Saturday, June 22, 2024

# Codeforces Round #411 (Div. 2), problem: (F) Expected diameter of a tree Solution In C/C++

#include <set>
#include <vector>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int N=200050;
vector<int>vec[N],dis[N],sum[N];
struct Node{int x,y;double ans;}JY;
bool operator<(Node a,Node b){if(a.x!=b.x)return a.x<b.x;return a.y<b.y;}
set<Node>s;set<Node>::iterator it;
int n,m,q,first[N],nxt[N],v[N],w[N],tot,root,xx,yy,vis[N];
int maxx[N][2],rec[N][2],f[N],Root[N],vv[N],fi,flag,size[N];
int find(int x){return x==f[x]?x:f[x]=find(f[x]);}
void get_dia(int x,int fa){
rec[x][0]=rec[x][1]=x;
for(int i=first[x];~i;i=nxt[i])if(v[i]!=fa){
get_dia(v[i],x);
if(maxx[v[i]][0]+w[i]>maxx[x][0])
maxx[x][1]=maxx[x][0],rec[x][1]=rec[x][0],
maxx[x][0]=maxx[v[i]][0]+w[i],rec[x][0]=rec[v[i]][0];
else if(maxx[v[i]][0]+w[i]>maxx[x][1])
maxx[x][1]=maxx[v[i]][0]+w[i],rec[x][1]=rec[v[i]][0];
}if(maxx[x][0]+maxx[x][1]>maxx[root][0]+maxx[root][1])root=x;
}
void DFS(int x,int fa,int deep){
vv[x]=max(vv[x],deep);
if(flag)vec[fi].push_back(vv[x]),size[fi]++;
for(int i=first[x];~i;i=nxt[i])if(v[i]!=fa){
DFS(v[i],x,deep+w[i]);
}
}
int main(){
memset(first,-1,sizeof(first));
scanf(“%d%d%d”,&n,&m,&q);
for(int i=1;i<=n;i++)f[i]=i;
for(int i=1;i<=m;i++)
for(int i=1;i<=n;i++){
fi=find(i);
if(!rec[fi][0]){
root=flag=0,get_dia(i,0),Root[fi]=root;
DFS(rec[root][0],0,0),flag=1,DFS(rec[root][1],0,0);
}
}
for(int i=1;i<=n;i++){
fi=find(i);
if(!vis[fi]){
vis[fi]=1;
dis[fi].resize(size[fi]+1),sum[fi].resize(size[fi]+1);
for(int j=0;j<vec[fi].size();j++)
dis[fi][vec[fi][j]]++,sum[fi][vec[fi][j]]+=vec[fi][j];
for(int j=size[fi]-1;j>=0;j–)
dis[fi][j]+=dis[fi][j+1],sum[fi][j]+=sum[fi][j+1];
}
}
while(q–){
scanf(“%d%d”,&xx,&yy);
int fx=find(xx),fy=find(yy);
if(fx==fy){puts(“-1”);continue;}
if(vec[fx].size()>vec[fy].size())swap(xx,yy),swap(fx,fy);
JY.x=fx,JY.y=fy;
if((it=s.find(JY))!=s.end()){printf(“%.10lf\n”,it->ans);continue;}
int dis1=maxx[Root[fx]][0]+maxx[Root[fx]][1];
int dis2=maxx[Root[fy]][0]+maxx[Root[fy]][1];
int Dis=max(dis1,dis2);
long long ans=0;
for(int i=0;i<vec[fx].size();i++){
ans+=sum[fy][Dis-vec[fx][i]]+1ll*dis[fy][Dis-vec[fx][i]]*(vec[fx][i]+1);
ans+=1ll*Dis*(size[fy]-dis[fy][Dis-vec[fx][i]]);
}
JY.ans=(double)ans/size[fx]/size[fy],s.insert(JY);
printf(“%.10lf\n”,(double)ans/size[fx]/size[fy]);
}
// for(int i=1;i<=n;i++)printf(“%d “,vv[i]);
}

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