[HNOI2015]实验比较 树形dp+组合数学

在合并的时候有可以加等于，或者继续用小于，

比如siz[x]和siz[y]合并，小于的区间为max(siz[x],siz[y])<=k<=siz[x]+siz[y]，

然后就是合并成多少个小于号的方案数了，

 #include<cstdio>
 #include<algorithm>
 #include<iostream>
 #include<cstring>
 #include<cmath>
 #include<cstdlib>
 #define N 107
 #define M 207
 #define mod 1000000007
 #define ll long long
 using namespace std;

 int n,m,S;
 int cnt,head[N],next[M],rea[M];
 int fa[N],du[N],siz[N];
 bool boo[N],hash[N];
 struct Node
 {
     int x,y;
 }a[N];
 ll c[N][N],f[N][N],g[N],ans;

 void add(int u,int v)
 {
     next[++cnt]=head[u];
     head[u]=cnt;
     rea[cnt]=v,du[v]++;
 }
 int find(int num)
 {
     if (fa[num]!=num) fa[num]=find(fa[num]);
     return fa[num];
 }
 void dfs(int u,int fa)
 {
     boo[u]=;bool flag=;
     for (int i=head[u];i!=-;i=next[i])
     {
         int v=rea[i];
         if (v==fa) continue;
         dfs(v,u);
         if (flag)
         {
             memset(g,,sizeof(g));
             for (int i1=;i1<=siz[u];i1++)
                 if (f[u][i1])
                 for (int j1=;j1<=siz[v];j1++)
                     if (f[v][j1])
                     for (int k1=max(i1,j1);k1<=i1+j1;k1++)
                         g[k1]=(g[k1]+f[u][i1]*f[v][j1]%mod*c[k1][i1]%mod*c[i1][j1-(k1-i1)]%mod)%mod;
             siz[u]+=siz[v];
             for (int i=;i<=siz[u];i++)
                 f[u][i]=g[i];
         }
         else
         {
             flag=;
             siz[u]=siz[v];
             for (int i=;i<=siz[v];i++)
                 f[u][i]=f[v][i];
         }
     }
     if (u!=S)
     {
         siz[u]++;if (!flag) f[u][]=;
         else for (int i=siz[u];i>=;i--) f[u][i]=f[u][i-];
     }
 }
 bool dfs_circle(int u)
 {
     for (int i=head[u];i!=-;i=next[i])
     {
         int v=rea[i];
         if (boo[v]) return false;
         boo[v]=true;
         if (!dfs_circle(v)) return false;
     }
     return true;
 }
 int main()
 {
     memset(head,-,sizeof(head));
     scanf("%d%d",&n,&m);
     for (int i=;i<=n;i++)
         fa[i]=i;
     for (int i=;i<=n;i++)
         c[i][]=;
     for (int i=;i<=n;i++)
         for (int j=;j<=i;j++)
             c[i][j]=(c[i-][j]+c[i-][j-])%mod;
 //========================================================================================
     int x,y,top=;char ch[];
     for (int i=;i<=m;i++)
     {
         scanf("%d%s%d",&x,&ch,&y);
         if (ch[]=='=')
         {
             int u=find(x),v=find(y);
             fa[v]=u;
             continue;
         }
         else if (ch[]=='>') swap(x,y);
         a[++top].x=x,a[top].y=y;
     }
     m=top;
     for (int i=;i<=m;i++)
     {
         int u=find(a[i].x),v=find(a[i].y);
         if (u!=v) add(u,v);//如果一个相等集合中有相互比较关系
         else
         {
             printf("0\n");
             return ;
         }
     }
     for (int i=;i<=n;i++)
         if (!boo[i])
         {
             boo[i]=;
             if (!dfs_circle(i))
             {
                 printf("0\n");
                 return ;
             }
         }
     S=n+;
     for (int i=;i<=n;i++)
     {
         int zhi=find(i);
         if (!du[zhi]&&!hash[zhi])
         {
             add(S,zhi);
             hash[zhi]=;
         }
     }
 //=========================================================================================
     dfs(S,-);
     for (int i=;i<=siz[S];i++)
         ans=(ans+f[S][i])%mod;
     printf("%lld\n",ans);
 }