cf 543 D. Road Improvement

（懒得想了，，又是DP）

 #include<bits/stdc++.h>
 #define N 200005
 #define LL long long
 #define inf 0x3f3f3f3f
 #define ls tr[x][0]
 #define rs tr[x][1]
 using namespace std;
 inline int ra()
 {
     int x=,f=; char ch=getchar();
     while (ch<'' || ch>'') {if (ch=='-') f=-; ch=getchar();}
     while (ch>='' && ch<='') {x=x*+ch-''; ch=getchar();}
     return x*f;
 }
 const int mod=1e9+;
 vector<LL > G[N],L[N],R[N];
 LL dp[N],up[N];
 int n;
 void dfsdown(int x, int fa)
 {
     dp[x]=;
     for (int i=; i<G[x].size(); i++)
     {
         int v=G[x][i];
         if (v==fa) {L[x].push_back(); R[x].push_back(); continue;}
         dfsdown(v,x);
         L[x].push_back(dp[v]+);
         R[x].push_back(dp[v]+);
         dp[x]=dp[x]*(dp[v]+)%mod;
     }
     for (int i=; i<L[x].size(); i++) L[x][i]=L[x][i]*L[x][i-]%mod;
     for (int i=R[x].size()-;i>=; i--) R[x][i]=R[x][i]*R[x][i+]%mod;
 }
 void dfsup(int x, int fa, int val)
 {
     up[x]=val; LL tem;
     for (int i=; i<G[x].size(); i++)
     {
         int v=G[x][i];
         tem=val;
         if (v==fa) continue;
         if (i>) tem=tem*L[x][i-]%mod;
         if (i<G[x].size()-) tem=tem*R[x][i+]%mod;
         dfsup(v,x,tem+);
     }
 }
 int main()
 {
     n=ra();
     for (int i=; i<=n; i++)
     {
         int x=ra();
         G[x].push_back(i);
         G[i].push_back(x);
     }
     dfsdown(,); dfsup(,,);
     for (int i=; i<=n; i++)
         printf("%I64d ",up[i]*dp[i]%mod);
 }