题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=6073
题意:给个图,求每个完全匹配的权值的积,最后再求和
解法:首先用拓扑排序处理一下度为1的边,这些边对答案的贡献就是它的权值,不难想到答案就是ans1*sigma(每个连通块的贡献),所谓连通块就是指删掉度为1的点,剩下的联通块的方案数,所以在拓扑的过程中直接乘以度为1的边的权值,之后对每个环DFS,得到当前这个环贡献的答案,由于是匹配只有两种答案,交替走就可以了,这个用DFS可以轻松搬办到。
#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int maxn = 300010;
const int mod = 998244353;
struct FastIO
{
static const int S = 1310720;
int wpos;
char wbuf[S];
FastIO() : wpos(0) {}
inline int xchar()
{
static char buf[S];
static int len = 0, pos = 0;
if (pos == len)
pos = 0, len = fread(buf, 1, S, stdin);
if (pos == len) return -1;
return buf[pos ++];
}
inline int xuint()
{
int c = xchar(), x = 0;
while (c <= 32) c = xchar();
for (; '0' <= c && c <= '9'; c = xchar()) x = x * 10 + c - '0';
return x;
}
inline int xint()
{
int s = 1, c = xchar(), x = 0;
while (c <= 32) c = xchar();
if (c == '-') s = -1, c = xchar();
for (; '0' <= c && c <= '9'; c = xchar()) x = x * 10 + c - '0';
return x * s;
}
inline void xstring(char *s)
{
int c = xchar();
while (c <= 32) c = xchar();
for (; c > 32; c = xchar()) * s++ = c;
*s = 0;
}
inline void wchar(int x)
{
if (wpos == S) fwrite(wbuf, 1, S, stdout), wpos = 0;
wbuf[wpos ++] = x;
}
inline void wint(LL x)
{
if (x < 0) wchar('-'), x = -x;
char s[24];
int n = 0;
while (x || !n) s[n ++] = '0' + x % 10, x /= 10;
while (n--) wchar(s[n]);
}
inline void wstring(const char *s)
{
while (*s) wchar(*s++);
}
~FastIO()
{
if (wpos) fwrite(wbuf, 1, wpos, stdout), wpos = 0;
}
} io;
struct edge{
int to,w,next;
bool mark;
}E[maxn*4];
int T, n, head[maxn*2], edgecnt, du[maxn*2], used[maxn*2];
LL temp[2];
void init(){
memset(head,-1,sizeof(head));
edgecnt=0;
}
void add(int u, int v, int w){
E[edgecnt].to=v,E[edgecnt].w=w,E[edgecnt].next=head[u],E[edgecnt].mark=0,head[u]=edgecnt++;
}
void dfs(int x, int id){
used[x]=1;
for(int i=head[x];~i;i=E[i].next){
if(E[i].mark) continue;
E[i].mark=E[i^1].mark=1;
temp[id]*=E[i].w;
temp[id]%=mod;
dfs(E[i].to, 1-id);
}
}
int main()
{
T = io.xint();
while(T--){
init();
n = io.xint();
memset(du, 0, sizeof(du));
memset(used, 0, sizeof(used));
int u,v,w;
for(u=1; u<=n; u++){
for(int i=1; i<=2; i++){
//scanf("%d%d",&v,&w);
v = io.xint();
w = io.xint();
add(u,v+n,w);
add(v+n,u,w);
du[u]++;
du[v+n]++;
}
}
LL ans=1;
queue <int> q;
for(u=n+1; u<=n+n; u++){
if(du[u]==1){
q.push(u);
}
}
while(q.size())
{
u=q.front(); q.pop();
used[u]=1;
for(int i=head[u]; ~i; i=E[i].next){
if(E[i].mark) continue;
E[i].mark=E[i^1].mark=1;
used[E[i].to]=1;
ans*=E[i].w;
ans%=mod;
for(int j=head[E[i].to]; ~j; j=E[j].next){
E[j].mark=E[j^1].mark=1;
du[E[j].to]--;
if(du[E[j].to]==1) q.push(E[j].to);
}
}
}
for(int i=1; i<=n; i++){
if(used[i]) continue;
temp[0]=temp[1]=1;
dfs(i,0);
ans=(ans%mod*(temp[0]+temp[1])%mod)%mod;
}
ans %= mod;
printf("%lld\n", ans);
}
return 0;
}