ZOJ 2676 Network Wars[01分数规划]

Input

Output

Example

6 8 1 2 3 1 3 3 2 4 2 2 5 2 3 4 2 3 5 2 5 6 3 4 6 3

4 3 4 5 6

4 5 1 2 2 1 3 2 2 3 1 2 4 2 3 4 2

3 1 2 3

include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
using namespace std;
typedef double real;
const real eps=1e-6;
const int Z=1e3+5,N=1e4+5,M=1e5+5;
struct data{int u,v,w;}a[Z];
struct edge{int v,next;real cap;}e[M];int tot=1,head
;
int n,m,S,T,cas,num,g[Z],dis
,q[M];bool vis[Z];
real L,R,ans;
inline int read(){
int x=0,f=1;char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
return x*f;
}
inline int dcmp(real x){
if(fabs(x)<eps) return 0;
return x>0?1:-1;
}
inline void add(int x,int y,real z){
e[++tot].v=y;e[tot].cap=z;e[tot].next=head[x];head[x]=tot;
e[++tot].v=x;e[tot].cap=z;e[tot].next=head[y];head[y]=tot;
}
inline bool bfs(){
for(int i=S;i<=T;i++) dis[i]=-1;
int h=0,t=1;q[t]=S;dis[S]=0;
while(h!=t){
int x=q[++h];
for(int i=head[x];i;i=e[i].next){
if(dcmp(e[i].cap)>0&&dis[e[i].v]==-1){
dis[e[i].v]=dis[x]+1;
if(e[i].v==T) return 1;
q[++t]=e[i].v;
}
}
}
return 0;
}
real dfs(int x,real f){
if(x==T) return f;
real used=0,t;
for(int i=head[x];i;i=e[i].next){
if(dcmp(e[i].cap)>0&&dis[e[i].v]==dis[x]+1){
t=dfs(e[i].v,min(e[i].cap,f));
e[i].cap-=t;e[i^1].cap+=t;
used+=t;f-=t;
if(!f) return used;
}
}
if(!used) dis[x]=-1;
return used;
}
inline real dinic(){
real res=0;
while(bfs()) res+=dfs(S,2e9);
return res;
}
inline void init(){
m=read();L=0;R=0;num=0;S=1;T=n;
for(int i=1;i<=m;i++) a[i].u=read(),a[i].v=read(),a[i].w=read(),R+=a[i].w;
}
inline real rebuild(real s){
tot=1;memset(head,0,n+1<<2);
real tans=0;
for(int i=1;i<=m;i++){
if(a[i].w>s){
add(a[i].u,a[i].v,a[i].w-s);
}
else tans+=a[i].w-s;
}
return tans+dinic();
}
inline real binary_search(){
real mid,now;
while(dcmp(R-L)>0){
mid=(L+R)/2;
now=rebuild(mid);
if(dcmp(now)>0) L=mid;
else R=mid;
}
return mid;
}
void DFS(int x){
vis[x]=1;
for(int i=head[x];i;i=e[i].next){
if(!vis[e[i].v]&&dcmp(e[i].cap)>0){
DFS(e[i].v);
}
}
}
inline void work(){
ans=binary_search();
memset(vis,0,n+1<<2);
//rebuild(ans);
DFS(S);
for(int i=1;i<=m;i++){
if(vis[a[i].u]+vis[a[i].v]==1||a[i].w<ans){
g[++num]=i;
}
}
if(cas++) putchar('\n');
printf("%d\n",num);
for(int i=1;i<num;i++) printf("%d ",g[i]);
if(num) printf("%d",g[num]);
putchar('\n');
}
int main(){
while(~scanf("%d",&n)) init(),work();
return 0;
}