题目大意: 给定n个点的树 问:对于以i为根时,把树边黑白染色,使得任意点走到根的路径上不超过一条黑边,输出染色的方案数(mod 1e9+7);
题目分析:对于节点u,与其所有联通的节点v,存在f[u]*=(f[v]+1); 即 当该边为白边时,方案数为f[v] ,该边为黑边时,方案数为1;用up[i]来计算当前节点其中一个联通节点的方案数(其他节点通过他来寻找到当前所要计算的节点);
#include<cstdio> #include<cstdlib> #include<cstring> #include<iostream> #include<algorithm> #include<functional> #include<cmath> #include<cctype> #include<cassert> #include<vector> #include<climits> using namespace std; #define For(i,n) for(int i=1;i<=n;i++) #define Rep(i,n) for(int i=0;i<n;i++) #define Fork(i,k,n) for(int i=k;i<=n;i++) #define ForD(i,n) for(int i=n;i;i--) #define Forp(x) for(int p=pre[x];p;p=next[p]) #define RepD(i,n) for(int i=n;i>=0;i--) #define MEM(a) memset(a,0,sizeof(a)) #define MEMI(a) memset(a,127,sizeof(a)) #define MEMi(a) memset(a,128,sizeof(a)) #define INF (2139062143) #define phiF (1000000006) #define MAXN (1000000+10) typedef long long LL; const LL MOD=1000000007; vector<int> e[200005]; vector<LL> l[200005],r[200005]; int n,x; LL f[200005],up[200005]; void dfs1(int u,int fa){ f[u]=1; Fork(p,0,e[u].size()-1){ int v=e[u][p]; if (v==fa){ l[u].push_back(1); r[u].push_back(1); continue; } dfs1(v,u); f[u]=(f[u]*(f[v]+1))%MOD; l[u].push_back(f[v]+1); r[u].push_back(f[v]+1); } For (i,l[u].size()-1){ l[u][i]=(l[u][i]*l[u][i-1])%MOD; } RepD(i,r[u].size()-2){ r[u][i]=(r[u][i]*r[u][i+1])%MOD; } } void dfs2(int u,int fa,LL sum){ up[u]=sum; LL tmp; Rep (p,e[u].size()){ int v=e[u][p]; if (v==fa) continue; tmp=sum; if (p>0) tmp=(tmp*l[u][p-1])%MOD; if (p<e[u].size()-1) tmp=(tmp*r[u][p+1])%MOD; dfs2(v,u,tmp+1); } } int main(){ scanf("%d",&n); Fork (i,2,n){ scanf("%d",&x); e[x].push_back(i); e[i].push_back(x); } dfs1(1,0); up[1]=1; dfs2(1,0,1LL); For (i,n){ printf("%I64d ",f[i]*up[i]%MOD); } }