E89 换根DP AT_dp_v Subtree

视频链接：E89 换根DP AT_dp_v Subtree_哔哩哔哩_bilibili

 

 

AT_dp_v Subtree - 洛谷 | 计算机科学教育新生态 (luogu.com.cn)

// 换根DP O(n)
#include<bits/stdc++.h>
using namespace std;

#define LL long long
const int N=100010;
vector<int> e[N];
int n,M;
LL f[N],g[N],pre[N],bac[N];

void dfs(int u,int fa){
  f[u]=1; vector<int> q;
  for(int v:e[u]){
    if(v==fa) continue;
    dfs(v,u);
    f[u]=f[u]*(f[v]+1)%M;
    q.push_back(v);
  }
  LL p=1,b=1;
  for(int i=0;i<q.size();i++){
    pre[q[i]]=p; p=p*(f[q[i]]+1)%M;
  }
  for(int i=q.size()-1;i>=0;i--){
    bac[q[i]]=b; b=b*(f[q[i]]+1)%M;
  }
}
void dfs2(int u,int fa){
  for(int v:e[u]){
    if(v==fa) continue;
    g[v]=(g[u]*(pre[v]*bac[v]%M)%M+1)%M;
    dfs2(v,u);
  }
}
int main(){
  scanf("%d%d",&n,&M);
  for(int i=1,u,v;i<n;i++){
    scanf("%d%d",&u,&v);
    e[u].push_back(v);
    e[v].push_back(u);
  }
  dfs(1,0);
  g[1]=1;
  dfs2(1,0);
  for(int i=1;i<=n;i++)
    printf("%d\n",f[i]*g[i]%M);
}

 

// 换根DP O(n)
#include<bits/stdc++.h>
using namespace std;

#define LL long long
const int N=100010;
vector<int> e[N];
int n,M;
LL f[N],g[N],pre[N],bac[N];

void dfs(int u,int fa){
  f[u]=1; vector<int> q;
  for(int v:e[u]){
    if(v==fa) continue;
    dfs(v,u);
    f[u]=f[u]*(f[v]+1)%M;
    q.push_back(v);
  }
  LL p=1,b=1;
  for(int i=0;i<q.size();i++){
    pre[q[i]]=p; p=p*(f[q[i]]+1)%M;
  }
  for(int i=q.size()-1;i>=0;i--){
    bac[q[i]]=b; b=b*(f[q[i]]+1)%M;
  }
}
void dfs2(int u,int fa){
  if(fa==0) g[u]=1;
  else g[u]=(g[fa]*(pre[u]*bac[u]%M)%M+1)%M;
  for(int v:e[u]){
    if(v==fa) continue;
    dfs2(v,u);
  }
}
int main(){
  scanf("%d%d",&n,&M);
  for(int i=1,u,v;i<n;i++){
    scanf("%d%d",&u,&v);
    e[u].push_back(v);
    e[v].push_back(u);
  }
  dfs(1,0);
  dfs2(1,0);
  for(int i=1;i<=n;i++)
    printf("%d\n",f[i]*g[i]%M);
}