#include<cstdio> #include<algorithm> using namespace std; const int N=500010,M=2000010,P=1000000007; int n,m,ca,cb,cnt,i,j,k,x,y,scc,base=1; bool vis[N]; int ed,g[N],v[M],nxt[M],G[N],V[M],NXT[M]; int id[N],at[N],q[N],t; int pool[N],st[N],en[N],cp,last[N]; int ce; struct Info{int a,b,c,d;}f[N]; struct E{int l,r;E(){}E(int _l,int _r){l=_l,r=_r;}}e[N<<1]; inline bool cmp(const E&a,const E&b){return a.l<b.l;} inline void read(int&a){char c;while(!(((c=getchar())>='0')&&(c<='9')));a=c-'0';while(((c=getchar())>='0')&&(c<='9'))(a*=10)+=c-'0';} inline void readch(char&a){while(!(((a=getchar())=='-')||(a=='>')));} inline void umin(int&a,int b){a>b?(a=b):0;} inline void umax(int&a,int b){a<b?(a=b):0;} inline void add(int x,int y){ v[++ed]=y;nxt[ed]=g[x];g[x]=ed; V[ed]=x;NXT[ed]=G[y];G[y]=ed; } void dfs(int x){ if(vis[x])return; vis[x]=1; for(int i=g[x];i;i=nxt[i])dfs(v[i]); } void dfs1(int x){ if(vis[x])return; vis[x]=1; for(int i=g[x];i;i=nxt[i])dfs1(v[i]); q[++t]=x; } void dfs2(int x){ if(!vis[x])return; vis[x]=0; at[x]=scc; pool[++cp]=x; for(int i=G[x];i;i=NXT[i])dfs2(V[i]); } inline void ext(int o,int x,int y){ if(!x)return; if(!f[o].a)f[o].a=x,f[o].b=y; else if(!f[o].c)f[o].c=x,f[o].d=y; else puts("GG"); } namespace COUNTING{ typedef unsigned int uint32; typedef long long int64; typedef unsigned long long uint64; typedef uint32 word; typedef uint64 dword; typedef int sword; const int word_bits=sizeof(word)*8; word mod,Modinv,r2; struct UnsafeMod{ word x; UnsafeMod(): x(0) {} UnsafeMod(word _x): x(init(_x)) {} UnsafeMod& operator += (const UnsafeMod& rhs) { (x += rhs.x) >= mod && (x -= mod); return *this; } UnsafeMod& operator -= (const UnsafeMod& rhs) { sword(x -= rhs.x) < 0 && (x += mod); return *this; } UnsafeMod& operator *= (const UnsafeMod& rhs) { x = reduce(dword(x) * rhs.x); return *this; } UnsafeMod operator + (const UnsafeMod &rhs) const { return UnsafeMod(*this) += rhs; } UnsafeMod operator - (const UnsafeMod &rhs) const { return UnsafeMod(*this) -= rhs; } UnsafeMod operator * (const UnsafeMod &rhs) const { return UnsafeMod(*this) *= rhs; } UnsafeMod pow(uint64 e) const { UnsafeMod ret(1); for (UnsafeMod base = *this; e; e >>= 1, base *= base) { if (e & 1) ret *= base; } return ret; } word get() const { return reduce(x); } static word modulus() { return mod; } static word init(word w) { return reduce(dword(w) * r2); } static void set_mod(word m) { mod = m; Modinv = mul_inv(mod); r2 = -dword(mod) % mod; } static word reduce(dword x) { word y = word(x >> word_bits) - word((dword(word(x) * Modinv) * mod) >> word_bits); return sword(y) < 0 ? y + mod : y; } static word mul_inv(word n, int e = 6, word x = 1) { return !e ? x : mul_inv(n, e - 1, x * (2 - x * n)); } }dp[N],v[N],ans; int n,m,_,ca,i,j,k,x,y,e[N][2],is[N],a[N]; int p[N],val[N]; int minlen,S,now,en; int g[N],q[N][2],h,t; int f[N<<1],lim[N]; inline void init(int A,int B,int C,int D){ //printf("init %d %d %d %d\n",A,B,C,D); if(!C){ //[A,B] e[++m][0]=A; e[m][1]=B; umax(f[B],A); umax(f[B+n],A+n); }else{ //[C,B] e[++m][0]=C; e[m][1]=B; umax(f[B+n],C); } } inline void add(int l,int r){ //printf("add %d %d\n",l,r); if(l<=r){ if(f[r]>l)return; is[l-1]=is[r]=1; }else{ if(f[r+n]>l)return; is[l-1]=is[r]=is[n]=1; } e[++_][0]=l; e[_][1]=r; } inline void ins(int x,int y){ if(h<=t&&q[t][1]>=y)return; q[++t][0]=x; q[t][1]=y; } inline int askmin(int x){ while(h<=t&&q[h][1]<=x)h++; if(h>t)return n; return q[h][0]; } inline void cal(int lim,int n){ for(int i=1;i<=n;i++){ dp[i]=dp[i-1]; if(f[i-1])dp[i]-=dp[f[i-1]-1]; if(i<=lim)dp[i]+=1; dp[i]=dp[i]*v[i]+dp[i-1]; } } int solve(){ UnsafeMod::set_mod(P); for(i=1;i<=n+n;i++)umax(f[i],f[i-1]); for(i=1;i<=m;i++)add(e[i][0],e[i][1]); m=_; for(p[0]=i=1;i<=n;i++)p[i]=p[i-1]*2%P; for(i=0;i<=n;i++)p[i]--; is[n]=1; for(i=1;i<=n;i++)if(is[i])a[is[i]=++ca]=i; for(i=n;i;i--)if(!is[i])is[i]=is[i+1]; //[a[i-1]+1..a[i]] n=ca; for(i=1;i<=n;i++)val[i]=p[a[i]-a[i-1]]; //printf("n=%d\n",n); //for(i=1;i<=n;i++)printf("%d ",val[i]);puts(""); minlen=n,S=1; for(i=1;i<=m;i++){ x=is[e[i][0]],y=is[e[i][1]]; //printf("%d %d\n",x,y); if(x<=y)now=y-x+1;else now=y-x+1+n; if(now<=minlen){ minlen=now; S=x; } } //printf("minlen=%d S=%d\n",minlen,S); for(i=1,j=S;i<=n;i++){ v[i]=val[j]; j++; if(j>n)j=1; } en=n; for(i=0;i<=n+1;i++)f[i]=0; for(i=1;i<=m;i++){ x=is[e[i][0]],y=is[e[i][1]]; if(y<x)y+=n; y=y-x; while(1){ if(S<=x&&x<S+n)break; x+=n; } x-=S-1; if(y==n-1)x=1,y=n;else y+=x; if(y>n)y-=n; //printf("-> %d %d\n",x,y); if(x<=y){ //[x..y] umax(f[y],x); umin(en,y); }else{ umax(g[y+1],x); //[1..y] [x..n] } } for(i=1;i<=n;i++)umax(f[i],f[i-1]); h=1,t=0; for(i=1;i<=n;i++){//last now=en;//first<=lim if(g[i])ins(i-1,g[i]); umin(now,askmin(i)); lim[i]=now; } for(i=max(f[n],1);i<=n;i=j){ for(j=i;j<=n&&lim[i]==lim[j];j++); cal(lim[i],j-1); ans+=dp[j-1]-dp[i-1]; } return ans.get(); } } int main(){ read(n);read(m);read(ca);read(cb); while(m--){ char ch; read(x); readch(ch); readch(ch); read(y); add(x,y); if(ch=='-')add(y,x); } for(i=1;i<=ca;i++)dfs(i); for(i=ca+1;i<=ca+cb;i++)if(vis[i])id[i]=++cnt;else base=base*2%P; for(i=1;i<=n;i++)vis[i]=0; for(i=1;i<=n;i++)if(!vis[i])dfs1(i); for(i=t;i;i--)if(vis[q[i]]){ scc++; st[scc]=cp+1; dfs2(q[i]); en[scc]=cp; } for(i=scc;i;i--){ ce=0; for(j=st[i];j<=en[i];j++){ x=pool[j]; if(id[x])e[++ce]=E(id[x],id[x]); for(k=g[x];k;k=nxt[k]){ y=at[v[k]]; if(y==i)continue; if(last[y]==i)continue; last[y]=i; if(f[y].a)e[++ce]=E(f[y].a,f[y].b); if(f[y].c)e[++ce]=E(f[y].c,f[y].d); } } if(!ce)continue; sort(e+1,e+ce+1,cmp); x=0,y=-1; for(j=1;j<=ce;j++){ if(e[j].l>y+1){ ext(i,x,y); x=e[j].l; } umax(y,e[j].r); } ext(i,x,y); } //puts("OK"); COUNTING::n=cnt; for(i=1;i<=ca;i++){ x=at[i]; if(f[x].a){ COUNTING::init(f[x].a,f[x].b,f[x].c,f[x].d); f[x].a=0; } } base=1LL*base*COUNTING::solve()%P; printf("%d",base); }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 | #include<cstdio> #include<algorithm> using namespace std; const int N=500010,M=2000010,P=1000000007; int n,m,ca,cb,cnt,i,j,k,x,y,scc,base=1; bool vis[N]; int ed,g[N],v[M],nxt[M],G[N],V[M],NXT[M]; int id[N],at[N],q[N],t; int pool[N],st[N],en[N],cp,last[N]; int ce; struct Info{int a,b,c,d;}f[N]; struct E{int l,r;E(){}E(int _l,int _r){l=_l,r=_r;}}e[N<<1]; inline bool cmp(const E&a,const E&b){return a.l<b.l;} inline void read(int&a){char c;while(!(((c=getchar())>='0')&&(c<='9')));a=c-'0';while(((c=getchar())>='0')&&(c<='9'))(a*=10)+=c-'0';} inline void readch(char&a){while(!(((a=getchar())=='-')||(a=='>')));} inline void umin(int&a,int b){a>b?(a=b):0;} inline void umax(int&a,int b){a<b?(a=b):0;} inline void add(int x,int y){ v[++ed]=y;nxt[ed]=g[x];g[x]=ed; V[ed]=x;NXT[ed]=G[y];G[y]=ed; } void dfs(int x){ if(vis[x])return; vis[x]=1; for(int i=g[x];i;i=nxt[i])dfs(v[i]); } void dfs1(int x){ if(vis[x])return; vis[x]=1; for(int i=g[x];i;i=nxt[i])dfs1(v[i]); q[++t]=x; } void dfs2(int x){ if(!vis[x])return; vis[x]=0; at[x]=scc; pool[++cp]=x; for(int i=G[x];i;i=NXT[i])dfs2(V[i]); } inline void ext(int o,int x,int y){ if(!x)return; if(!f[o].a)f[o].a=x,f[o].b=y; else if(!f[o].c)f[o].c=x,f[o].d=y; else puts("GG"); } namespace COUNTING{ typedef unsigned int uint32; typedef long long int64; typedef unsigned long long uint64; typedef uint32 word; typedef uint64 dword; typedef int sword; const int word_bits=sizeof(word)*8; word mod,Modinv,r2; struct UnsafeMod{ word x; UnsafeMod(): x(0) {} UnsafeMod(word _x): x(init(_x)) {} UnsafeMod& operator += (const UnsafeMod& rhs) { (x += rhs.x) >= mod && (x -= mod); return *this; } UnsafeMod& operator -= (const UnsafeMod& rhs) { sword(x -= rhs.x) < 0 && (x += mod); return *this; } UnsafeMod& operator *= (const UnsafeMod& rhs) { x = reduce(dword(x) * rhs.x); return *this; } UnsafeMod operator + (const UnsafeMod &rhs) const { return UnsafeMod(*this) += rhs; } UnsafeMod operator - (const UnsafeMod &rhs) const { return UnsafeMod(*this) -= rhs; } UnsafeMod operator * (const UnsafeMod &rhs) const { return UnsafeMod(*this) *= rhs; } UnsafeMod pow(uint64 e) const { UnsafeMod ret(1); for (UnsafeMod base = *this; e; e >>= 1, base *= base) { if (e & 1) ret *= base; } return ret; } word get() const { return reduce(x); } static word modulus() { return mod; } static word init(word w) { return reduce(dword(w) * r2); } static void set_mod(word m) { mod = m; Modinv = mul_inv(mod); r2 = -dword(mod) % mod; } static word reduce(dword x) { word y = word(x >> word_bits) - word((dword(word(x) * Modinv) * mod) >> word_bits); return sword(y) < 0 ? y + mod : y; } static word mul_inv(word n, int e = 6, word x = 1) { return !e ? x : mul_inv(n, e - 1, x * (2 - x * n)); } }dp[N],v[N],ans; int n,m,_,ca,i,j,k,x,y,e[N][2],is[N],a[N]; int p[N],val[N]; int minlen,S,now,en; int g[N],q[N][2],h,t; int f[N<<1],lim[N]; inline void init(int A,int