codeforces 510E Fox And Dinner 奇偶建图+最大流

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题意：n个fox，年龄为a[i]。

现在要将n个fox分配入座，保证与相邻数的和为质数。一桌至少三个fox。

输出要分几桌，每桌几个fox，按顺序输出每桌坐的fox的id

思路：我们按奇偶将n个fox分成2类，如果左边的a[i]+右边的a[j]和为质数，那么建i->j建容量为1的边，超级起点0连a[i]为奇数的i，

从0->i建容量为2的边(因为i要与两个偶数fox相连)，a[i]为偶数的i连超级终点，从i->(n+1)建容量为2的边。求最大流maxflow,如果

maxflow!=n，那么Impossible。如果存在解，dfs下把对应桌的id找到即可，详见代码：

/*********************************************************  file name: codeforces510E.cpp  author : kereo  create time:  2015年02月03日 星期二 20时19分27秒*********************************************************/#include<iostream>#include<cstdio>#include<cstring>#include<queue>#include<set>#include<map>#include<vector>#include<stack>#include<cmath>#include<string>#include<algorithm>using namespace std;typedef long long ll;const int sigma_size=26;const int N=200+50;const int MAXN=40000+50;const int inf=0x3fffffff;const double eps=1e-8;const int mod=100000000+7;#define L(x) (x<<1)#define R(x) (x<<1|1)#define PII pair<int, int>#define mk(x,y) make_pair((x),(y))int n,edge_cnt,top,cnt;int a[N],head[N],vis[N],que[N],cur[N],s[N],gap[N],dep[N],num[N];vector<int>mp[N];struct Edge{    int u,v,cap,flow,next;}edge[MAXN];void init(){    edge_cnt=top=0;    memset(head,-1,sizeof(head));    for(int i=1;i<=n;i++)        mp[i].clear();}void addedge(int u,int v,int cap){    edge[edge_cnt].u=u; edge[edge_cnt].v=v;     edge[edge_cnt].cap=cap; edge[edge_cnt].flow=0;     edge[edge_cnt].next=head[u]; head[u]=edge_cnt++;    edge[edge_cnt].u=v; edge[edge_cnt].v=u;     edge[edge_cnt].cap=0; edge[edge_cnt].flow=0;     edge[edge_cnt].next=head[v]; head[v]=edge_cnt++; }void bfs(int st,int ed){      memset(gap,0,sizeof(gap));      memset(dep,-1,sizeof(dep));      int front=0,rear=0;       gap[0]=1; dep[ed]=0; que[rear++]=ed;      while(front!=rear){          int u=que[front++];          for(int i=head[u];i!=-1;i=edge[i].next){              int v=edge[i].v;              if(dep[v]!=-1)                  continue;              que[rear++]=v;              dep[v]=dep[u]+1; gap[dep[v]]++;          }      }  }  int isap(int st,int ed){      bfs(st,ed);      memcpy(cur,head,sizeof(head));      int ans=0,u=st;      while(dep[st]<n+2){          if(u == ed){              int Min=inf,inser;              for(int i=0;i<top;i++){                  if(edge[s[i]].cap-edge[s[i]].flow<Min){                      Min=edge[s[i]].cap-edge[s[i]].flow;                      inser=i;                  }              }              for(int i=0;i<top;i++)                  edge[s[i]].flow+=Min,edge[s[i]^1].flow-=Min;              ans+=Min; top=inser;              u=edge[s[top]^1].v;              continue;          }          int flag=0,v;          for(int i=cur[u];i!=-1;i=edge[i].next){              v=edge[i].v;              if(edge[i].cap-edge[i].flow>0 && dep[v]+1 == dep[u]){                  flag=1; cur[u]=i;                  break;              }          }          if(flag){              s[top++]=cur[u]; u=v;              continue;          }        int d=n+2;        for(int i=head[u];i!=-1;i=edge[i].next){              int v=edge[i].v;              if(edge[i].cap-edge[i].flow>0 && dep[v]<d)                  cur[u]=i,d=dep[v];          }          gap[dep[u]]--;           if(!gap[dep[u]]) return ans;          dep[u]=d+1; gap[dep[u]]++;          if(u!=st)              u=edge[s[--top]^1].v;      }      return ans;  }  bool ok(int x){    int flag=1;    for(int i=2;i*i<=x;i++){        if((x%i) == 0){            flag=0;             break;        }    }    return flag;}void dfs(int u){    num[++cnt]=u;    for(int i=0;i<mp[u].size();i++){        int v=mp[u][i];        if(vis[v])            continue;        vis[v]=1;        dfs(v);    }}int main(){    //freopen("in.txt","r",stdin);    while(~scanf("%d",&n)){        init();        for(int i=1;i<=n;i++)            scanf("%d",&a[i]);        for(int i=1;i<=n;i++){            if(a[i]&1)                addedge(0,i,2);            else                 addedge(i,n+1,2);        }        for(int i=1;i<=n;i++){            if((a[i]&1) == 0)                continue;            for(int j=1;j<=n;j++){                if(a[j]&1)                    continue;                if(ok(a[i]+a[j]))                    addedge(i,j,1);            }        }        int ans=isap(0,n+1);        if(ans!=n){            printf("Impossible\n");            continue;        }        for(int i=0;i<edge_cnt;i++){            if(edge[i].u>0 && edge[i].u<n+1 && edge[i].v>0 && edge[i].v<n+1){                int u=edge[i].u,v=edge[i].v;                if((a[u]&1) && edge[i].cap-edge[i].flow == 0){                    mp[u].push_back(v); mp[v].push_back(u);                }            }        }        int count=0;        memset(vis,0,sizeof(vis));        for(int i=1;i<=n;i++)            if(!vis[i]){                ++count;                vis[i]=1;                dfs(i);            }        printf("%d\n",count);        memset(vis,0,sizeof(vis));        for(int i=1;i<=n;i++){            if(!vis[i]){                cnt=0;                vis[i]=1;                dfs(i);            printf("%d",cnt);            for(int j=1;j<=cnt;j++)                printf(" %d",num[j]);            printf("\n");            }        }    }return 0;}

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