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Created Aug 3, 2014

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BZOJ 2725 : [Violet 6]故乡的梦
/**************************************************************
Problem: 2725
User: zrts
Language: C++
Result: Accepted
Time:13512 ms
Memory:49700 kb
****************************************************************/
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<queue>
#include<vector>
//by zrt
//problem:
using namespace std;
typedef long long LL;
const LL inf(0x3f3f3f3f3f3f3f3fLL);
const double eps(1e-9);
int H0[200005],X0[400005],P0[400005],tot0,E0[400005];
void add0(int x,int y,int z){
P0[++tot0]=y;X0[tot0]=H0[x];H0[x]=tot0;E0[tot0]=z;
}
int H1[200005],X1[400005],P1[400005],tot1,flow[400005],from[400005],E1[400005];
void add1(int x,int y,int z){
P1[++tot1]=y;X1[tot1]=H1[x];H1[x]=tot1;flow[tot1]=z;from[tot1]=x;
}
int H2[200005],X2[400005],P2[400005],tot2,E2[400005],from2[400005];
void add2(int x,int y,int z){
P2[++tot2]=y;X2[tot2]=H2[x];H2[x]=tot2;E2[tot2]=z;from2[tot2]=x;
}
int n,m,Q,S,T;
int cut[200005];
LL ds[200005],dt[200005];
bool vis[200005];
struct N{
int x;LL w;
N(int a=0,LL b=0){
x=a,w=b;
}
friend bool operator < (N a,N b){
return a.w>b.w;
}
};
priority_queue<N> q;
int d[200005];
queue<int> qu;
deque<int> dq;
bool bfs(){
memset(d,0,sizeof d);
d[S]=1;int x;qu.push(S);
while(!qu.empty()){
x=qu.front();qu.pop();
if(x==T) continue;
for(int i=H1[x];i;i=X1[i]){
if(flow[i]>0&&!d[P1[i]]){
d[P1[i]] =d[x]+1;
qu.push(P1[i]);
}
}
}
return d[T];
}
int dfs(int x,int a){
if(x==T||a==0) return a;
int tmp,f=a;
for(int i=H1[x];i;i=X1[i]){
if(flow[i]>0&&d[P1[i]]==d[x]+1){
tmp=dfs(P1[i],min(flow[i],a));
a-=tmp;
flow[i]-=tmp;
flow[i^1]+=tmp;
if(!a) break;
}
}
if(a==f) d[x]=-1;
return f-a;
}
int ff;
int low[200005],tim;
int stk[200005],top;
bool instk[200005];
int id[200005];
int cnt;
void tarjan(int x){
stk[top++]=x;instk[x]=1;
int dfn=low[x]=++tim;
for(int i=H1[x];i;i=X1[i]){
if(flow[i]==0) continue;
if(!low[P1[i]]){
tarjan(P1[i]);
low[x]=min(low[x],low[P1[i]]);
}else if(instk[P1[i]]) low[x]=min(low[x],low[P1[i]]);
}
if(dfn==low[x]){
cnt++;
int k;
do{
k=stk[--top];
instk[k]=0;
id[k]=cnt;
}while(k!=x);
}
}
int Ds[200005],Dt[200005];
LL ans[200005];
vector<int> v[200005];
struct A{
int x,y;
LL w;
A(int a=0,int b=0,LL c=0){
x=a,y=b,w=c;
}
friend bool operator < (A a,A b){
return a.w>b.w;
}
};
priority_queue<A> pq;
int main(){
#ifdef LOCAL
freopen("in.txt","r",stdin);
freopen("out.txt","w",stdout);
#endif
tot0=tot1=1;
scanf("%d%d",&n,&m);
for(int i=0,x,y,z;i<m;i++){
scanf("%d%d%d",&x,&y,&z);