B,int C,int D){ //printf("init %d %d %d %d\n",A,B,C,D); if(!C){ //[A,B] e[++m][0]=A; e[m][1]=B; umax(f[B],A); umax(f[B+n],A+n); }else{ //[C,B] e[++m][0]=C; e[m][1]=B; umax(f[B+n],C); } } inline void add(int l,int r){ //printf("add %d %d\n",l,r); if(l<=r){ if(f[r]>l)return; is[l-1]=is[r]=1; }else{ if(f[r+n]>l)return; is[l-1]=is[r]=is[n]=1; } e[++_][0]=l; e[_][1]=r; } inline void ins(int x,int y){ if(h<=t&&q[t][1]>=y)return; q[++t][0]=x; q[t][1]=y; } inline int askmin(int x){ while(h<=t&&q[h][1]<=x)h++; if(h>t)return n; return q[h][0]; } inline void cal(int lim,int n){ for(int i=1;i<=n;i++){ dp[i]=dp[i-1]; if(f[i-1])dp[i]-=dp[f[i-1]-1]; if(i<=lim)dp[i]+=1; dp[i]=dp[i]*v[i]+dp[i-1]; } } int solve(){ UnsafeMod::set_mod(P); for(i=1;i<=n+n;i++)umax(f[i],f[i-1]); for(i=1;i<=m;i++)add(e[i][0],e[i][1]); m=_; for(p[0]=i=1;i<=n;i++)p[i]=p[i-1]*2%P; for(i=0;i<=n;i++)p[i]--; is[n]=1; for(i=1;i<=n;i++)if(is[i])a[is[i]=++ca]=i; for(i=n;i;i--)if(!is[i])is[i]=is[i+1]; //[a[i-1]+1..a[i]] n=ca; for(i=1;i<=n;i++)val[i]=p[a[i]-a[i-1]]; //printf("n=%d\n",n); //for(i=1;i<=n;i++)printf("%d ",val[i]);puts(""); minlen=n,S=1; for(i=1;i<=m;i++){ x=is[e[i][0]],y=is[e[i][1]]; //printf("%d %d\n",x,y); if(x<=y)now=y-x+1;else now=y-x+1+n; if(now<=minlen){ minlen=now; S=x; } } //printf("minlen=%d S=%d\n",minlen,S); for(i=1,j=S;i<=n;i++){ v[i]=val[j]; j++; if(j>n)j=1; } en=n; for(i=0;i<=n+1;i++)f[i]=0; for(i=1;i<=m;i++){ x=is[e[i][0]],y=is[e[i][1]]; if(y<x)y+=n; y=y-x; while(1){ if(S<=x&&x<S+n)break; x+=n; } x-=S-1; if(y==n-1)x=1,y=n;else y+=x; if(y>n)y-=n; //printf("-> %d %d\n",x,y); if(x<=y){ //[x..y] umax(f[y],x); umin(en,y); }else{ umax(g[y+1],x); //[1..y] [x..n] } } for(i=1;i<=n;i++)umax(f[i],f[i-1]); h=1,t=0; for(i=1;i<=n;i++){//last now=en;//first<=lim if(g[i])ins(i-1,g[i]); umin(now,askmin(i)); lim[i]=now; } for(i=max(f[n],1);i<=n;i=j){ for(j=i;j<=n&&lim[i]==lim[j];j++); cal(lim[i],j-1); ans+=dp[j-1]-dp[i-1]; } return ans.get(); } } int main(){ read(n);read(m);read(ca);read(cb); while(m--){ char ch; read(x); readch(ch); readch(ch); read(y); add(x,y); if(ch=='-')add(y,x); } for(i=1;i<=ca;i++)dfs(i); for(i=ca+1;i<=ca+cb;i++)if(vis[i])id[i]=++cnt;else base=base*2%P; for(i=1;i<=n;i++)vis[i]=0; for(i=1;i<=n;i++)if(!vis[i])dfs1(i); for(i=t;i;i--)if(vis[q[i]]){ scc++; st[scc]=cp+1; dfs2(q[i]); en[scc]=cp; } for(i=scc;i;i--){ ce=0; for(j=st[i];j<=en[i];j++){ x=pool[j]; if(id[x])e[++ce]=E(id[x],id[x]); for(k=g[x];k;k=nxt[k]){ y=at[v[k]]; if(y==i)continue; if(last[y]==i)continue; last[y]=i; if(f[y].a)e[++ce]=E(f[y].a,f[y].b); if(f[y].c)e[++ce]=E(f[y].c,f[y].d); } } if(!ce)continue; sort(e+1,e+ce+1,cmp); x=0,y=-1; for(j=1;j<=ce;j++){ if(e[j].l>y+1){ ext(i,x,y); x=e[j].l; } umax(y,e[j].r); } ext(i,x,y); } //puts("OK"); COUNTING::n=cnt; for(i=1;i<=ca;i++){ x=at[i]; if(f[x].a){ COUNTING::init(f[x].a,f[x].b,f[x].c,f[x].d); f[x].a=0; } } base=1LL*base*COUNTING::solve()%P; printf("%d",base); } |