結果
問題 | No.1301 Strange Graph Shortest Path |
ユーザー |
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提出日時 | 2020-11-27 22:36:03 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 414 ms / 3,000 ms |
コード長 | 6,667 bytes |
コンパイル時間 | 2,085 ms |
コンパイル使用メモリ | 214,340 KB |
最終ジャッジ日時 | 2025-01-16 07:59:32 |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 33 |
ソースコード
#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 edgestd::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)Cfor (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 = nCCost 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)Cdual[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#include <bits/stdc++.h>using namespace std;using namespace atcoder;#define INF_LL 100000000000000000LL#define INF 200000000#define MOD 1000000007#define ll long long#define all(x) x.begin(), x.end()#define REP(i, a, b) for(int i = a; i < b; i++)#define rep(i, n) REP(i, 0, n)// typedef float double;// typedef priority_queue prique;typedef pair<ll, ll> P;typedef vector<int> vi;typedef vector<vi> vvi;typedef vector<P> vp;typedef vector<ll> vl;typedef vector<vi> matrix;int dx[4] = {0, 1, 0, -1};int dy[4] = {1, 0, -1, 0};int sign[2] = {1, -1};template <class T> bool chmax(T &a, T b) {if(a < b) {a = b;return 1;}return 0;}template <class T> bool chmin(T &a, T b) {if(a > b) {a = b;return 1;}return 0;}ll modpow(ll a, ll b, ll m) {if(b == 0)return 1;ll t = modpow(a, b / 2, m);if(b & 1) {return (t * t % m) * a % m;} else {return t * t % m;}}struct edge {int to;ll cost;edge(int t, ll c) { to = t, cost = c; }};// using mint = modint998244353;int main() {int n, m;cin >> n >> m;mcf_graph<ll, ll> g(n);rep(i, m) {int u, v, c, d;cin >> u >> v >> c >> d;g.add_edge(u - 1, v - 1, 1, c);g.add_edge(u - 1, v - 1, 1, d);g.add_edge(v - 1, u - 1, 1, c);g.add_edge(v - 1, u - 1, 1, d);}cout << (g.flow(0, n - 1, 2)).second << endl;return 0;}