loj#2340. 「WC2018」州区划分
FWT&&FMT板子
#include<cstdio> #include<iostream> #include<cstring> #include<cstdlib> #include<algorithm> #include<cmath> using namespace std; typedef long long LL; const int _=1e2; const int maxn=21+5; const int fbin=(1<<21)+_; const LL mod=998244353; LL quick_pow(LL A,int p) { LL ret=1; while(p!=0) { if(p%2==1)ret=ret*A%mod; A=A*A%mod;p/=2; } return ret; } //--------------------------------------------------def-------------------------------------------------------- struct node { int x,y,next; }a[maxn*maxn];int len,last[maxn]; void ins(int x,int y) { len++; a[len].x=x;a[len].y=y; a[len].next=last[x];last[x]=len; } int w[maxn],du[maxn]; int fa[maxn]; int findfa(int x) { if(x==fa[x])return x; fa[x]=findfa(fa[x]);return fa[x]; } //--------------------------------------------pre-------------------------------------------------------------- int cnt[fbin]; LL h[fbin],g[maxn][fbin],f[maxn][fbin]; void FWT(LL *a,int n,int op) { for(int i=1;i<n;i<<=1) for(int j=0;j<n;j+=(i<<1)) for(int k=0;k<i;k++) if(op==1)a[j+k+i]=(a[j+k+i]+a[j+k])%mod; else a[j+k+i]=(a[j+k+i]-a[j+k]+mod)%mod; } int main() { int n,li,m,p,x,y; scanf("%d%d%d",&n,&m,&p); li=(1<<n); len=1; for(int i=1;i<=m;i++) { scanf("%d%d",&x,&y); ins(x,y),ins(y,x); } for(int i=1;i<=n;i++)scanf("%d",&w[i]); for(int zt=1;zt<li;zt++) { for(int i=1;i<=n;i++) if((1<<(i-1))&zt)h[zt]+=w[i],cnt[zt]++; h[zt]=quick_pow(quick_pow(h[zt],mod-2),p); bool bk=true; memset(du,0,sizeof(du)); for(int i=1;i<=n;i++)fa[i]=i; for(int i=2;i<=len;i+=2) if( ((1<<(a[i].x-1))&zt) && ((1<<(a[i].y-1))&zt) ) du[a[i].x]++,du[a[i].y]++,fa[findfa(a[i].x)]=fa[findfa(a[i].y)]; int rt=0; for(int i=1;i<=n;i++) { if(du[i]%2==1){bk=false;break;} if((1<<(i-1))&zt) { if(rt==0)rt=findfa(i); else if(rt!=findfa(i)){bk=false;break;} } } if(bk==false) { for(int i=1;i<=n;i++) if((1<<(i-1))&zt)g[cnt[zt]][zt]+=w[i]; g[cnt[zt]][zt]=quick_pow(g[cnt[zt]][zt],p); } } //......pre......... for(int i=0;i<=n;i++)FWT(g[i],li,1); f[0][0]=1;FWT(f[0],li,1); for(int i=1;i<=n;i++) { for(int j=0;j<i;j++) for(int zt=0;zt<li;zt++) f[i][zt]=(f[i][zt]+f[j][zt]*g[i-j][zt])%mod; FWT(f[i],li,-1); for(int zt=0;zt<li;zt++) { if(cnt[zt]!=i)f[i][zt]=0; f[i][zt]=f[i][zt]*h[zt]%mod; } if(i!=n)FWT(f[i],li,1); } printf("%lld\n",f[n][li-1]); return 0; }
#include<cstdio> #include<iostream> #include<cstring> #include<cstdlib> #include<algorithm> #include<cmath> using namespace std; typedef long long LL; const int _=1e2; const int maxn=21+5; const int fbin=(1<<21)+_; const LL mod=998244353; const LL inv2=mod/2+1; LL quick_pow(LL A,int p) { LL ret=1; while(p!=0) { if(p%2==1)ret=ret*A%mod; A=A*A%mod;p/=2; } return ret; } //--------------------------------------------------def-------------------------------------------------------- struct node { int x,y,next; }a[maxn*maxn];int len,last[maxn]; void ins(int x,int y) { len++; a[len].x=x;a[len].y=y; a[len].next=last[x];last[x]=len; } int w[maxn],du[maxn]; int fa[maxn]; int findfa(int x) { if(x==fa[x])return x; fa[x]=findfa(fa[x]);return fa[x]; } //--------------------------------------------pre-------------------------------------------------------------- int cnt[fbin]; LL h[fbin],g[maxn][fbin],f[maxn][fbin]; void FWT(LL *a,int n,int op) { for(int i=1;i<n;i<<=1) for(int j=0;j<n;j+=(i<<1)) for(int k=0;k<i;k++) { LL t1=a[j+k],t2=a[j+k+i]; a[j+k]=(t1+t2)%mod; a[j+k+i]=(t1-t2+mod)%mod; if(op==-1)a[j+k]=a[j+k]*inv2%mod,a[j+k+i]=a[j+k+i]*inv2%mod; } } int