题目一：树形​​​​​​dp​​   ​​​​​​   https://codeforces.com/problemset/problem/1866/C

#include<bits/stdc++.h>
#define int long long
#define x first
#define y second
#define endl '\n'
#define pq priority_queue
using namespace std;
typedef pair<int,int> pii;
const int mod = 998244353;

void solve(){
    int n;
    cin >> n;
    vector<vector<pair<int,int>>>e(n + 1);
    for(int i = 0;i < n;i ++){
        int s;
        cin >> s;
        while(s --){
            int l, w;
            cin >> l >> w;
            e[i + 1].push_back({w, l});
        }
    }

    vector<array<int,3>>dp(n + 1);
    vector<int> st(n + 1);

    auto dfs =[&](auto self, int x){
        if(st[x]){
            return dp[x];
        }
        st[x] = true;

        for(auto [w, l] : e[x]){
            dp[x][2] = (dp[x][2] + dp[x][1] * (w == 0)) % mod;
            dp[x][w] += 1;
            auto g = self(self, l);
            dp[x][2] = ((dp[x][2] + g[0] * dp[x][1] % mod) % mod + g[2]) % mod;
            dp[x][1] += g[1];
            dp[x][1] %= mod;
            dp[x][0] += g[0];
            dp[x][0] %= mod;
        }
        return dp[x];
    };

    cout << dfs(dfs, 1)[2] << endl;

}

signed main()
{
    ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    int t = 1;
    while(t--)
    {
        solve();
    }
    return 0;
}
  

题目二（树形背包）：https://codeforces.com/problemset/problem/1856/E1

#include<bits/stdc++.h>
#define int long long
#define x first
#define y second
#define endl '\n'
#define pq priority_queue
using namespace std;
typedef pair<int,int> pii;

void solve(){
    int n;
    cin >> n;
    vector<vector<int>>e(n + 1);
    for(int i = 2;i <= n;i ++){
        int p;
        cin >> p;
        e[p].push_back(i);
    }

    vector<int>sz(5050);
    int ans = 0;

    auto dfs =[&](auto self, int u) -> void{
        bitset<5050>dp;
        dp.set(0);
        for(auto j : e[u]){
            self(self, j);
            sz[u] += sz[j];
            dp |= dp << sz[j];
        }
        int t = 0;
        for(int i = 0;i <= n / 2;i ++){
            if(dp.test(i)){
                t = max(t, i * (sz[u] - i));
            }
        }
        ans += t;
        sz[u] += 1;
    };

    dfs(dfs, 1);

    cout << ans << endl;

}

signed main()
{
    ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    int t = 1;
    while(t--)
    {
        solve();
    }
    return 0;
}
  

题目三(dp + 二分)：https://codeforces.com/problemset/problem/1862/F

#include<bits/stdc++.h>
#define int long long
#define x first
#define y second
#define endl '\n'
#define pq priority_queue
using namespace std;
typedef pair<int,int> pii;

void solve(){
    int w, f;
    cin >> w >> f;
    int n;
    cin >> n;
    vector<int>dp(1e6 + 10);
    int sum = 0;
    dp[0] = 1;
    for(int i = 1;i <= n;i ++){
        int x;
        cin >> x;
        sum += x;
        for(int i = 1e6;i >= x;i --)
            dp[i] |= dp[i - x];
    }

    auto check =[&](int mid) -> bool{
        int x = mid * w, y = mid * f;
        int ok = false;
        if(x >= sum || y >= sum)
            ok = true;
        for(int i = 0;i <= sum;i ++){
            if(dp[i] && x >= i && y >= (sum - i))
                ok = true;
        }
        return ok;
    };


    int l = 0, r = 1e9 + 1;
    while(l + 1 != r){
        int mid = l + r >> 1;
        if(check(mid))
            r = mid;
        else
            l = mid;
    }
    cout << r << endl;
}

signed main()
{
    ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    int t;cin>>t;
    while(t--)
    {
        solve();
    }
    return 0;
}