[BZOJ2725/Violet 6]故乡的梦

Description

Input

Output

Sample Input
6 7
1 2 1
2 3 1
3 4 2
4 5 1
5 6 1
1 3 3
4 6 3
1 6
4
1 2
1 3
4 3
6 5

Sample Output
7
6
Infinity
7

HINT

---

其实这题和[TJOI2012]桥基本差不多，如果不是最短路径上的边，那直接输出最短路即可。否则就按照[TJOI2012]桥那题来即可

/*program from Wolfycz*/
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<unordered_set>
#define inf 0x7f7f7f7f7f7f7f7f
using namespace std;
typedef long long ll;
typedef unsigned int ui;
typedef unsigned long long ull;
inline int read(){
	int x=0,f=1;char ch=getchar();
	for (;ch<'0'||ch>'9';ch=getchar())	if (ch=='-')    f=-1;
	for (;ch>='0'&&ch<='9';ch=getchar())	x=(x<<1)+(x<<3)+ch-'0';
	return x*f;
}
inline void print(int x){
	if (x>=10)	print(x/10);
	putchar(x%10+'0');
}
const int N=2e5,M=2e5;
int pre[(M<<1)+10],now[N+10],child[(M<<1)+10],val[(M<<1)+10];
int Fa[N+10],Lca[N+10],stack[N+10],dfn[N+10];
bool vis[N+10],flag[(M<<1)+10];
int n,m,tot,num,Max;
ll Dis,Ans[N+10];
struct MyHash{
	size_t operator ()(const pair<int,int> &x)const{
		return ((hash<int>()(x.first)<<1)^(hash<int>()(x.second)))>>1;
	}
};
unordered_set<pair<int,int>,MyHash>st;
struct S1{
	#define ls (p<<1)
	#define rs (p<<1|1)
	#define fa (p>>1)
	struct node{
		int x;ll v;
		bool operator <(const node &a)const{return v<a.v;}
	}Q[N+10];
	int tot;
	void insert(int x,ll v){
		Q[++tot]=(node){x,v};
		int p=tot;
		while (p!=1&&Q[p]<Q[fa])	swap(Q[p],Q[fa]),p=fa;
	}
	void Delete(){
		Q[1]=Q[tot--];
		int p=1,son;
		while (ls<=tot){
			if (rs>tot||Q[ls]<Q[rs])	son=ls;
			else	son=rs;
			if (Q[son]<Q[p])	swap(Q[p],Q[son]),p=son;
			else	break;
		}
	}
}Heap;
struct Segment{
	ll tree[(N<<2)+10];
	Segment(){memset(tree,127,sizeof(tree));}
	void Add_tag(int p,ll v){tree[p]=min(tree[p],v);}
	void pushdown(int p){
		if (tree[p]==inf)	return;
		Add_tag(ls,tree[p]);
		Add_tag(rs,tree[p]);
	}
	void Modify(int p,int l,int r,int x,int y,ll v){
		if (x<=l&&r<=y){
			Add_tag(p,v);
			return;
		}
		int mid=(l+r)>>1;
		if (x<=mid)	Modify(ls,l,mid,x,y,v);
		if (y>mid)	Modify(rs,mid+1,r,x,y,v);
	}
	void traversals(int p,int l,int r){
		if (l==r){
			Ans[l]=tree[p];
			return;
		}
		pushdown(p);
		int mid=(l+r)>>1;
		traversals(ls,l,mid);
		traversals(rs,mid+1,r);
	}
}Tree;
struct S2{
	ll dis[N+10];
	S2(){memset(dis,63,sizeof(dis));}
}Frw,Bck;
void join(int x,int y,int z){pre[++tot]=now[x],now[x]=tot,child[tot]=y,val[tot]=z;}
void insert(int x,int y,int z){join(x,y,z),join(y,x,z);}
void dijkstra(int x,ll *dis){
	memset(vis,0,sizeof(vis));
	Heap.insert(x,dis[x]=0);
	while (Heap.tot){
		int Now=Heap.Q[1].x;
		Heap.Delete();
		if (vis[Now])	continue;
		vis[Now]=1;
		for (int p=now[Now],son=child[p];p;p=pre[p],son=child[p]){
			if (dis[son]>dis[Now]+val[p]){
				dis[son]=dis[Now]+val[p];
				Heap.insert(son,dis[son]);
			}
		}
	}
}
void put_flag(int x){
	for (int p=now[x],son=child[p];p;p=pre[p],son=child[p]){
		if (Frw.dis[x]+val[p]+Bck.dis[son]==Dis){
			st.insert(make_pair(x,son));
			st.insert(make_pair(son,x));
			flag[p]=flag[p+(p&1?1:-1)]=1;
			put_flag(son);
			return;
		}
	}
}
void Find_fa(int x){
	for (int p=now[x],son=child[p];p;p=pre[p],son=child[p])
		if (Frw.dis[x]+val[p]==Frw.dis[son]&&!Fa[son])	Fa[son]=x,Find_fa(son);
}
void Fill(int x,int v){
	if (Lca[x])	return;
	Lca[x]=v;
	for (int p=now[x],son=child[p];p;p=pre[p],son=child[p])	if (Fa[son]==x)	Fill(son,v);
}
void Get_Lca(int x){
	int top=0;
	while (x){
		Fill(x,x);
		stack[++top]=x;
		x=Fa[x];
	}
	for (int i=top;i;i--)	dfn[stack[i]]=num++;
	num--;
}
int main(){
	int n=read(),m=read();
	for (int i=1;i<=m;i++){
		int x=read(),y=read(),z=read();
		insert(x,y,z);
	}
	int S=read(),T=read();
	dijkstra(S,Frw.dis);
	dijkstra(T,Bck.dis);
	Dis=Frw.dis[T];
	put_flag(S);
	Find_fa(S);
	Get_Lca(T);
	for (int i=1;i<=tot;i+=2){
		if (flag[i])	continue;
		int x=child[i],y=child[i+1],v=val[i];
		if (Lca[x]==Lca[y])	continue;
		if (dfn[Lca[x]]>dfn[Lca[y]])	swap(x,y);
		ll tmp=Frw.dis[x]+v+Bck.dis[y];
		Tree.Modify(1,1,num,dfn[Lca[x]]+1,dfn[Lca[y]],tmp);
	}
	Tree.traversals(1,1,num);
	int Q=read();
	for (int i=1;i<=Q;i++){
		int x=read(),y=read();
		if (!st.count(make_pair(x,y))){
			printf("%lld\n",Dis);
			continue;
		}
		printf(Ans[max(dfn[x],dfn[y])]==inf?"Infinity\n":"%lld\n",Ans[max(dfn[x],dfn[y])]);
	}
	return 0;
}