結果
問題 | No.1301 Strange Graph Shortest Path |
ユーザー | tabae326 |
提出日時 | 2020-11-27 23:38:30 |
言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 193 ms / 3,000 ms |
コード長 | 5,890 bytes |
コンパイル時間 | 2,315 ms |
コンパイル使用メモリ | 188,884 KB |
実行使用メモリ | 36,796 KB |
最終ジャッジ日時 | 2024-09-13 01:12:48 |
合計ジャッジ時間 | 8,854 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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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
6,812 KB |
testcase_01 | AC | 2 ms
6,812 KB |
testcase_02 | AC | 143 ms
36,000 KB |
testcase_03 | AC | 118 ms
33,368 KB |
testcase_04 | AC | 181 ms
34,944 KB |
testcase_05 | AC | 127 ms
35,368 KB |
testcase_06 | AC | 155 ms
32,404 KB |
testcase_07 | AC | 143 ms
34,116 KB |
testcase_08 | AC | 120 ms
32,816 KB |
testcase_09 | AC | 130 ms
30,844 KB |
testcase_10 | AC | 118 ms
32,312 KB |
testcase_11 | AC | 149 ms
33,348 KB |
testcase_12 | AC | 149 ms
33,400 KB |
testcase_13 | AC | 130 ms
35,580 KB |
testcase_14 | AC | 157 ms
31,240 KB |
testcase_15 | AC | 132 ms
31,868 KB |
testcase_16 | AC | 169 ms
34,716 KB |
testcase_17 | AC | 157 ms
36,796 KB |
testcase_18 | AC | 143 ms
33,084 KB |
testcase_19 | AC | 138 ms
32,548 KB |
testcase_20 | AC | 165 ms
31,444 KB |
testcase_21 | AC | 151 ms
34,932 KB |
testcase_22 | AC | 175 ms
32,296 KB |
testcase_23 | AC | 135 ms
36,368 KB |
testcase_24 | AC | 164 ms
32,204 KB |
testcase_25 | AC | 161 ms
34,824 KB |
testcase_26 | AC | 153 ms
33,348 KB |
testcase_27 | AC | 140 ms
34,168 KB |
testcase_28 | AC | 124 ms
35,192 KB |
testcase_29 | AC | 193 ms
34,028 KB |
testcase_30 | AC | 148 ms
34,628 KB |
testcase_31 | AC | 171 ms
34,280 KB |
testcase_32 | AC | 2 ms
6,940 KB |
testcase_33 | AC | 98 ms
29,600 KB |
testcase_34 | AC | 149 ms
36,264 KB |
ソースコード
#include <bits/stdc++.h> using namespace std; using ll = long long; #define rep(i, srt, end) for (long long i = (srt); i < (long long)(end); i++) /*---------- I love AtCoder Library ---------*/ #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 atcoder; void solve() { ll n, m; cin >> n >> m; mcf_graph<ll, ll> graph(n); rep(i, 0, m) { ll u, v, c, d; cin >> u >> v >> c >> d; u--; v--; graph.add_edge(u, v, 1, c); graph.add_edge(v, u, 1, c); graph.add_edge(u, v, 1, d); graph.add_edge(v, u, 1, d); } auto res = graph.flow(0, n-1, 2); cout << res.second << endl; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); solve(); return 0; }