Codeforces 461 B. Appleman and Tree

標籤：des   style   color   os   io   ar   for   art   div   

樹形DP。。。

B. Appleman and Treetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

Appleman has a tree with n vertices. Some of the vertices (at least one) are colored black and other vertices are colored white.

Consider a set consisting of k (0?≤?k?<?n) edges of Appleman‘s tree. If Appleman deletes these edges from the tree, then it will split into (k?+?1) parts. Note, that each part will be a tree with colored vertices.

Now Appleman wonders, what is the number of sets splitting the tree in such a way that each resulting part will have exactly one black vertex? Find this number modulo 1000000007 (109?+?7).

Input

The first line contains an integer n (2??≤?n?≤?105) — the number of tree vertices.

The second line contains the description of the tree: n?-?1 integers p0,?p1,?...,?pn?-?2 (0?≤?pi?≤?i). Where pi means that there is an edge connecting vertex (i?+?1) of the tree and vertex pi. Consider tree vertices are numbered from 0 to n?-?1.

The third line contains the description of the colors of the vertices: n integers x0,?x1,?...,?xn?-?1 (xi is either 0 or 1). If xi is equal to1, vertex i is colored black. Otherwise, vertex i is colored white.

Output

Output a single integer — the number of ways to split the tree modulo 1000000007 (109?+?7).

Sample test(s)input

30 00 1 1

output

2

input

60 1 1 0 41 1 0 0 1 0

output

1

input

100 1 2 1 4 4 4 0 80 0 0 1 0 1 1 0 0 1

output

27

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>using namespace std;const int maxn=100010;const long long int mod=1000000007LL;int n;struct Edge{int to,next;}edge[3*maxn];int Adj[maxn],Size;void init(){Size=0;memset(Adj,-1,sizeof(Adj));}void Add_Edge(int u,int v){edge[Size].to=v;edge[Size].next=Adj[u];Adj[u]=Size++;}int c[maxn];long long int dp[maxn][2];void dfs(int u,int fa){dp[u][c[u]]=1;for(int i=Adj[u];~i;i=edge[i].next){int v=edge[i].to;if(v==fa) continue;dfs(v,u);dp[u][1]=(dp[u][1]*dp[v][1]%mod+dp[u][0]*dp[v][1]%mod+dp[u][1]*dp[v][0]%mod)%mod;dp[u][0]=(dp[u][0]*dp[v][0]%mod+dp[u][0]*dp[v][1]%mod)%mod;}}int main(){init();scanf("%d",&n);for(int i=1;i<n;i++){int v;scanf("%d",&v);Add_Edge(i,v);Add_Edge(v,i);}for(int i=0;i<n;i++)scanf("%d",c+i);dfs(0,0);printf("%I64d\n",dp[0][1]);return 0;}

Codeforces 461 B. Appleman and Tree