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