[Violet 6]故乡的梦

Posted 2021-01-10 wolfycz

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
",Dis);
            continue;
        }
        printf(Ans[max(dfn[x],dfn[y])]==inf?"Infinity
":"%lld
",Ans[max(dfn[x],dfn[y])]);
    }
    return 0;
}