[BZOJ 2303][Apio2011]方格染色：并查集

/*
User:Small
Language:C++
Problem No.:2303
*/
#include<bits/stdc++.h>
#define ll long long
#define inf 999999999
using namespace std;
const int M=1e6+5,mod=1e9;
int n,m,k,tot,f[M],F[M];
bool c[M],vis[M],mark[M];
vector<int> r[M],g[M];
int pow(int a,int b){
int res=1;
while(b){
if(b&1) res=(ll)res*a%mod;
a=(ll)a*a%mod;
b>>=1;
}
return res;
}
int find(int x){
return x==f[x]?x:f[x]=find(f[x]);
}
int find2(int x){
if(x==F[x]) return x;
int tmp=find2(F[x]);
c[x]^=c[F[x]];
return F[x]=tmp;
}
bool add(int x,int y,int t){
int p=find2(x),q=find2(y);
if(p==q) return (c[x]^c[y])==t;
F[p]=q;
c[p]=(c[x]^c[y]^t);
return 1;
}
int main(){
freopen("data.in","r",stdin);//
scanf("%d%d%d",&n,&m,&k);
for(int i=1;i<=k;i++){
int x,y,p;
scanf("%d%d%d",&x,&y,&p);
if(x==1) vis[y]=1;
mark[x]=1;
r[x].push_back(y);
g[x].push_back(p);
}
for(int i=1;i<=m;i++) f[i]=F[i]=i;
for(int i=1;i<=n;i++){
int siz=r[i].size();
for(int j=1;j<siz;j++){
int x=r[i][j],y=r[i][j-1],cx=g[i][j],cy=g[i][j-1];
int p=find(x),q=find(y);
f[p]=q;
if(vis[p]) vis[q]=1;
int t=cx^cy;
if(x%2!=y%2) t=(t^(i-1))&1;
if(!add(x,y,t)){
printf("0\n");
return 0;
}
}
}
int tot=0;
for(int i=1;i<=m;i++) tot+=(f[i]==i&&!vis[i]);
for(int i=2;i<=n;i++) tot+=(!mark[i]);
printf("%d\n",pow(2,tot));
return 0;
}