1 #include <bits/stdc++.h>
2 #define maxn 100000
3 #define maxm 2000000
4 #define eps 1e-7
5 #define INF 1<<30
6 using namespace std;
7
8 struct Edge{
9 int u; //u表示边的起点
10 int v; //v表示边的终点
11 int next; //next表示下一条边编号
12 double w; //w表示边的容量
13 }edge[maxm]; //网络流建模时用到的边
14
15 int e; //边的计数器
16 int S; //超级源点
17 int T; //超级汇点
18 int first[maxn]; //图邻接表头结点
19 int d[maxn]; //层次图距离标记
20 int work[maxn]; //dinic优化
21 int q[maxn]; //bfs队列
22 int deg[maxn]; //每个点的度数
23 set<int>::iterator iter;
24 set<int> A; //A集合中的点
25 vector<int> G[maxn]; //原始图上的边
26
27 bool f1[maxn]; //残量网络与S连通的点集
28 bool f2[maxn]; //残量网络与T连通的点集
29
30 int n; //图上的点数
31 int m; //图上的边数
32 int k; //A集合中点的数量
33 int vol_a; //A集合的容量vol(A)
34 int cut_a; //跨越A和V-A的边数
35 double f; //f(A)=vol(A)/vol(V-A)
36 double alpha; //与网络流边容量相关的参数α
37 /*图的初始化*/
38 void init(){
39 e = 0;
40 memset(first,-1,sizeof(first));
41 }
42
43 /*加边*/
44 void add_edge(int a,int b,double c){
45 //printf("add_edge:from %d to %d,val = %.4f\n",a,b,c);
46 edge[e].u = a;
47 edge[e].v = b;
48 edge[e].next = first[a];
49 edge[e].w = c;
50 first[a] = e++;
51
52 edge[e].u = b;
53 edge[e].v = a;
54 edge[e].next = first[b];
55 edge[e].w = 0;
56 first[b] = e++;
57 }
58
59 /*bfs构造层次图*/
60 int bfs(){
61 int rear = 0;
62 memset(d,-1,sizeof(d));
63 d[S] = 0;q[rear++] = S;
64 for(int i = 0;i < rear;i++){
65 for(int j = first[q[i]];j != -1;j = edge[j].next){
66 int to = edge[j].v;
67 double val = edge[j].w;
68 if(abs(val) > eps && d[to] == -1){
69 d[to] = d[q[i]]+1;
70 q[rear++] = to;
71 if(to == T) return 1;
72 }
73 }
74 }
75 return 0;
76 }
77
78 /*dfs计算阻塞流*/
79 double dfs(int cur,double a){
80 if(cur == T) return a;
81 for(int &i = work[cur];i != -1;i = edge[i].next){
82 int to = edge[i].v;
83 double val = edge[i].w;
84 if(abs(val) > eps && d[to] == d[cur]+1){
85 if(double t = dfs(to,min(a,val))){
86 edge[i].w -= t;edge[i^1].w += t;
87 return t;
88 }
89 }
90 }
91 return 0;
92 }
93
94 void dfs1(int u){
95 f1[u] = 1;
96 for(int i = first[u];i != -1;i = edge[i].next){
97 int to = edge[i].v;
98 double val = edge[i].w;
99 if(!f1[to] && val > eps) dfs1(to);
100 }
101 }
102
103 void dfs2(int u){
104 f2[u] = 1;
105 for(int i = first[u];i != -1;i = edge[i].next){
106 int to = edge[i].v;
107 double val = edge[i^1].w;
108 if(!f2[to] && val > eps) dfs2(to);
109 }
110 }
111
112 void build(double alpha){
113 init();
114 for(int i = 1;i <= n;i++){
115 if(A.find(i) != A.end()){
116 add_edge(S,i,deg[i]);
117 }else{
118 add_edge(i,T,f*deg[i]);
119 }
120 }
121 for(int u = 1;u <= n;u++){
122 for(int i = 0;i < G[u].size();i++){
123 int v = G[u][i];
124 add_edge(u,v,1.0/alpha);
125 add_edge(v,u,1.0/alpha);
126 }
127 }
128 }
129
