AOJ2748.cpp

#include <bits/stdc++.h>

#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()

using namespace std;

using ld = long double;

struct Edge{ int src, dest; };

typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

void add_edge(Graph &g, int from, int to) {
  g[from].push_back((Edge){from, to});
}

int scc(Graph &graph, vector<int> &cmp) {
  int V = graph.size();
  vector<vector<int>> g(V), rg(V);
  vector<int> vs;
  vector<bool> used(V, false);
  cmp.resize(V);
  REP(i,V) {
    for (Edge e: graph[i]) {
      g[i].push_back(e.dest);
      rg[e.dest].push_back(i);
    }
  }
  function<void(int)> dfs = [&g, &vs, &used, &dfs](int v) {
    used[v] = true;
    for (int i: g[v]) if (!used[i]) dfs(i);
    vs.push_back(v);
  };
  function<void(int,int)> rdfs = [&rg, &cmp, &used, &rdfs](int v, int k) {
    used[v] = true; cmp[v] = k;
    for (int i: rg[v]) if (!used[i]) rdfs(i, k);
  };
  REP(v,V) if (!used[v]) dfs(v);
  used = vector<bool>(V, false);
  reverse(ALL(vs));
  int k = 0;
  for(int i: vs) if (!used[i]) rdfs(i, k++);
  return k;
}

int main() {
  int N;
  while (cin >> N, N) {
    vector<ld> p(N);
    Graph g(N);
    REP(i,N) {
      cin >> p[i];
      int m, a;
      cin >> m;
      REP(j,m) {
        cin >> a;
        add_edge(g, i, a - 1);
      }
    }
    vector<int> cmp;
    int K = scc(g, cmp);
    vector<int> is_ok(K, 1);
    for (const auto &es: g)
      for (auto &&e: es)
        if (cmp[e.src] != cmp[e.dest])
          is_ok[cmp[e.dest]] = 0;
    vector<ld> prod(K, 1.0);
    REP(i,N) prod[cmp[i]] *= p[i];
    ld res = 1;
    REP(i,K) if (is_ok[i]) res *= 1 - prod[i];
    cout << setprecision(9) << fixed << res << endl;
  }
  return 0;
}