洛谷P6383 『MdOI R2』Resurrection 题解 树形DP

题目链接：https://www.luogu.com.cn/problem/P6383

解题思路：完全来自 冰冷的心 大佬的博客

示例程序（\(O(n^3)\)，TLE）：

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll mod = 998244353;
const int maxn = 3005;

int n;
bool vis[maxn][maxn];
ll f[maxn][maxn];
vector<int> g[maxn];

ll dfs(int u, int p, int i) {
    if (g[u].size() == 1) {
        return i;
    }
    if (vis[u][i])
        return f[u][i];
    vis[u][i] = true;
    for (int j = 2; j <= i+1; j++) {
        ll tmp = 1;
        for (auto v : g[u]) {
            if (v != p)
                (tmp *= dfs(v, u, j)) %= mod;
        }
        (f[u][i] += tmp) %= mod;
    }
    return f[u][i];
}

int main() {
    scanf("%d", &n);
    for (int i = 1, u, v; i < n; i++) {
        scanf("%d%d", &u, &v);
        g[u].push_back(v);
        g[v].push_back(u);
    }
    ll ans = 1;
    for (auto u : g[n]) {
        (ans *= dfs(u, n, 1)) %= mod;
    }
    printf("%lld\n", ans);
    return 0;
}

示例程序（\(O(n^2)\)，AC）：

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll mod = 998244353;
const int maxn = 3005;

int n;
bool vis[maxn][maxn];
ll f[maxn][maxn];
vector<int> g[maxn];

ll dfs(int u, int p, int i) {
    if (g[u].size() == 1) {
        return i;
    }
    if (vis[u][i])
        return f[u][i];
    vis[u][i] = true;

    if (i > 1) {
        f[u][i] = dfs(u, p, i-1);
    }

    ll tmp = 1;
    for (auto v : g[u]) {
        if (v != p)
            (tmp *= dfs(v, u, i+1)) %= mod;
    }
    (f[u][i] += tmp) %= mod;
    return f[u][i];
}

int main() {
    scanf("%d", &n);
    for (int i = 1, u, v; i < n; i++) {
        scanf("%d%d", &u, &v);
        g[u].push_back(v);
        g[v].push_back(u);
    }
    ll ans = 1;
    for (auto u : g[n]) {
        (ans *= dfs(u, n, 1)) %= mod;
    }
    printf("%lld\n", ans);
    return 0;
}