【JZOJ 省选模拟】向日葵人生

Description

Input

Output

Sample Input

样例 1 输入:
2
3 2
1 2
2 3

Sample Output

样例 1 输出:
665496241

Data Constraint

Hint

思路

树上一条路径可行的概率是1/len.（len个点，第一个点要第一个选到）
环上做一个容斥：路径A可行+路径B可行-路径AB均可行。
仙人掌上做dp容斥即可。

代码

#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int mod = 998244353,N = 477;
int n,m;
ll fac[N],unfac[N],inv[N];
ll power(ll x,ll y)
{
	ll ret = 1;
	for(; y; y >>= 1)
	{
		if (y & 1) ret = ret * x % mod;
		x = x * x % mod;
	}
	return ret;
}

int len[N];
ll f[N][N];
int no[N],cir[N],cnt,cirbel[N];
int ls[N],nx[N * 8],to[N * 8],tot = 1;

void add(int x,int y) {
	to[++tot] = y,nx[tot] = ls[x],ls[x] = tot;
}

int dfn[N],stm,p[N],e[N * 8]; 
int cirfa[N],dep[N];
void dfs(int x) {
	dfn[x] = ++ stm;
	for(int i = ls[x]; i; i = nx[i]) {
		if (i == p[x]) continue;
		int y = to[i];
		if (dfn[y] == 0) {
			p[y] = i ^ 1;
			dep[y] = dep[x] + 1;
			dfs(y);
		} else if(dfn[y] < dfn[x]) {
			e[i] = e[i ^ 1] = 1;
			++cnt;
			for(int z = x,w = 1; z != y; z = to[p[z]],w++) {
				no[z] = w;
				len[z] = dep[x] - dep[y] + 1;
				add(z,y),add(y,z);
				e[p[z]] = e[p[z] ^ 1] = 1;
				cirfa[z] = y;
				cirbel[z] = cnt;
			}
		}
	}
}

ll ans;
void work(int x,int from) {
	for(int i = 1; i <= n; i ++) {
		ans = (ans + inv[i] * f[x][i]) % mod;
	}
	for(int i = ls[x]; i; i = nx[i]) if (e[i] == 0) {
		int y = to[i];
		if (y == from) continue;
		if (y != cirfa[x] && cirfa[y] != x) { 
			for(int i = 1; i <= n; i++) f[y][i] = f[x][i - 1];
			work(y,x);
		} else {
			int ori = 0,a = 0,b = 0,cirlen = 0;
			if (cirfa[x] == y) {
				ori = x,a = no[x],b = len[x] - no[x],cirlen = len[x];
			} else {
				if (cirbel[y] == cirbel[from]) {
					cirlen = len[y];
					ori = from,a = (no[from] - no[y] + len[y]) % cirlen,b = cirlen - a;
				} else {
					ori = x,a = no[y],b = len[y] - no[y],cirlen = len[y];
				}
			}
			for(int i = 1; i <= n; i++) {
				if (i - a > 0) f[y][i] = f[ori][i - a];
				if (i - b > 0) f[y][i] = (f[y][i] + f[ori][i - b]) % mod;
				if (i - cirlen + 1 > 0) f[y][i] = (f[y][i] - f[ori][i - cirlen + 1]) % mod;
			}
			work(y,x);
		}
	}
}

int main() {
	freopen("falldream.in","r",stdin);freopen("falldream.out","w",stdout);
	cin >> n >> n >> m;
	for(int i = 1; i <= m; i++) {
		int x,y; scanf("%d %d",&x,&y);
		add(x,y),add(y,x);
	}
	dfs(1);
	fac[0] = 1;
	for(int i = 1; i <= n; i++) fac[i] = fac[i - 1] * i % mod;
	unfac[n] = power(fac[n],mod - 2);
	for(int i = n - 1; ~i; i--) unfac[i] = unfac[i + 1] * (i + 1) % mod;
	for(int i = 1; i <= n; i++) inv[i] = unfac[i] * fac[i - 1] % mod;
	for(int r = 1; r <= n; r++)
	{
		memset(f,0,sizeof f);
		f[r][1] = 1;
		work(r,0);
	}
	cout << (ans + mod) % mod << endl;
}

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