[UVa] 13301 – Impossible Communication

Author            : Dipu Kumar Mohanto 
                    CSE, Batch - 6
                    BRUR.
Problem Statement : 13301 – Impossible Communication
Source            : UVa Online Judge
Category          : Graph Theory
Algorithm         : Strongly Connected Component, Disjoint Set Union
Verdict           : Accepted

#include "bits/stdc++.h"
 
using namespace std;
 
#define FI              freopen("in.txt", "r", stdin)
#define FO              freopen("out.txt", "w", stdout)
#define FAST            ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL)
 
#define FOR(i, n)       for (int i = 1; i <= n; i++)
#define For(i, n)       for (int i = 0; i < n; i++)
#define ROF(i, n)       for (int i = n; i >= 1; i--)
#define Rof(i, n)       for (int i = n-1; i >= 0; i--)
#define FORI(i, n)      for (auto i : n)
 
#define ll              long long
#define ull             unsigned long long
#define vi              vector <int>
#define vl              vector <ll>
#define pii             pair <int, int>
#define pll             pair <ll, ll>
#define mk              make_pair
#define ff              first
#define ss              second
#define eb              emplace_back
#define em              emplace
#define pb              push_back
#define ppb             pop_back
#define All(a)          a.begin(), a.end()
#define memo(a, b)      memset(a, b, sizeof a)
#define Sort(a)         sort(All(a))
#define ED(a)           Sort(a), a.erase(unique(All(a)), a.end())
#define rev(a)          reverse(All(a))
#define sz(a)           (int)a.size()
#define max3(a, b, c)   max(a, max(b, c))
#define min3(a, b, c)   min(a, min(b, c))
#define maxAll(a)       *max_element(All(a))
#define minAll(a)       *min_element(All(a))
#define allUpper(a)     transform(All(a), a.begin(), :: toupper)
#define allLower(a)     transform(All(a), a.begin(), :: tolower)
#define endl            '\n'
#define nl              puts("")
#define ub              upper_bound
#define lb              lower_bound
#define Exp             exp(1.0)
#define PIE             2*acos(0.0)
#define Sin(a)          sin(((a)*PIE)/180.0)
#define EPS             1e-9

#include "ext/pb_ds/assoc_container.hpp"
#include "ext/pb_ds/tree_policy.hpp"

using namespace __gnu_pbds;
 
template <typename T> using orderset = tree <T, null_type, less <T>, rb_tree_tag, tree_order_statistics_node_update>;
 
#include "ext/rope"
using namespace __gnu_cxx;
 
// rope <int> Rope;
 
// int dr[] = {1, -1, 0, 0}; // 4 Direction
// int dc[] = {0, 0, 1, -1};
// int dr[] = {0, 0, 1, -1, 1, 1, -1, -1}; // 8 Direction
// int dc[] = {1, -1, 0, 0, 1, -1, 1, -1};
// int dr[] = {-1, 1, -2, -2, -1, 1, 2, 2}; // knight Moves
// int dc[] = {-2, -2, -1, 1, 2, 2, 1, -1};
 
#define trace1(x)                           cerr << #x << ": " << x << endl;
#define trace2(x, y)                        cerr << #x << ": " << x << " | " << #y << ": " << y << endl;
#define trace3(x, y, z)                     cerr << #x << ": " << x << " | " << #y << ": " << y << " | " << #z << ": " << z << endl;
#define trace4(a, b, c, d)                  cerr << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": " << c << " | " << #d << ": " << d << endl;
#define trace5(a, b, c, d, e)               cerr << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": " << c << " | " << #d << ": " << d << " | " << #e << ": " << e << endl;
#define trace6(a, b, c, d, e, f)            cerr << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": " << c << " | " << #d << ": " << d << " | " << #e << ": " << e << " | " << #f << ": " << f << endl;
 
inline int setbit(int mask, int pos)        { return mask |= (1 << pos); }
inline int resetbit(int mask, int pos)      { return mask &= ~(1 << pos); }
inline int togglebit(int mask, int pos)     { return mask ^= (1 << pos); }
inline bool checkbit(int mask, int pos)     { return (bool)(mask & (1 << pos)); }
 
#define popcount(mask)                       __builtin_popcount(mask) // count set bit
#define popcountLL(mask)                     __builtin_popcountll(mask) // for long long
 
inline int read()                           { int a; scanf("%d", &a); return a; }
inline ll readLL()                          { ll a; scanf("%lld", &a); return a; }
inline double readDD()                      { double a; scanf("%lf", &a); return a; }
 
template <typename T> string toString(T num) { stringstream ss; ss << num; return ss.str(); }
int toInt(string s)                          { int num; istringstream iss(s); iss >> num; return num;  }
ll toLLong(string s)                         { ll num; istringstream iss(s); iss >> num; return num; }
 
#define inf             1e17
#define mod             1000000007
 
static const int maxn = 1e5 + 5;
static const int logn = 18;
 
int par[maxn];
 
inline void makeSet()
{
      for (int i = 0; i < maxn; i++) par[i] = i;
}
 
inline int findRep(int r)
{
      if (r == par[r]) return r;
      return par[r] = findRep(par[r]);
}
 
inline void Union(int u, int v)
{
      int p = findRep(u);
      int q = findRep(v);
      if (p != q) par[q] = p;
}
 
int tnode, tedge;
vi graph[maxn], rgraph[maxn];
vector <pii> all_simple_edge;
vi topo;
bool vis[maxn];
 
inline void dfs(int u)
{
      vis[u] = 1;
      for (int v : graph[u])
      {
            if (vis[v]) continue;
            dfs(v);
      }
      topo.eb(u);
}
inline void SCC(int u)
{
      vis[u] = 1;
      for (int v : rgraph[u])
      {
            if (vis[v]) continue;
            SCC(v);
      }
}
 
inline void clean()
{
      topo.clear();
      all_simple_edge.clear();
      for (int i = 0; i < maxn; i++)
      {
            graph[i].clear();
            rgraph[i].clear();
            vis[i] = 0;
      }
}
 
int main()
{
//      FI;
      while (scanf("%d %d", &tnode, &tedge) == 2)
      {
            makeSet();
            clean();
            for (int e = 1; e <= tedge; e++)
            {
                  int m;
                  scanf("%d", &m);
                  if (m == 1)
                  {
                        int u, v;
                        scanf("%d %d", &u, &v);
                        all_simple_edge.eb(u, v);
                  }
                  else
                  {
                        int p = -1;
                        for (int i = 0; i < m; i++)
                        {
                              int u;
                              scanf("%d", &u);
                              if (p == -1) p = u;
                              else Union(p, u);
                        }
                  }
            }
            for (pii p : all_simple_edge)
            {
                  int u = findRep(p.ff);
                  int v = findRep(p.ss);
                  graph[u].eb(v);
                  rgraph[v].eb(u);
            }
            for (int i = 1; i <= tnode; i++)
            {
                  int p = findRep(i);
                  if (!vis[p]) dfs(p);
            }
            memo(vis, 0);
            int scc = 0;
            int len = sz(topo);
            for (auto it = topo.rbegin(); it != topo.rend(); it++)
            {
                  if (!vis[*it])
                  {
                        SCC(*it);
                        scc++;
                  }
            }
            puts(scc == 1 ? "YES" : "NO");
      }
}