1 //------------------------------------------------------------- 1 //------------------------------------------------------------- 2 // MinCost-MaxFlow 2 // MinCost-MaxFlow 3 // O(??) | 3 // O(F E log E) // F:flow > 4 // See http://d.hatena.ne.jp/tsukuno/20120320#1332179143 4 // 5 // 5 // Verified by 6 // Verified by 6 // - SRM 487 Div2 LV3 | 7 // - (SRM 487 Div2 LV3) in previous version > 8 // - (SRM 526 Div1 LV1) in previous version 7 // - SRM 491 Div1 LV3 9 // - SRM 491 Div1 LV3 8 // - SRM 526 Div1 LV1 < 9 //------------------------------------------------------------- 10 //------------------------------------------------------------- 10 11 11 #include <iostream> 12 #include <iostream> 12 #include <string> 13 #include <string> 13 #include <vector> 14 #include <vector> 14 #include <map> 15 #include <map> 15 #include <queue> 16 #include <queue> ................................................................................................................................................................................ 49 F[s][t] = f; 50 F[s][t] = f; 50 F[t][s] = 0; 51 F[t][s] = 0; 51 } 52 } 52 53 53 pair<Cost, Flow> calc( Vert s_, Vert t_ ) 54 pair<Cost, Flow> calc( Vert s_, Vert t_ ) 54 { 55 { 55 const int N=idgen.size(), S=idgen.v2id(s_), T=idgen.v2id(t_); 56 const int N=idgen.size(), S=idgen.v2id(s_), T=idgen.v2id(t_); 56 static const Cost COST_INF = // 0x7fffffff; // !!EDIT HERE!! | 57 static const Cost COST_INF = 1e+300; // !!EDIT HERE!! 57 static const Flow FLOW_INF = // 0x7fffffff; | 58 static const Flow FLOW_INF = 0x7fffffff; 58 59 59 Cost total_cost = 0; 60 Cost total_cost = 0; 60 Flow total_flow = 0; 61 Flow total_flow = 0; 61 vector<Cost> h(N, 0); // potential | 62 vector<Cost> dist(N, 0); // Distance from S : initially unknown. 62 for(Flow RF=FLOW_INF; RF>0; ) // residual flow | 63 for(;;) 63 { 64 { 64 // Dijkstra -- find the min-cost path | 65 // Dijkstra : find the "shortest path" from S to T wrt C > 66 // C[][] can be <0 so we must be careful. Instead of c > 67 // we compute the increase ("delta") from the shortest > 68 // Since shortest path cannot decrease, delta is alway > 69 // Smallest delta implies smallest dist[T]+delta[T]. 65 vector<Cost> d(N, COST_INF); d[S] = 0; | 70 vector<Cost> delta(N, COST_INF); delta[S] = 0; 66 vector<int> prev(N, -1); 71 vector<int> prev(N, -1); 67 72 68 typedef pair< Cost, pair<int,int> > cedge; | 73 typedef pair< Cost, pair<int, int> > cedge; 69 priority_queue< cedge, vector<cedge>, greater<cedge> > Q 74 priority_queue< cedge, vector<cedge>, greater<cedge> > Q 70 Q.push( cedge(0, make_pair(S,S)) ); | 75 Q.push( cedge(0, make_pair(S, S)) ); 71 while( !Q.empty() ) { 76 while( !Q.empty() ) { 72 cedge e = Q.top(); Q.pop(); | 77 const cedge e = Q.top(); Q.pop(); > 78 const int u_prev = e.second.first; 73 if( prev[e.second.second] >= 0 ) | 79 const int u = e.second.second; > 80 if( prev[u] >= 0 ) // visited 74 continue; 81 continue; 75 prev[e.second.second] = e.second.first; | 82 prev[u] = u_prev; 76 83 77 int u = e.second.second; < 78 for(int i=0; i<G[u].size(); ++i) { 84 for(int i=0; i<G[u].size(); ++i) { 79 int v = G[u][i]; | 85 const int v = G[u][i]; 80 Cost r_cost = C[u][v] + h[u] - h[v]; | 86 const Cost v_delta = dist[u]+delta[u]+C[ 81 if( F[u][v] > 0 && d[v] > d[u]+r_cost ) | 87 if( F[u][v]>0 && delta[v]>v_delta ) 82 Q.push( cedge(d[v]=d[u]+r_cost, | 88 Q.push( cedge(delta[v]=v_delta, 83 } 89 } 84 } 90 } 85 91 > 92 // If T is unreachable, finished. 86 if( prev[T] < 0 ) 93 if( prev[T] < 0 ) 87 break; // Finished | 94 break; > 95 > 96 // Update the distance table. > 97 for(int u=0; u<N; ++u) > 98 if( delta[u] != COST_INF ) > 99 dist[u] += delta[u]; 88 100 89 // Run the flow as much as possible | 101 // How much water can flow on the min-cost path? 90 Flow f = RF; | 102 Flow f = FLOW_INF; 91 for(int u=T; u!=S; u=prev[u]) 103 for(int u=T; u!=S; u=prev[u]) 92 f = min(f, F[prev[u]][u]); 104 f = min(f, F[prev[u]][u]); 93 RF -= f; < 94 total_flow += f; < 95 105 > 106 // Run the flow as much as possible > 107 total_flow += f; 96 for(int u=T; u!=S; u=prev[u]) | 108 for(int u=T; u!=S; u=prev[u]) { 97 { < 98 total_cost += f * C[prev[u]][u]; 109 total_cost += f * C[prev[u]][u]; 99 F[prev[u]][u] -= f; 110 F[prev[u]][u] -= f; 100 F[u][prev[u]] += f; 111 F[u][prev[u]] += f; 101 } 112 } 102 < 103 // Update the potential < 104 for(int u=0; u<N; ++u) < 105 h[u] += d[u]; < 106 } 113 } 107 return make_pair(total_cost, total_flow); 114 return make_pair(total_cost, total_flow); 108 } 115 } 109 }; 116 };