130 double dinic(){
131 double ans = 0,t;
132 while(bfs()){
133 memcpy(work,first,sizeof(first));
134 while(true){
135 t = dfs(S,INF);
136 if(t < eps) break;
137 ans += t;
138 }
139 }
140 return ans;
141 }
142
143 double min_cut(){
144 memset(f1,0,sizeof(f1));
145 memset(f2,0,sizeof(f2));
146 dfs1(S);
147 dfs2(T);
148
149 int cnt = 0; //表示跨越集合的边数
150
151 //printf("min_cut edge:\n");
152 for(int i = 0;i < e;i += 2){
153 if(f1[edge[i].u] && f2[edge[i].v] && edge[i].w < eps){
154 //printf("from %d to %d\n",edge[i].u,edge[i].v);
155 if(edge[i].u == S || edge[i].u == T) continue;
156 if(edge[i].v == S || edge[i].v == T) continue;
157 cnt++;
158 }
159 }
160
161 int vol1 = 0,vol2 = 0;
162 for(int i = S+1;i < T;i++){
163 if(f1[i]){
164 vol1 += deg[i];
165 //printf("flag1:%d\n",i);
166 }
167 if(f2[i]){
168 if(A.find(i) != A.end()) vol2 += deg[i];
169 }
170 }
171
172 printf("cnt = %d,vol1 = %d,total-vol1 = %d\n",cnt,vol1,2*m-vol1);
173 if(cnt == 0) return 0;
174 double conductance = cnt*1.0/min(vol1,2*m-vol1);
175 printf("conductance = %.5f\n",conductance);
176
177 double QAS = cnt*1.0/(vol1-f*vol2);
178 return QAS;
179 }
180
181 int main()
182 {
183 freopen("wing_nodal.txt","r",stdin);
184 freopen("output.txt","w",stdout);
185 scanf("%d%d%d",&n,&m,&k);
186 S = 0,T = n+1;
187 vol_a = cut_a = 0;
188 for(int i = 0;i < m;i++){
189 int a,b;
190 scanf("%d%d",&a,&b);
191 G[a].push_back(b);
192 G[b].push_back(a);
193 deg[a]++;deg[b]++;
194 }
195 for(int i = 0;i < k;i++){
196 int a;
197 scanf("%d",&a);
198 A.insert(a);
199 vol_a += deg[a];
200 }
201 for(iter = A.begin();iter != A.end();iter++){
202 int u = *iter;
203 for(int i = 0;i < G[u].size();i++){
204 int v = G[u][i];
205 if(A.find(v) != A.end()) continue;
206 cut_a++;
207 }
208 }
209 f = vol_a*1.0/(2*m-vol_a);
210 alpha = cut_a*1.0/vol_a;
211 double best_alpha = alpha;
212 printf("init:cut_a = %d,vol_a = %d\n",cut_a,vol_a);
213 printf("before algorithm,conductance = %.5f\n",alpha);
214 clock_t time_begin,time_end;
215 time_begin = clock();
216 while(true){
217 build(alpha);
218 double maxflow = dinic();
219 double QAS = min_cut();
220 printf("maxflow = %.5f\n",maxflow);
221 printf("QAS = %.5f\n",QAS);
222 if(abs(QAS) < eps){
223 break;
224 }else{
225 best_alpha = alpha;
226 }
227 if(QAS < alpha){
228 alpha = QAS;
229 }else{
230 break;
231 }
232 }
233 puts("------------------result-----------------");
234 printf("best alpha = %.5f\n",best_alpha);
235 build(best_alpha);
236 dinic();
237 min_cut();
238
239 time_end = clock();
240 double delta = (double)(time_end - time_begin) / CLOCKS_PER_SEC;
241 printf("\n,delta_time = %.5f s\n",delta);
242 return 0;
243 }
时间： 2024-08-25 03:06:17