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;
}
