【换根DP】Subtree-蒲公英云

【换根DP】Subtree

Subtree - 洛谷

题意：

思路：

Code：

#include <bits/stdc++.h>
#define int long long
using namespace std;
const int mxn=1e5+10;
const int mxv=1e5+10;
vector<int> G[mxn]; 
int N,P,u,v;
int f[mxn],g[mxn],son[mxn],pre[mxn],suf[mxn];
void dfs(int u,int fa){
    f[u]=1;
    for(auto v:G[u]){
        if(v==fa) continue;
        dfs(v,u);
        f[u]*=(f[v]+1)%P;
        f[u]%=P;
    }
}
void dfs2(int u,int fa){
    if(G[u].size()==1&&G[u][0]==fa) return;
    int idx=0;
    for(auto v:G[u]){
        if(v==fa) continue;
        son[++idx]=v;
    }
    pre[0]=suf[idx+1]=1;
    for(int i=1;i<=idx;i++){
        pre[i]=pre[i-1]*(f[son[i]]+1)%P;
    }
    for(int i=idx;i>=1;i--){
        suf[i]=suf[i+1]*(f[son[i]]+1)%P;
    }
    for(int i=1;i<=idx;i++){
        g[son[i]]=(pre[i-1]*suf[i+1]%P*g[u]%P+1ll)%P;
    }
    for(auto v:G[u]){
        if(v==fa) continue;
        dfs2(v,u);
    }
}
void solve(){
    cin>>N>>P;
    for(int i=1;i<=N-1;i++){
        cin>>u>>v;
        G[u].push_back(v);
        G[v].push_back(u);
    }
    dfs(1,0);
    g[1]=1;
    dfs2(1,0);
    for(int i=1;i<=N;i++){ 
        cout<<f[i]*g[i]%P<<'\n';
    }
}
signed main(){
    ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
    int __=1;//cin>>__;
    while(__--)solve();return 0;
}

优美版（重生之我是jiangly)：

#include <bits/stdc++.h>
using i64 = long long;
using namespace std;
const int N = 1e5 + 10;
const int Inf = 1e18;
vector<int> adj[N];
int m;
int dp[N], dp2[N], num[N];
int pre[N], suf[N];
void dfs1(int u,int fa) {
    dp[u] = 1;
    for (auto v : adj[u]) {
        if (v == fa) continue;
        dfs1(v, u);
        dp[u] = dp[u] * (dp[v] + 1) % m;
        dp[u] %= m;
    }
}
void dfs2(int u,int fa) {
    if (adj[u].size() == 1 && adj[u][0] == fa) return;
    int len = 0;
    for (auto v : adj[u]) {
        if (v == fa) continue;
        num[++len] = v;
    }
    pre[0] = suf[len + 1] = 1;
    for (int i = 1; i <= len; i ++) {
        pre[i] = pre[i - 1] * (dp[num[i]] + 1) % m;
    }
    for (int i = len ; i >= 1; i --) {
        suf[i] = suf[i + 1] * (dp[num[i]] + 1) % m;
    }
    for (int i = 1; i <= len; i ++) {
        dp2[num[i]] = (pre[i - 1] * suf[i + 1] %m * dp2[u] %m + 1) % m;
    }
    for (auto v : adj[u]) {
        if (v == fa) continue;
        dfs2(v, u);
    }
}
void solve() {
    int n;
    cin >> n >> m;
    for (int i = 1; i <= n - 1; i ++) {
        int u, v;
        cin >> u >> v;
        adj[u].push_back(v);
        adj[v].push_back(u);
    }
    dfs1(1, 0);
    dp2[1] = 1;
    dfs2(1, 0);
    for (int i = 1; i <= n; i ++) {
        cout << dp2[i] * dp[i] % m << "\n";
    }
}
signed main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int t = 1;
    while (t-- ) {
        solve();
    }
    return 0;
}