【换根DP】Subtree

古城微笑少年丶 2024-03-22 22:15 70阅读 0赞

[Subtree - 洛谷][Subtree -]

题意：

![2f05b09dc4aa4486aa9beb190e4cc95f.png][]

思路：

![c69aa721f5f942ae9b567a6372051967.png][]

![01f46b29aa2d457591395189c1390ad6.png][]

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;
    }

[Subtree -]: https://www.luogu.com.cn/problem/AT_dp_v
[2f05b09dc4aa4486aa9beb190e4cc95f.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/03/14/abf43c0d6bd24ec88b1d52cbbc9ddeb1.png
[c69aa721f5f942ae9b567a6372051967.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/03/14/ad5acb1a486a42088d8389aad7da16f0.png
[01f46b29aa2d457591395189c1390ad6.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/03/14/a1c29a9207f146a8bc7bc5adbd849b17.png