bzoj2303 [apio2011 color] 分类： apio bzoj 2015-05-05 14:03 38人阅读 评论(0) 收藏

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ppfish的题解

由题意，Ai,j^Ai−1,j ^ Ai,j−1^ Ai−1,j−1=1

只有当i, j全部为偶数时候， Ai,j^ Ai,1^ A1,j ^A1,1=1
其他情况， Ai,j^ Ai,1^ A1,j ^ A1,1=0

所以，只要确定了第一行和第一列，整个矩阵就确定了。

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#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>

const int MAXN = 1e6+5, MAXP = 1e6+5, Mod = 1e9;
#define L(x) (x)
#define U(x) ((x)+n)

int n, m, p, pl, ans;
bool ff[2] = {true,true};
struct node{int x,y,t;}h[MAXP];
int fa[MAXN<<1], g[MAXN<<1], area;

int read()
{
    int x = 0; char c = getchar();
    while(c < '0' || c > '9') c = getchar();
    while(c >= '0' && c <= '9')
        x = (x<<3) + (x<<1) + (c-'0'), c = getchar();
    return x;
}
void write(int x)
{
    static char s[20];int sl = 0;
    while(x) s[++sl] = x%10 + '0',x /= 10;
    if(!sl) {putchar('0');return;}
    while(sl) putchar(s[sl--]);
}
void Init()
{
    n = read(), m = read(), p = read();
    for(int i = 1; i <= p; i++)
     h[i].x = read(),
     h[i].y = read(),
     h[i].t = read();
}
void Build()
{
    for(int i = 1; i <= n+m; i++)
      fa[i] = i, g[i] = 0;
    fa[n + 1] = 1, area = n+m-1;  
}
int Find(int x)
{
    if (fa[x] == x) return x;
    else
    {
        Find(fa[x]);
        g[x] ^= g[fa[x]];
        fa[x] = fa[fa[x]];
        return fa[x];
    }
}
int PowerMod(int a,int b)
{
    int ret = 1;
    while(b)
    {
        if(b&1) ret = (long long)ret * a % Mod;
        a = (long long)a * a % Mod, b >>= 1; 
    }
    return ret;
}

int GetAns(int st)
{
    Build();

    for(int i = 1,fl,fu,x,y,k; i <= p; i++)
    {
//     st^h[i].t^L(x)^U(y) = 0
       k = st^h[i].t;

       x = L(h[i].x), y = U(h[i].y);
       fl = Find(x), fu = Find(y);

       if(fl != fu)
       {
          fa[fu] = fl, g[fu] = g[x]^g[y]^k, area--;
       }
       else
       {
          if(g[x]^g[y]^k) return 0;
       }
    }

    return PowerMod(2,area-1);
}

void Solve()
{
    pl = 0;
    for(int i = 1; i <= p; i++)
    {
      if(h[i].x == 1 && h[i].y == 1)
       {ff[h[i].t^1] = false; continue;}

      if(!(h[i].x&1) && !(h[i].y&1))
         h[i].t ^= 1;

      h[++pl] = h[i]; 
    }
    p = pl;

    ans = 0;

    if(ff[0]) ans = (ans + GetAns(0))%Mod;

    if(ff[1]) ans = (ans + GetAns(1))%Mod;

    return;
}
void Output()
{
    write(ans);
}

int main()
{
#ifndef ONLINE_JUDGE    
    freopen("color.in","r",stdin);
    freopen("color.out","w",stdout);
#endif

    Init();

    Solve();

    Output();

#ifndef ONLINE_JUDGE    
    fclose(stdin);
    fclose(stdout);
#endif  
    return 0;
}