HDU 5556 最大独立集

这题主要有了中间的一些连通块的限制，不太好直接用二分图最大独立集做。考虑到图比较小，可以作补图求最大团来求解。

 #include <iostream>
 #include <vector>
 #include <algorithm>
 #include <string>
 #include <string.h>
 #include <stdio.h>
 #include <queue>
 #include <stack>
 #include <map>
 #include <set>
 #include <cmath>
 #include <ctime>
 #include <cassert>
 #include <sstream>
 using namespace std;

 const int N=;

 char s[N][N];
 int id[N][N];
 int dx[]={,,,-};
 int dy[]={,-,,};
 int n,m;

 struct MC{
     bool graph[N][N];
     int stk[N][N],dp[N],mc;
     int choice[N],vertex[N];
     void dfs(int n,int sz,int dep){
         if (sz==){
             if (dep>mc){
                 mc=dep;
                 for (int i=;i<mc;i++)
                     vertex[i]=choice[i];
             }
             return;
         }
         for (int i=;i<sz;i++){
             int u=stk[dep][i];
             if (dep+dp[u]<=mc) return;
             if (dep+sz-i<=mc) return;
             choice[dep]=u;
             int cnt=;
             for (int j=i+;j<sz;j++){
                 int v=stk[dep][j];
                 if (graph[u][v])
                     stk[dep+][cnt++]=v;
             }
             dfs(n,cnt,dep+);
         }
     }
     int maxClique(int n){
         mc=;
         //节点从1开始标号
         dp[n]=;
         for (int i=n-;i>=;i--){
             int sz=;
             for (int j=i+;j<=n;j++)
                 if (graph[i][j])
                     stk[][sz++]=j;
             choice[]=i;
             dfs(n,sz,);
             dp[i]=mc;
         }
         return mc;
     }
     void solve(int &cas) {
         map<char,int> mp;
         int cnt=;
         for (int i=;i<=n;i++) {
             for (int j=;j<=m;j++) {
                 if (s[i][j]=='.')
                     id[i][j]=++cnt;
                 else if (mp.find(s[i][j])==mp.end())
                     id[i][j]=mp[s[i][j]]=++cnt;
                 else
                     id[i][j]=mp[s[i][j]];
             }
         }
         //for (int i=1;i<=n;i++) for (int j=1;j<=m;j++) cout<<id[i][j]<<" ";cout<<endl;
         for (int i=;i<=cnt;i++) {
             for (int j=;j<=cnt;j++) {
                 if (i==j) graph[i][j]=false;
                 graph[i][j]=true;
             }
         }
         for (int i=;i<=n;i++) {
             for (int j=;j<=m;j++) {
                 int u=id[i][j];
                 for (int k=;k<;k++) {
                     int ni=i+dx[k];
                     int nj=j+dy[k];
                     if (ni<=||nj<=||ni>n||nj>m) continue;
                     int v=id[ni][nj];
                     graph[u][v]=false;
                     graph[v][u]=false;
                 }
             }
         }
         printf("Case #%d: %d\n",cas,maxClique(cnt));
     }
 }mc;

 int main () {
     //freopen("out.txt","r",stdin);
     int T;
     scanf("%d",&T);
     while (T--) {
         scanf("%d %d",&n,&m);
         for (int i=;i<=n;i++) {
             scanf("%s",s[i]+);
         }
         static int cas=;
         mc.solve(cas);
         cas++;
     }
     return ;
 }