http://acm.hdu.edu.cn/showproblem.php?pid=3435
题意:
有n个点和m条边,你可以删去任意条边,使得所有点在一个哈密顿路径上,路径的权值得最小。
思路:
费用流,注意判断重边,否则会超时。
1 #include<iostream> 2 #include<cstdio> 3 #include<cmath> 4 #include<cstring> 5 #include<queue> 6 using namespace std; 7 typedef long long LL; 8 9 const int maxn=2000+5; 10 const int INF=0x3f3f3f3f; 11 12 int map[maxn][maxn]; 13 14 struct Edge 15 { 16 int from, to, cap, flow, cost; 17 Edge(int u, int v, int c, int f, int w) :from(u), to(v), cap(c), flow(f), cost(w) {} 18 }; 19 20 struct MCMF 21 { 22 int n, m; 23 vector<Edge> edges; 24 vector<int> G[maxn]; 25 int inq[maxn]; 26 int d[maxn]; 27 int p[maxn]; 28 int a[maxn]; 29 30 void init(int n) 31 { 32 this->n = n; 33 for (int i = 0; i<n; i++) G[i].clear(); 34 edges.clear(); 35 } 36 37 void AddEdge(int from, int to, int cap, int cost) 38 { 39 edges.push_back(Edge(from, to, cap, 0, cost)); 40 edges.push_back(Edge(to, from, 0, 0, -cost)); 41 m = edges.size(); 42 G[from].push_back(m - 2); 43 G[to].push_back(m - 1); 44 } 45 46 bool BellmanFord(int s, int t, int &flow, LL & cost) 47 { 48 for (int i = 0; i<n; i++) d[i] = INF; 49 memset(inq, 0, sizeof(inq)); 50 d[s] = 0; inq[s] = 1; p[s] = 0; a[s] = INF; 51 52 queue<int> Q; 53 Q.push(s); 54 while (!Q.empty()){ 55 int u = Q.front(); Q.pop(); 56 inq[u] = 0; 57 for (int i = 0; i<G[u].size(); i++){ 58 Edge& e = edges[G[u][i]]; 59 if (e.cap>e.flow && d[e.to]>d[u] + e.cost){ 60 d[e.to] = d[u] + e.cost; 61 p[e.to] = G[u][i]; 62 a[e.to] = min(a[u], e.cap - e.flow); 63 if (!inq[e.to]) { Q.push(e.to); inq[e.to] = 1; } 64 } 65 } 66 } 67 if (d[t] == INF) return false; 68 flow += a[t]; 69 cost += (LL)d[t] * (LL)a[t]; 70 for (int u = t; u != s; u = edges[p[u]].from){ 71 edges[p[u]].flow += a[t]; 72 edges[p[u] ^ 1].flow -= a[t]; 73 74 } 75 return true; 76 } 77 78 int MincostMaxdflow(int s, int t, LL & cost) 79 { 80 int flow = 0; cost = 0; 81 while (BellmanFord(s, t, flow, cost) ); 82 return flow; 83 } 84 }t; 85 86 int n,m; 87 88 int main() 89 { 90 //freopen("D:\\input.txt", "r", stdin); 91 int T; 92 int kase=0; 93 scanf("%d",&T); 94 int u,v,d; 95 while(T--) 96 { 97 memset(map,0,sizeof(map)); 98 scanf("%d%d",&n,&m); 99 int src=0,dst=2*n+1; 100 t.init(dst+1); 101 for(int i=1;i<=n;i++) 102 { 103 t.AddEdge(src,i,1,0); 104 t.AddEdge(i+n,dst,1,0); 105 } 106 for(int i=0;i<m;i++) 107 { 108 scanf("%d%d%d",&u,&v,&d); 109 if(map[u][v]==0 || map[u][v]>d) 110 { 111 t.AddEdge(u,v+n,1,d); 112 t.AddEdge(v,u+n,1,d); 113 map[u][v]=map[v][u]=d; 114 } 115 } 116 long long cost; 117 int flow=t.MincostMaxdflow(src,dst,cost); 118 printf("Case %d: ",++kase); 119 if(flow==n) printf("%d\n",cost); 120 else printf("NO\n"); 121 } 122 return 0; 123 }
时间: 2024-11-01 09:44:40