結果
問題 | No.1301 Strange Graph Shortest Path |
ユーザー | pockyny |
提出日時 | 2020-11-27 21:37:07 |
言語 | C++17 (gcc 13.2.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 293 ms / 3,000 ms |
コード長 | 5,583 bytes |
コンパイル時間 | 1,182 ms |
コンパイル使用メモリ | 100,504 KB |
実行使用メモリ | 36,420 KB |
最終ジャッジ日時 | 2023-10-10 21:39:18 |
合計ジャッジ時間 | 10,759 ms |
ジャッジサーバーID (参考情報) |
judge15 / judge12 |
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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
4,352 KB |
testcase_01 | AC | 1 ms
4,352 KB |
testcase_02 | AC | 231 ms
35,948 KB |
testcase_03 | AC | 196 ms
32,376 KB |
testcase_04 | AC | 271 ms
34,688 KB |
testcase_05 | AC | 212 ms
35,556 KB |
testcase_06 | AC | 248 ms
32,252 KB |
testcase_07 | AC | 236 ms
33,972 KB |
testcase_08 | AC | 203 ms
32,640 KB |
testcase_09 | AC | 212 ms
31,000 KB |
testcase_10 | AC | 201 ms
33,060 KB |
testcase_11 | AC | 246 ms
33,296 KB |
testcase_12 | AC | 241 ms
33,296 KB |
testcase_13 | AC | 223 ms
35,700 KB |
testcase_14 | AC | 241 ms
30,820 KB |
testcase_15 | AC | 215 ms
31,744 KB |
testcase_16 | AC | 267 ms
34,576 KB |
testcase_17 | AC | 253 ms
36,420 KB |
testcase_18 | AC | 229 ms
32,780 KB |
testcase_19 | AC | 225 ms
32,328 KB |
testcase_20 | AC | 250 ms
31,160 KB |
testcase_21 | AC | 246 ms
34,816 KB |
testcase_22 | AC | 262 ms
32,240 KB |
testcase_23 | AC | 227 ms
35,680 KB |
testcase_24 | AC | 264 ms
32,016 KB |
testcase_25 | AC | 260 ms
35,144 KB |
testcase_26 | AC | 235 ms
33,424 KB |
testcase_27 | AC | 231 ms
33,576 KB |
testcase_28 | AC | 209 ms
35,004 KB |
testcase_29 | AC | 293 ms
33,864 KB |
testcase_30 | AC | 236 ms
34,312 KB |
testcase_31 | AC | 251 ms
34,384 KB |
testcase_32 | AC | 1 ms
4,348 KB |
testcase_33 | AC | 171 ms
29,280 KB |
testcase_34 | AC | 225 ms
36,196 KB |
ソースコード
#include <iostream> #include <algorithm> #include <cassert> #include <limits> #include <queue> #include <vector> 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); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); g[from].push_back(_edge{to, int(g[to].size()), cap, cost}); g[to].push_back(_edge{from, int(g[from].size()) - 1, 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 = -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 == d) { result.pop_back(); } result.push_back({flow, cost}); prev_cost = cost; } 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 namespace std; using namespace atcoder; int main(){ int i,n,m; cin >> n >> m; mcf_graph<int,long long> g(n); int s = 0,t = n - 1; for(i=0;i<m;i++){ int a,b,c,d; cin >> a >> b >> c >> d; a--; b--; g.add_edge(a,b,1,c); g.add_edge(a,b,1,d); g.add_edge(b,a,1,c); g.add_edge(b,a,1,d); } cout << g.flow(s,t,2LL).second << endl; }