# Codeforces 1051E. Vasya and Big integers

Source: Internet
Author: User

Test instructions: Give you N a point M edge, m-n<=20, there are 1e5 inquiries, ask two points of the shortest distance. No self-loops and heavy edges are guaranteed.

Problem: Even the topic is prompt you this 20 is very useful, so if it is a tree, then the shortest distance of any two points is to ask for an LCA to engage in a problem. So we can first find the smallest spanning tree, then there will be a maximum of 42 points, we know that the non-tree edge may be better, so for each non-tree edge corresponding two points run over Dij, try to update the answer Ans=min (Ans,dis[i][u]+dis[i][v]). Correctness: Possible through multiple non-tree edges? In the run Dij in fact has been dealt with the shortest way, if it is more than the tree edge more excellent, then it records is such a value. Why is the code of the other person so short ...

`#include <bits/stdc++.h> #define LL long long#define PB push_back#define ls x<<1#define rs x<<1|1# Define ull unsigned long long#define _mp make_pair#define ldb long doubleusing namespace Std;const int Maxn=1e5+100;const    ll inf=1e18;int bcg[maxn];struct edge{int u,v,nxt; ll W;}    Edge[maxn*2],edge1[maxn*2];vector<edge>vec[maxn];struct node{ll P;    int V;    friend bool operator< (Node A,node b) {return a.p>b.p; } node () {} node (ll x,int y) {p=x,v=y;}}; int head[maxn],head1[maxn];ll deep[maxn];int depth[maxn];int bian[maxn*2];ll dis[50][maxn];int lca[maxn][25];int vis[ Maxn];int cnt,cnt1,tot;int n,m;int findd (int x) {return bcg[x]==x?bcg[x]:bcg[x]=findd (bcg[x]);} BOOL CMP (Edge A,edge b) {return A.W&LT;B.W;} void add_e1 (int x,int y,ll W) {++cnt1;edge1[cnt1].u=x;edge1[cnt1].v=y;edge1[cnt1].w=w;edge1[cnt1].nxt=head1[x]; Head1[x]=cnt1;} void add_e (int x,int y,ll W) {++cnt;edge[cnt].u=x;edge[cnt].v=y;edge[cnt].w=w;edge[cnt].nxt=head[x];head[x]=cnt;}    int merges (int x,int y) {int xx=findd (x);    int yy=findd (y);        if (xx!=yy) {bcg[xx]=yy;    return 1; } return 0;}    void Init () {cnt=cnt1=0;    tot=0;    memset (deep,0,sizeof (deep));    memset (head,0,sizeof (head)); memset (head1,0,sizeof (Head1));}    void Dfs (int x,int ff) {lca[x][0]=ff;    for (int i=1;i<=20;i++) lca[x][i]=lca[lca[x][i-1]][i-1];        for (int i=head[x];i;i=edge[i].nxt) {int v=edge[i].v;        if (V==FF) continue;        DEEP[V]=DEEP[X]+EDGE[I].W;        depth[v]=depth[x]+1;    DFS (V,X);    }}int LCA (int x,int y) {if (Depth[x]<depth[y]) swap (x, y);    int ff=depth[x]-depth[y];    for (int i=20;i>=0;i--) {if (ff& (1<<i)) x=lca[x][i];    } if (x==y) return y;    for (int i=20;i>=0;i--) {if (Lca[x][i]!=lca[y][i]) x=lca[x][i],y=lca[y][i]; } return lca[y][0];}        Priority_queue<node>que;void dij (int id,int x) {for (int i=0;i<=n+4;i++) {dis[id][i]=inf; vis[i]=0;    } dis[id][x]=0;    while (!que.empty ()) Que.pop ();    Que.push (Node (0,x));        while (!que.empty ()) {Node vv=que.top (); Que.pop (); if (vis[vv.v]| |        VV.P&GT;DIS[ID][VV.V]) continue;        Vis[vv.v]=1;            for (int i=0;i< (int) vec[vv.v].size (); i++) {Edge k=vec[vv.v][i];            int sw=k.v;            if (VIS[SW]) continue;                if (DIS[ID][SW]&GT;DIS[ID][VV.V]+K.W) {DIS[ID][SW]=DIS[ID][VV.V]+K.W;            Que.push (Node (DIS[ID][SW],SW));    }}}}int Main () {scanf ("%d%d", &n,&m);    int u,v;    ll W;    Init ();        for (int i=1;i<=m;i++) {scanf ("%d%d%lld", &u,&v,&w);        Add_e1 (U,V,W);        Vec[u].push_back (Edge) {u,v,0,w});    Vec[v].push_back (Edge) {v,u,0,w});    } sort (edge1+1,edge1+cnt1+1,cmp);    for (int i=1;i<=n+4;i++) bcg[i]=i;        for (int i=1;i<=cnt1;i++) {int x=edge1[i].u,y=edge1[i].v;    if (merges (x, y)) {        Add_e (X,Y,EDGE1[I].W);        Add_e (Y,X,EDGE1[I].W);            } else {bian[++tot]=x;        Bian[++tot]=y;    }} depth[1]=0;    deep[1]=0;    DFS (1,0);    Sort (bian+1,bian+1+tot);    int Sz=unique (Bian+1,bian+1+tot)-(bian+1);    for (int i=1;i<=sz;i++) {dij (i,bian[i]);    } int q;    scanf ("%d", &q);    int x, y;        while (q--) {scanf ("%d%d", &x,&y);        ll Ans=inf;        int Pq=lca (x, y);        ANS=DEEP[X]+DEEP[Y]-2*DEEP[PQ];        for (int i=1;i<=sz;i++) {ans=min (ans,dis[i][x]+dis[i][y]);    } cout<<ans<< "\ n"; } return 0;}`

Codeforces 1051E. Vasya and Big integers

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