P4221 [WC2018]州區劃分 無向圖歐拉回路 FST FWT
阿新 • • 發佈:2020-07-28
LINK:州區劃分
把題目中四個條件進行規約 容易想到不合法當前僅噹噹前狀態是一個無向圖歐拉回路.
充要條件有兩個 聯通 每個點度數為偶數.
預處理出所有狀態.
然後設\(f_i\)表示組成情況為i的值.
列舉子集轉移 可以發現利用FST進行優化.
FST怎麼做?詳見另一篇文章史上最詳細FST解釋
code
//#include<bits/stdc++.h> #include<iostream> #include<cstdio> #include<ctime> #include<cctype> #include<queue> #include<deque> #include<stack> #include<iostream> #include<iomanip> #include<cstdio> #include<cstring> #include<string> #include<ctime> #include<cmath> #include<cctype> #include<cstdlib> #include<queue> #include<deque> #include<stack> #include<vector> #include<algorithm> #include<utility> #include<bitset> #include<set> #include<map> #define ll long long #define db double #define INF 1000000000000000000ll #define inf 100000000000000000ll #define ldb long double #define pb push_back #define put_(x) printf("%d ",x); #define get(x) x=read() #define gt(x) scanf("%d",&x) #define gi(x) scanf("%lf",&x) #define put(x) printf("%d\n",x) #define putl(x) printf("%lld\n",x) #define rep(p,n,i) for(RE int i=p;i<=n;++i) #define go(x) for(int i=lin[x],tn=ver[i];i;tn=ver[i=nex[i]]) #define fep(n,p,i) for(RE int i=n;i>=p;--i) #define vep(p,n,i) for(RE int i=p;i<n;++i) #define pii pair<int,int> #define mk make_pair #define RE register #define P 1000000007ll #define gf(x) scanf("%lf",&x) #define pf(x) ((x)*(x)) #define uint unsigned long long #define ui unsigned #define EPS 1e-10 #define sq sqrt #define S second #define F first #define mod 998244353 #define max(x,y) ((x)<(y)?y:x) using namespace std; char *fs,*ft,buf[1<<15]; inline char gc() { return (fs==ft&&(ft=(fs=buf)+fread(buf,1,1<<15,stdin),fs==ft))?0:*fs++; } inline int read() { RE int x=0,f=1;RE char ch=gc(); while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=gc();} while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=gc();} return x*f; } const int MAXN=1<<21,maxn=22; int n,m,p,maxx; int f[maxn][MAXN],c[MAXN],g[maxn][MAXN],w[MAXN],in[MAXN]; int d[maxn],fa[maxn]; struct wy { int x,y; }t[MAXN]; inline int getfather(int x){return x==fa[x]?x:fa[x]=getfather(fa[x]);} inline int ksm(int b,int p) { int cnt=1; while(p) { if(p&1)cnt=(ll)cnt*b%mod; b=(ll)b*b%mod;p=p>>1; } return cnt; } inline void FWT(int *f,int op) { for(int len=2;len<=maxx+1;len=len<<1) { int mid=len>>1; for(int j=0;j<=maxx;j+=len) { vep(0,mid,i) { if(op==1)f[i+j+mid]=(f[i+j+mid]+f[i+j])%mod; else f[i+j+mid]=(f[i+j+mid]-f[i+j]+mod)%mod; } } } } inline int pd(int x) { if(c[x]<=1)return 0; int cnt=c[x]; rep(1,n,i)fa[i]=i,d[i]=0; rep(1,m,i) { if(((1<<(t[i].x-1))&x)&&((1<<(t[i].y-1))&x)) { d[t[i].x]^=1;d[t[i].y]^=1; int xx=getfather(t[i].x); int yy=getfather(t[i].y); if(xx==yy)continue; fa[xx]=yy;--cnt; } } if(cnt!=1)return 1; rep(1,n,i)if(d[i])return 1; return 0; } int main() { //freopen("1.in","r",stdin); get(n);get(m);get(p); rep(1,m,i) { int get(x),get(y); t[i]=(wy){x,y}; } rep(1,n,i)get(w[i]); maxx=1<<n;--maxx; rep(1,maxx,i) { int sum=0;c[i]=c[i>>1]+(i&1); rep(1,n,j)if(i&(1<<(j-1)))sum+=w[j]; sum=ksm(sum,p);in[i]=ksm(sum,mod-2); //cout<<pd(i)<<' '<<i<<endl; //cout<<sum<<endl; if(pd(i))g[c[i]][i]=sum; //cout<<g[c[i]][i]<<endl; } rep(1,n,i)FWT(g[i],1); f[0][0]=1;FWT(f[0],1); rep(1,n,i) { vep(0,i,j) rep(0,maxx,k)f[i][k]=(f[i][k]+(ll)f[j][k]*g[i-j][k])%mod; FWT(f[i],-1); rep(0,maxx,k)f[i][k]=(ll)f[i][k]*in[k]%mod; FWT(f[i],1); } FWT(f[n],-1); put(f[n][maxx]); return 0; }