/* Things to notice: 1. do not calculate useless values 2. do not use similar names Things to check: 1. submit the correct file 2. time (it is log^2 or log) 3. memory 4. prove your naive thoughts 5. long long 6. corner case like n=0,1,inf or n=m 7. check if there is a mistake in the ds or other tools you use 8. fileio in some oi-contest 9. module on time 10. the number of a same divisor in a math problem 11. multi-information and queries for dp and ds problems */ #include<bits/stdc++.h> using namespace std; #define int long long #define fi first #define se second #define pii pair<long long,long long> #define mp make_pair #define pb push_back const int mod=1e9+7; const int inf=0x3f3f3f3f; const int INF=1e18; int fpow(int x,int b) { if(x==0) return 0; if(b==0) return 1; int res=1; while(b>0) { if(b&1) res=1LL*res*x%mod; x=1LL*x*x%mod; b>>=1; } return res; } int fac[400005],ifac[400005]; int C(int x,int y) { if(y>x) return 0; if(x==y||y==0) return 1; return 1LL*fac[x]*ifac[x-y]%mod*ifac[y]%mod; } void init(int x) { fac[0]=fac[1]=1; for(int i=2;i<=x;i++) fac[i]=1LL*fac[i-1]*i%mod; ifac[x]=fpow(fac[x],mod-2); // x should be less than mod!!! for(int i=x-1;i>=0;i--) ifac[i]=1LL*ifac[i+1]*(i+1)%mod; } int ans=1; int n,m; int c[200005],col[200005]; vector <int> g[200005]; int c0,c1,ok=1,d0,d1; void dfs0(int u,int co) { col[u]=co; if(co==0) { if(c[u]==1) c0++,d0++; else d0++; } else { if(c[u]==1) c1++,d1++; else d1++; } for(int i=0;i<g[u].size();i++) { int v=g[u][i]; if(col[v]==-1) dfs0(v,co^1); else if(col[v]!=(co^1)) ok=0; } } void solve() { init(400000); cin>>n>>m; for(int i=1;i<=n;i++) cin>>c[i]; memset(col,-1,sizeof(col)); while(m--) { int u,v; cin>>u>>v; g[u].pb(v),g[v].pb(u); } for(int i=1;i<=n;i++) if(col[i]==-1) { c0=c1=d0=d1=0,ok=1,dfs0(i,0); if(!ok) ans=1LL*ans*fpow(2,d0+d1-1)%mod; else { int nw=0; for(int j=0;j<=d0;j++) { int k=j+c1-c0; if(0<=k&&k<=d1) nw=(nw+C(d0,j)%mod*C(d1,k))%mod; } ans=1LL*ans*nw%mod; } } cout<<ans<<"\n"; } signed main() { ios::sync_with_stdio(0); cin.tie(0); int _=1; // cin>>_; while(_--) solve(); return 0; }
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 | /* Things to notice: 1. do not calculate useless values 2. do not use similar names Things to check: 1. submit the correct file 2. time (it is log^2 or log) 3. memory 4. prove your naive thoughts 5. long long 6. corner case like n=0,1,inf or n=m 7. check if there is a mistake in the ds or other tools you use 8. fileio in some oi-contest 9. module on time 10. the number of a same divisor in a math problem 11. multi-information and queries for dp and ds problems */ #include<bits/stdc++.h> using namespace std; #define int long long #define fi first #define se second #define pii pair<long long,long long> #define mp make_pair #define pb push_back const int mod=1e9+7; const int inf=0x3f3f3f3f; const int INF=1e18; int fpow(int x,int b) { if(x==0) return 0; if(b==0) return 1; int res=1; while(b>0) { if(b&1) res=1LL*res*x%mod; x=1LL*x*x%mod; b>>=1; } return res; } int fac[400005],ifac[400005]; int C(int x,int y) { if(y>x) return 0; if(x==y||y==0) return 1; return 1LL*fac[x]*ifac[x-y]%mod*ifac[y]%mod; } void init(int x) { fac[0]=fac[1]=1; for(int i=2;i<=x;i++) fac[i]=1LL*fac[i-1]*i%mod; ifac[x]=fpow(fac[x],mod-2); // x should be less than mod!!! for(int i=x-1;i>=0;i--) ifac[i]=1LL*ifac[i+1]*(i+1)%mod; } int ans=1; int n,m; int c[200005],col[200005]; vector <int> g[200005]; int c0,c1,ok=1,d0,d1; void dfs0(int u,int co) { col[u]=co; if(co==0) { if(c[u]==1) c0++,d0++; else d0++; } else { if(c[u]==1) c1++,d1++; else d1++; } for(int i=0;i<g[u].size();i++) { int v=g[u][i]; if(col[v]==-1) dfs0(v,co^1); else if(col[v]!=(co^1)) ok=0; } } void solve() { init(400000); cin>>n>>m; for(int i=1;i<=n;i++) cin>>c[i]; memset(col,-1,sizeof(col)); while(m--) { int u,v; cin>>u>>v; g[u].pb(v),g[v].pb(u); } for(int i=1;i<=n;i++) if(col[i]==-1) { c0=c1=d0=d1=0,ok=1,dfs0(i,0); if(!ok) ans=1LL*ans*fpow(2,d0+d1-1)%mod; else { int nw=0; for(int j=0;j<=d0;j++) { int k=j+c1-c0; if(0<=k&&k<=d1) nw=(nw+C(d0,j)%mod*C(d1,k))%mod; } ans=1LL*ans*nw%mod; } } cout<<ans<<"\n"; } signed main() { ios::sync_with_stdio(0); cin.tie(0); int _=1; // cin>>_; while(_--) solve(); return 0; } |