网络流。
原点到偶数连边,容量为2,
奇数到汇点连边,容量为2,
偶数到与之能凑成素数的奇数连边,容量为1
如果奇数个数不等于偶数个数,输出不可能
如果原点到偶数的边不满流,输出不可能
剩下的情况有解:因为一个偶数点选了两个奇数点,一个奇数点被两个偶数点选择,一定能构造出环。
#include<cstdio>
#include<cstring>
#include<string>
#include<cmath>
#include<vector>
#include<queue>
#include<algorithm>
using namespace std; const int maxn = + ;
const int INF = 0x7FFFFFFF;
struct Edge
{
int from, to, cap, flow;
Edge(int u, int v, int c, int f) :from(u), to(v), cap(c), flow(f){}
};
vector<Edge>edges;
vector<int>G[maxn];
bool vis[maxn];
int d[maxn];
int cur[maxn];
int n, m, s, t;
int num[maxn]; vector<int>g[maxn];
vector<int> ans[maxn];
bool f[maxn];
int block; void init()
{
for (int i = ; i < maxn; i++) G[i].clear();
edges.clear();
}
void AddEdge(int from, int to, int cap)
{
edges.push_back(Edge(from, to, cap, ));
edges.push_back(Edge(to, from, , ));
int w = edges.size();
G[from].push_back(w - );
G[to].push_back(w - );
}
bool BFS()
{
memset(vis, , sizeof(vis));
queue<int>Q;
Q.push(s);
d[s] = ;
vis[s] = ;
while (!Q.empty())
{
int x = Q.front();
Q.pop();
for (int i = ; i<G[x].size(); i++)
{
Edge e = edges[G[x][i]];
if (!vis[e.to] && e.cap>e.flow)
{
vis[e.to] = ;
d[e.to] = d[x] + ;
Q.push(e.to);
}
}
}
return vis[t];
}
int DFS(int x, int a)
{
if (x == t || a == )
return a;
int flow = , f;
for (int &i = cur[x]; i<G[x].size(); i++)
{
Edge e = edges[G[x][i]];
if (d[x]+ == d[e.to]&&(f=DFS(e.to,min(a,e.cap-e.flow)))>)
{
edges[G[x][i]].flow+=f;
edges[G[x][i] ^ ].flow-=f;
flow+=f;
a-=f;
if(a==) break;
}
}
if(!flow) d[x] = -;
return flow;
}
int dinic(int s, int t)
{
int flow = ;
while (BFS())
{
memset(cur, , sizeof(cur));
flow += DFS(s, INF);
}
return flow;
} bool prime(int x)
{
for(int i=;i*i<=x;i++)
if(x%i==) return ;
return ;
} void Find(int now)
{
f[now]=;
ans[block].push_back(now);
for(int i=;i<g[now].size();i++)
{
if(f[g[now][i]]) continue;
Find(g[now][i]);
}
} int main()
{
while(~scanf("%d",&n))
{
for(int i=;i<=n;i++) scanf("%d",&num[i]);
init();
s=;t=n+; int e1=,e2=;
int flag=;
for(int i=;i<=n;i++)
{
if(num[i]%==) { e1++; AddEdge(s,i,); }
else { e2++; AddEdge(i,t,); }
}
if(e1!=e2) flag=;
else
{
for(int i=;i<=n;i++)
for(int j=;j<=n;j++)
if(num[i]%==&&num[j]%==&&prime(num[i]+num[j]))
AddEdge(i,j,);
int Flow=dinic(s,t);
if(Flow!=*e1) flag=;
}
if(flag==) printf("Impossible\n");
else
{
block=; memset(f,,sizeof f);
for(int i=;i<maxn;i++) { g[i].clear(); ans[i].clear(); }
for(int i=;i<edges.size();i=i+)
{
if(edges[i].flow==)
{
int u=edges[i].from;
int v=edges[i].to;
g[u].push_back(v);
g[v].push_back(u);
}
} for(int i=;i<=n;i++)
{
if(f[i]) continue;
Find(i); block++;
} printf("%d\n",block);
for(int i=;i<block;i++)
{
printf("%d ",ans[i].size());
for(int j=;j<ans[i].size();j++)
printf("%d ",ans[i][j]);
printf("\n");
}
}
}
return ;
}