牛客多校（7） J题 Melborp Elcissalc & 杭电多校（7）1003 Counting Stickmen

这两场多校的两道计数dp
参考博客：

蔚来杯2022牛客暑期多校训练营7 CFGJ
“蔚来杯“2022牛客暑期多校训练营7 J题: Melborp Elcissalc
2022 杭电多校7 个人题解

#include<bits/stdc++.h>
using namespace std;

#define fr first
#define se second
#define et0 exit(0);
#define rep(i, a, b) for(int i = (int)(a); i <= (int)(b); i ++)
#define rrep(i, a, b) for(int i = (int)(a); i >= (int)(b); i --)
#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);

typedef long long LL;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef unsigned long long ULL;

const int INF = 0X3f3f3f3f, N = 70, MOD = 998244353;
const double eps = 1e-7, pi = acos(-1);

int f[N][N][N * N], C[N][N];

inline void qadd(int&a, int b) {
	a += b;
	if (a >= MOD) a -= MOD;
}

void Init() {
	C[0][0] = 1;
	rep (i, 1, N - 1) {
		C[i][0] = 1;
		rep (j, 1, i) {
			C[i][j] = C[i - 1][j - 1];
			qadd(C[i][j], C[i - 1][j]);
		}
	}
}

void work() {
	int n, k, t;
	cin >> n >> k >> t;
	
	f[0][0][0] = 1;
	rep (i, 1, k) {
		for (int j = 0; j <= n; j++) {
			rep (u, 0, t) {
				if (!f[i - 1][j][u]) continue;
				for (int v = 0; v + j <= n; v++) {
					if (i == 1) {
						qadd(f[i][v + j][u + C[v + 1][2]], (LL)C[v + j][v] * f[i - 1][j][u] % MOD);
					}
					else {
						qadd(f[i][v + j][u + C[v][2]], (LL)C[v + j][v] * f[i - 1][j][u] % MOD);
					}
				}
			}
		}
	}
	
	cout << f[k][n][t] << endl;
}

signed main() {
	IO
	Init();

	int test = 1;
//	cin >> test;


	while (test--) {
		work();
	}

	return 0;
}

#include<bits/stdc++.h>
using namespace std;

#define fr first
#define se second
#define et0 exit(0);
#define rep(i, a, b) for(int i = (int)(a); i <= (int)(b); i ++)
#define rrep(i, a, b) for(int i = (int)(a); i >= (int)(b); i --)
#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);

typedef long long LL;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef unsigned long long ULL;

const int INF = 0X3f3f3f3f, N = 5e5 + 10, MOD = 998244353;
const double eps = 1e-7, pi = acos(-1);

LL n, ans;

LL d[N];
LL hand[N], body[N];

vector<int> g[N];

LL qmi(LL a, LL b, LL p) {
	LL base = a, res = 1;
	while (b) {
		if (b & 1) res = res * base % p;
		base = base * base % p;
		b >>= 1;
	}
	return res % p;
}

int C2(LL x) {
	return x * (x - 1) / 2 % MOD;
}

void dfs(int u, int fa) {
	LL b = 0, h = 0;
	for (auto v : g[u]) {
		b += body[v];
		h += hand[v];
		b %= MOD, h %= MOD;
		if (v == fa) continue;
		dfs(v, u);
	}

	if (d[u] < 4) return;

	for (auto v : g[u]) {
		LL res = (body[v] * (d[u] - 3) % MOD * ((C2((h - hand[v] + MOD) % MOD) - ((b - body[v] + MOD) % MOD) + MOD) % MOD)) % MOD;
		ans = (ans + res) % MOD;
	}

}

void work() {
	cin >> n;
	rep (i, 1, n) g[i].clear(), body[i] = hand[i] = d[i] = 0;
	rep (i, 2, n) {
		int x, y;
		cin >> x >> y;
		g[x].push_back(y), g[y].push_back(x);
		d[x]++, d[y]++;
	}

	rep (i, 1, n) {
		if (d[i] >= 2) hand[i] = d[i] - 1;
		if (d[i] >= 3) body[i] = C2(d[i] - 1);
	}

	ans = 0;
	dfs(1, 0);

	cout << ans << endl;
}

signed main() {
	IO
	int test = 1;
	cin >> test;

	while (test--) {
		work();
	}

	return 0;
}