28:25
合計ジャッジ時間 17,033 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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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 375 ms
65,416 KB
testcase_03 AC 318 ms
57,356 KB
testcase_04 AC 462 ms
66,896 KB
testcase_05 AC 365 ms
68,532 KB
testcase_06 AC 436 ms
62,264 KB
testcase_07 AC 407 ms
64,008 KB
testcase_08 AC 345 ms
57,680 KB
testcase_09 AC 328 ms
57,784 KB
testcase_10 AC 309 ms
57,732 KB
testcase_11 AC 391 ms
63,844 KB
testcase_12 AC 384 ms
63,940 KB
testcase_13 AC 350 ms
64,836 KB
testcase_14 AC 445 ms
58,020 KB
testcase_15 AC 339 ms
60,352 KB
testcase_16 AC 448 ms
66,668 KB
testcase_17 AC 399 ms
66,620 KB
testcase_18 AC 396 ms
61,004 KB
testcase_19 AC 354 ms
62,052 KB
testcase_20 AC 413 ms
60,912 KB
testcase_21 AC 408 ms
64,984 KB
testcase_22 AC 461 ms
63,304 KB
testcase_23 AC 348 ms
65,264 KB
testcase_24 AC 447 ms
62,328 KB
testcase_25 AC 440 ms
66,348 KB
testcase_26 AC 397 ms
64,508 KB
testcase_27 AC 351 ms
63,076 KB
testcase_28 AC 326 ms
62,904 KB
testcase_29 AC 533 ms
66,752 KB
testcase_30 AC 381 ms
65,268 KB
testcase_31 AC 418 ms
65,784 KB
testcase_32 AC 2 ms
6,940 KB
testcase_33 AC 263 ms
66,512 KB
testcase_34 AC 389 ms
72,644 KB
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ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;

namespace atcoder {

template <class Cap, class Cost>
struct mcf_graph {
public:
	mcf_graph() {}
	mcf_graph(int n) : _n(n), g(n) {}

	int add_edge(int from, int to, Cap cap, Cost cost) {
		assert(0 <= from && from < _n);
		assert(0 <= to && to < _n);
		assert(0 <= cap);
		assert(0 <= cost);
		int m = int(pos.size());
		pos.push_back({from, int(g[from].size())});
		int from_id = int(g[from].size());
		int to_id = int(g[to].size());
		if(from == to) to_id++;
		g[from].push_back(_edge{to, to_id, cap, cost});
		g[to].push_back(_edge{from, from_id, 0, -cost});
		return m;
	}

	struct edge {
		int from, to;
		Cap cap, flow;
		Cost cost;
	};

	edge get_edge(int i) {
		int m = int(pos.size());
		assert(0 <= i && i < m);
		auto _e = g[pos[i].first][pos[i].second];
		auto _re = g[_e.to][_e.rev];
		return edge{
		    pos[i].first,
		    _e.to,
		    _e.cap + _re.cap,
		    _re.cap,
		    _e.cost,
		};
	}
	std::vector<edge> edges() {
		int m = int(pos.size());
		std::vector<edge> result(m);
		for(int i = 0; i < m; i++) {
			result[i] = get_edge(i);
		}
		return result;
	}

	std::pair<Cap, Cost> flow(int s, int t) {
		return flow(s, t, std::numeric_limits<Cap>::max());
	}
	std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) {
		return slope(s, t, flow_limit).back();
	}
	std::vector<std::pair<Cap, Cost>> slope(int s, int t) {
		return slope(s, t, std::numeric_limits<Cap>::max());
	}
	std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {
		assert(0 <= s && s < _n);
		assert(0 <= t && t < _n);
		assert(s != t);
		// variants (C = maxcost):
		// -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0
		// reduced cost (= e.cost + dual[e.from] - dual[e.to]) >= 0 for all edge
		std::vector<Cost> dual(_n, 0), dist(_n);
		std::vector<int> pv(_n), pe(_n);
		std::vector<bool> vis(_n);
		auto dual_ref = [&]() {
			std::fill(dist.begin(), dist.end(), std::numeric_limits<Cost>::max());
			std::fill(pv.begin(), pv.end(), -1);
			std::fill(pe.begin(), pe.end(), -1);
			std::fill(vis.begin(), vis.end(), false);
			struct Q {
				Cost key;
				int to;
				bool operator<(Q r) const { return key > r.key; }
			};
			std::priority_queue<Q> que;
			dist[s] = 0;
			que.push(Q{0, s});
			while(!que.empty()) {
				int v = que.top().to;
				que.pop();
				if(vis[v]) continue;
				vis[v] = true;
				if(v == t) break;
				// dist[v] = shortest(s, v) + dual[s] - dual[v]
				// dist[v] >= 0 (all reduced cost are positive)
				// dist[v] <= (n-1)C
				for(int i = 0; i < int(g[v].size()); i++) {
					auto e = g[v][i];
					if(vis[e.to] || !e.cap) continue;
					// |-dual[e.to] + dual[v]| <= (n-1)C
					// cost <= C - -(n-1)C + 0 = nC
					Cost cost = e.cost - dual[e.to] + dual[v];
					if(dist[e.to] - dist[v] > cost) {
						dist[e.to] = dist[v] + cost;
						pv[e.to] = v;
						pe[e.to] = i;
						que.push(Q{dist[e.to], e.to});
					}
				}
			}
			if(!vis[t]) {
				return false;
			}

			for(int v = 0; v < _n; v++) {
				if(!vis[v]) continue;
				// dual[v] = dual[v] - dist[t] + dist[v]
				//         = dual[v] - (shortest(s, t) + dual[s] - dual[t]) +
				//         (shortest(s, v) + dual[s] - dual[v]) = - shortest(s, t) +
				//         dual[t] + shortest(s, v) = shortest(s, v) - shortest(s, t) >=
				//         0 - (n-1)C
				dual[v] -= dist[t] - dist[v];
			}
			return true;
		};
		Cap flow = 0;
		Cost cost = 0, prev_cost_per_flow = -1;
		std::vector<std::pair<Cap, Cost>> result;
		result.push_back({flow, cost});
		while(flow < flow_limit) {
			if(!dual_ref()) break;
			Cap c = flow_limit - flow;
			for(int v = t; v != s; v = pv[v]) {
				c = std::min(c, g[pv[v]][pe[v]].cap);
			}
			for(int v = t; v != s; v = pv[v]) {
				auto& e = g[pv[v]][pe[v]];
				e.cap -= c;
				g[v][e.rev].cap += c;
			}
			Cost d = -dual[s];
			flow += c;
			cost += c * d;
			if(prev_cost_per_flow == d) {
				result.pop_back();
			}
			result.push_back({flow, cost});
			prev_cost_per_flow = d;
		}
		return result;
	}

private:
	int _n;

	struct _edge {
		int to, rev;
		Cap cap;
		Cost cost;
	};

	std::vector<std::pair<int, int>> pos;
	std::vector<std::vector<_edge>> g;
};

}  // namespace atcoder

using ll = long long;

int n, m, u, v, w;
ll c, d;
int main() {
	cin >> n >> m;

	atcoder::mcf_graph<int, ll> mcf(n + 2 * m);

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

	while(m--) {
		cin >> u >> v >> c >> d;
		assert(c <= d);
		u--, v--;
		add(u, v);
		add(v, u);
	}

	auto p = mcf.flow(0, n - 1, 2);

	assert(p.first == 2);

	printf("%lld\n", p.second);

	return 0;
}
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