add0(x,y,z);
add0(y,x,z);
}
scanf("%d%d%d",&S,&T,&Q);
memset(ds,0x3f,sizeof ds);memset(dt,0x3f,sizeof dt);
ds[S]=dt[T]=0;int x;
q.push(N(S,0));
while(!q.empty()){
x=q.top().x; q.pop();
if(vis[x]) continue;
vis[x]=1;
if(x==T) continue;//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
for(int i=H0[x];i;i=X0[i]){
if(!vis[P0[i]]&&ds[P0[i]]>ds[x]+E0[i]){
ds[P0[i]]=ds[x]+E0[i];
q.push(N(P0[i],ds[P0[i]]));
}
}
}
memset(vis,0,sizeof vis);
q.push(N(T,0));
while(!q.empty()){
x=q.top().x;q.pop();
if(vis[x]) continue;
vis[x]=1;
if(x==S) continue;//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
for(int i=H0[x];i;i=X0[i]){
if(!vis[P0[i]]&&dt[P0[i]]>dt[x]+E0[i]){
dt[P0[i]]=dt[x]+E0[i];
q.push(N(P0[i],dt[P0[i]]));
}
}
}
if(ds[T]==inf) {
for(int i=0;i<Q;i++){
puts("Infinity");
}
goto ed;
}
for(int i=1;i<=n;i++){
for(int j=H0[i];j;j=X0[j]){
if(ds[P0[j]]==ds[i]+E0[j]){
add1(i,P0[j],1);
add1(P0[j],i,0);
}
if(dt[P0[j]]==dt[i]+E0[j]){
add2(i,P0[j],0);
}
}
}
ff=0;
if(bfs()) ff+=dfs(S,1);
if(bfs()) ff+=dfs(S,1);
if(ff==2){
for(int i=0;i<Q;i++) printf("%lld\n",ds[T]);
goto ed;
}
for(int i=1;i<=n;i++) if(!low[i]) tarjan(i);
for(int i=2;i<=tot1;i+=2){
if(flow[i]==0&&id[from[i]]!=id[P1[i]]) cut[from[i]]=P1[i],E1[i]=1;
}
for(int i=1;i<=tot2;i++){
if(cut[P2[i]]==from2[i]) E2[i]=1;
}
memset(vis,0,sizeof vis);
memset(Ds,0x3f,sizeof Ds);
memset(Dt,0x3f,sizeof Dt);
Ds[S]=Dt[T]=0;
dq.push_back(S);
while(!dq.empty()){
x=dq.front();dq.pop_front();
if(vis[x]) continue;
vis[x]=1;
for(int i=H1[x];i;i=X1[i]){
if(i&1) continue;
Ds[P1[i]]=min(Ds[P1[i]],Ds[x]+E1[i]);
if(E1[i]){
dq.push_back(P1[i]);
}else dq.push_front(P1[i]);
}
}
memset(vis,0,sizeof vis);
dq.push_back(T);
while(!dq.empty()){
x=dq.front();dq.pop_front();
if(vis[x]) continue;
vis[x]=1;
for(int i=H2[x];i;i=X2[i]){
Dt[P2[i]]=min(Dt[P2[i]],Dt[x]+E2[i]);
if(E2[i]){
dq.push_back(P2[i]);
}else dq.push_front(P2[i]);
}
}
for(int i=1;i<=n;i++) if(ds[i]!=inf)v[Ds[i]].push_back(i);
for(int num=0;num<cnt;num++){
int siz=v[num].size();
while(!pq.empty()&&Dt[pq.top().y]>=Ds[T]-num) pq.pop();
for(int j=0;j<siz;j++){
x=v[num][j];
for(int i=H0[x];i;i=X0[i]){
if(Ds[P0[i]]>num&&cut[x]!=P0[i])
pq.push(A(x,P0[i],ds[x]+E0[i]+dt[P0[i]]));
}
}
int xx,yy;
if(!pq.empty()) xx=pq.top().x,yy=pq.top().y,ans[num]=pq.top().w;
}
for(int i=0,x,y;i<Q;i++){
scanf("%d%d",&x,&y);
if(cut[x]==y){
if(ans[Ds[x]]) printf("%lld\n",ans[Ds[x]]);
else puts("Infinity");
}else if(cut[y]==x){
if(ans[Ds[y]]) printf("%lld\n",ans[Ds[y]]);
else puts("Infinity");
}else{
printf("%lld\n",ds[T]);
}
}
ed:return 0;
}
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