ZJU 2676 Network Wars

  1 #include <iostream>
  2 #include <cstdio>
  3 #include <cstring>
  4 #include <cmath>
  5 #include <algorithm>
  6 #include <climits>
  7 #include <vector>
  8 #include <queue>
  9 #include <cstdlib>
 10 #include <string>
 11 #include <set>
 12 #include <stack>
 13 #define LL long long
 14 #define pii pair<int,int>
 15 #define INF 0x3f3f3f3f
 16 using namespace std;
 17 const int maxn = 110;
 18 const double exps = 1e-8;
 19 struct arc{
 20     int to,next,id;
 21     double flow;
 22     arc(int x = 0,double y = 0,int z = 0,int nxt = -1){
 23         to = x;
 24         flow = y;
 25         id = z;
 26         next = nxt;
 27     }
 28 };
 29 arc e[20000];
 30 int head[maxn],d[maxn],cur[maxn],xx[maxn<<2],yy[maxn<<2];
 31 int tot,S,T,n,m;
 32 double ww[maxn<<2];
 33 bool used[maxn<<2],vis[maxn<<2];
 34 void add(int u,int v,double flow,int id){
 35     e[tot] = arc(v,flow,id,head[u]);
 36     head[u] = tot++;
 37     e[tot] = arc(u,0,id,head[v]);
 38     head[v] = tot++;
 39 }
 40 bool bfs(){
 41     queue<int>q;
 42     memset(d,-1,sizeof(d));
 43     d[S] = 1;
 44     q.push(S);
 45     while(!q.empty()){
 46         int u = q.front();
 47         q.pop();
 48         for(int i = head[u]; ~i; i = e[i].next){
 49             if(e[i].flow > exps && d[e[i].to] == -1){
 50                 d[e[i].to] = d[u] + 1;
 51                 q.push(e[i].to);
 52             }
 53         }
 54     }
 55     return d[T] > -1;
 56 }
 57 double dfs(int u,double low){
 58     if(u == T) return low;
 59     double tmp = 0,a;
 60     for(int &i = cur[u]; ~i; i = e[i].next){
 61         if(e[i].flow > exps && d[e[i].to] == d[u] + 1 && (a = dfs(e[i].to,min(low,e[i].flow))) > exps){
 62             e[i].flow -= a;
 63             e[i^1].flow += a;
 64             tmp += a;
 65             low -= a;
 66             if(low < exps) break;
 67         }
 68     }
 69     if(tmp < exps) d[u] = -1;
 70     return tmp;
 71 }
 72 double dinic(){
 73     double tmp = 0;
 74     while(bfs()){
 75         memcpy(cur,head,sizeof(head));
 76         tmp += dfs(S,INF);
 77     }
 78     return tmp;
 79 }
 80 double init(double delta){
 81     double tmp = tot = 0;
 82     memset(head,-1,sizeof(head));
 83     memset(used,false,sizeof(used));
 84     for(int i = 1; i <= m; ++i){
 85         if(ww[i] - delta <= exps){
 86             used[i] = true;
 87             tmp += ww[i] - delta;
 88         }else{
 89             add(xx[i],yy[i],ww[i]-delta,i);
 90             add(yy[i],xx[i],ww[i]-delta,i);
 91         }
 92     }
 93     return tmp;
 94 }
 95 void dfs2(int u){
 96     vis[u] = true;
 97     for(int i = head[u]; ~i; i = e[i].next)
 98         if(e[i].flow > exps && !vis[e[i].to]) dfs2(e[i].to);
 99 }
100 int main(){
101     bool flag = false;
102     while(~scanf("%d %d",&n,&m)){
103         S = 1;
104         T = n;
105         if(flag) puts("");
106         flag = true;
107         for(int i = 1; i <= m; ++i) scanf("%d %d %lf",xx+i,yy+i,ww+i);
108         double mid,low = 0,high = INF,ans = 0;
109         while(fabs(high - low) > 1e-3){
110             mid = (low + high)/2.0;
111             ans = init(mid);
112             ans += dinic();
113             if(ans > 0) low = mid;
114             else high = mid;
115         }
116         memset(vis,false,sizeof(vis));
117         dfs2(S);
118         vector<int>res;
119         for(int i = 1; i < n; ++i)
120         for(int j = head[i]; ~j; j = e[j].next)
121             if(vis[i] != vis[e[j].to]) used[e[j].id] = true;
122         for(int i = 1; i <= m; ++i)
123             if(used[i]) res.push_back(i);
124         printf("%d\n",res.size());
125         for(int i = 0; i < res.size(); ++i)
126             printf("%d%c",res[i],i == res.size()-1?‘\n‘:‘ ‘);
127     }
128     return 0;
129 }