[NOIP2016 Improve Group A Simulation 7.17] Looking for

topic

Bob and Alice went out for their honeymoon, but Alice got lost accidentally. After Bob was sad, he decided to go to find Alice.
Where they honeymoon is a tree with N nodes, Bob will traverse the tree using the following DFS algorithm.
starting_time is an array of capacity n
current_time = 0
dfs(v):
current_time = current_time + 1
starting_time[v] = current_time
Randomize the order of children[v] (each with the same probability)
// children[v] Array of direct children of
v for u in children[v]:
dfs(u)
1 is the root of this tree, Bob will start from 1, i.e. run dfs(1), now he wants to know the expected value of starting_time at each point .

analyze

It is found that when a node is traversed, the subtree rooted at the node must be traversed earlier than its siblings.
If node x is requested, its siblings must contribute to it.
For a parent node F, its sons are S1, S2, S3...
Suppose now to find S1,
because the order of children[v] is randomly arranged, so the probability of its brothers in front of it is \( \dfrac{1}{2}\) .
Total contribution
starting_time[S1]=starting_time[F]+(size[S2]+size[S3]+...)/2+1=starting_time[F]+(size[F]-1-size[S1]) /2+1

#include <cmath>
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <queue>
const int maxlongint=2147483647;
const int mo=1000000007;
const int N=100005;
using namespace std;
double f[N];
int size[N],fa[N],next[N*2],last[N*2],to[N*2],n,m,tot;
int bj(int x,int y)
{
    next[++tot]=last[x];
    last[x]=tot;
    to[tot]=y;
}
int dg(int x)
{
    size[x]=1;
    for(int i=last[x];i;i=next[i])
    {
        int j=to[i];
        if(j!=fa[x])
        {
            dg(j);
            size[x]+=size[j];
        }
    }
}
int dg1(int x)
{
    for(int i=last[x];i;i=next[i])
    {
        int j=to[i];
        if(j!=fa[x])
        {
            f[j]=f[x]+double(size[x]-1-size[j])*0.5+1;
            dg1(j);
        }
    }
}
int main()
{
    scanf("%d",&n);
    for(int i=2;i<=n;i++)
    {
        scanf("%d",&fa[i]);
        bj(fa[i],i);
        bj(i,fa[i]);
    }
    dg(1);
    f[1]=1;
    dg1(1);
    for(int i=1;i<=n;i++)
    {
        printf("%.1lf ",f[i]);
    }
}