main() { int n,li,m,p,x,y; scanf("%d%d%d",&n,&m,&p); li=(1<<n); len=1; for(int i=1;i<=m;i++) { scanf("%d%d",&x,&y); ins(x,y),ins(y,x); } for(int i=1;i<=n;i++)scanf("%d",&w[i]); for(int zt=1;zt<li;zt++) { for(int i=1;i<=n;i++) if((1<<(i-1))&zt)h[zt]+=w[i],cnt[zt]++; h[zt]=quick_pow(quick_pow(h[zt],mod-2),p); bool bk=true; memset(du,0,sizeof(du)); for(int i=1;i<=n;i++)fa[i]=i; for(int i=2;i<=len;i+=2) if( ((1<<(a[i].x-1))&zt) && ((1<<(a[i].y-1))&zt) ) du[a[i].x]++,du[a[i].y]++,fa[findfa(a[i].x)]=fa[findfa(a[i].y)]; int rt=0; for(int i=1;i<=n;i++) { if(du[i]%2==1){bk=false;break;} if((1<<(i-1))&zt) { if(rt==0)rt=findfa(i); else if(rt!=findfa(i)){bk=false;break;} } } if(bk==false) { for(int i=1;i<=n;i++) if((1<<(i-1))&zt)g[cnt[zt]][zt]+=w[i]; g[cnt[zt]][zt]=quick_pow(g[cnt[zt]][zt],p); } } //......pre......... for(int i=0;i<=n;i++)FWT(g[i],li,1); f[0][0]=1;FWT(f[0],li,1); for(int i=1;i<=n;i++) { for(int j=0;j<i;j++) for(int zt=0;zt<li;zt++) f[i][zt]=(f[i][zt]+f[j][zt]*g[i-j][zt])%mod; FWT(f[i],li,-1); for(int zt=0;zt<li;zt++) { if(cnt[zt]!=i)f[i][zt]=0; f[i][zt]=f[i][zt]*h[zt]%mod; } if(i!=n)FWT(f[i],li,1); } printf("%lld\n",f[n][li-1]); return 0; }
#include<cstdio> #include<iostream> #include<cstring> #include<cstdlib> #include<algorithm> #include<cmath> using namespace std; typedef long long LL; const int _=1e2; const int maxn=21+5; const int fbin=(1<<21)+_; const LL mod=998244353; const LL inv2=mod/2+1; LL quick_pow(LL A,int p) { LL ret=1; while(p!=0) { if(p%2==1)ret=ret*A%mod; A=A*A%mod;p/=2; } return ret; } //--------------------------------------------------def-------------------------------------------------------- struct node { int x,y,next; }a[maxn*maxn];int len,last[maxn]; void ins(int x,int y) { len++; a[len].x=x;a[len].y=y; a[len].next=last[x];last[x]=len; } int w[maxn],du[maxn]; int fa[maxn]; int findfa(int x) { if(x==fa[x])return x; fa[x]=findfa(fa[x]);return fa[x]; } //--------------------------------------------pre-------------------------------------------------------------- int cnt[fbin]; LL h[fbin],g[maxn][fbin],f[maxn][fbin]; void FMT(LL *a,int n,int li,int op) { for(int i=1;i<=n;i++) for(int zt=0;zt<li;zt++) if((1<<(i-1))&zt)a[zt]=(a[zt]+op*a[zt^(1<<i-1)]+mod)%mod; } int main() { int n,li,m,p,x,y; scanf("%d%d%d",&n,&m,&p); li=(1<<n); len=1; for(int i=1;i<=m;i++) { scanf("%d%d",&x,&y); ins(x,y),ins(y,x); } for(int i=1;i<=n;i++)scanf("%d",&w[i]); for(int zt=1;zt<li;zt++) { for(int i=1;i<=n;i++) if((1<<(i-1))&zt)h[zt]+=w[i],cnt[zt]++; h[zt]=quick_pow(quick_pow(h[zt],mod-2),p); bool bk=true; memset(du,0,sizeof(du)); for(int i=1;i<=n;i++)fa[i]=i; for(int i=2;i<=len;i+=2) if( ((1<<(a[i].x-1))&zt) && ((1<<(a[i].y-1))&zt) ) du[a[i].x]++,du[a[i].y]++,fa[findfa(a[i].x)]=fa[findfa(a[i].y)]; int rt=0; for(int i=1;i<=n;i++) { if(du[i]%2==1){bk=false;break;} if((1<<(i-1))&zt) { if(rt==0)rt=findfa(i); else if(rt!=findfa(i)){bk=false;break;} } } if(bk==false) { for(int i=1;i<=n;i++) if((1<<(i-1))&zt)g[cnt[zt]][zt]+=w[i]; g[cnt[zt]][zt]=quick_pow(g[cnt[zt]][zt],p); } } //......pre......... for(int i=0;i<=n;i++)FMT(g[i],n,li,1); f[0][0]=1;FMT(f[0],n,li,1); for(int i=1;i<=n;i++) { for(int j=0;j<i;j++) for(int zt=0;zt<li;zt++) f[i][zt]=(f[i][zt]+f[j][zt]*g[i-j][zt])%mod; FMT(f[i],n,li,-1); for(int zt=0;zt<li;zt++) { if(cnt[zt]!=i)f[i][zt]=0; f[i][zt]=f[i][zt]*h[zt]%mod; } if(i!=n)FMT(f[i],n,li,1); } printf("%lld\n",f[n][li-1]); return 0; }
pain and happy in the cruel world.
