10779-Collectors-Problem-UVa-mr.convict

/*author* Priyanshu Shrivastav (from IIT Palakkad) *
 * *_ __ ___  _ ______ ___  _ ____   ___  ___| |_  *
 * | '_ ` _ \| '__/ __/ _ \| '_ \ \ / / |/ __| __| *
 * | | | | | | | | (_| (_) | | | \ V /| | (__| |_  *
 * |_| |_| |_|_|(_)___\___/|_| |_|\_/ |_|\___|\__| *
When I wrote this, only God and I understood what I was doing
 ** * * * * * * * Now, only God knows * * * * * * */
//TODO with less vertices merge all mm * i + j in one for each i, i.e. merge j vertex to one for each player except bob
#include         <bits/stdc++.h>
#pragma GCC      optimize ("Ofast")
#pragma GCC      optimize ("unroll-loops")
#pragma GCC      target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

#define IOS      ios_base::sync_with_stdio(false); cin.tie (nullptr)
#define PREC     cout.precision (10); cout << fixed
#define bg(x)    "[ " << #x << " : " << x << " ]"
#define x        first
#define y        second
using namespace std;
using pii = pair <int, int>;

const int N = 10 * 25 + 2;
const int infi = (int)1e9;

int f[N][N];
vector < vector <int> > Adj;
int n, m, nn, mm;
int Par[N];

int bfs (int s, int t) {
   fill (Par, Par + n, -1);
   Par[s] = -2;

   queue <pii> Q;
   Q.push(pii(s, infi));

   while (!Q.empty()) {
      pii tmp = Q.front();
      Q.pop();
      int u = tmp.x, flow = tmp.y;

      for (int v : Adj[u]) {
         if (Par[v] == -1 && f[u][v]) {
            Par[v] = u;
            int newFlow = min(flow, f[u][v]);
            if (v == t) {
               return newFlow;
            }
            Q.push(pii(v, newFlow));
         }
      }
   }
   return 0;
}

int edmondsKarp(int s, int t) {
   int flow = 0;
   int newFlow;

   while ((newFlow = bfs (s, t))) {
      flow += newFlow;
      int cur = t;
      while (cur != s) {
         int prv = Par[cur];
         f[prv][cur] -= newFlow;
         f[cur][prv] += newFlow;
         cur = prv;
      }
   }
   return flow;
}

void solve(int tc) {
   int s, t;
   for (int i = 0; i < N; ++i)
      for (int j = 0; j < N; ++j)
         f[i][j] = 0;

   cin >> nn >> mm;
   n = nn * mm + 2;
   s = nn * mm, t = nn * mm + 1;
   Adj.assign(n, vector <int> ());

   int val[25];
   for (int i = 0; i < nn; ++i) {
      fill (val, val + 25, 0);
      int ki, kval;
      cin >> ki;
      while (ki--) {
         cin >> kval;
         --kval;
         val[kval] += 1;
      }
      for (int j = 0; j < mm; ++j) {
         int w = val[j];
         if (i == 0) {
            Adj[j].push_back(s);
            Adj[s].push_back(j);
            f[s][j] = w;

            Adj[j].push_back(t);
            Adj[t].push_back(j);
            f[j][t] = 1;
         }
         else {
            w -= 1;
            Adj[mm * i + j].push_back(j);
            Adj[j].push_back(mm * i + j);
            if (w > 0)
               f[mm * i + j][j] = w;
            else if (w < 0) {
               f[j][mm * i + j] = -w;
            }
         }
      }

      if (i) {
         for (int j = 0; j < mm; ++j) {
            for (int k = j + 1; k < mm; ++k) {
               Adj[mm * i + j].push_back(mm * i + k);
               Adj[mm * i + k].push_back(mm * i + j);
               f[mm * i + j][mm * i + k] = 1;
               f[mm * i + k][mm * i + j] = 1;
            }
         }
      }
   }
   cout << "Case #" << tc << ": " << edmondsKarp(s, t) << '\n';;
}

signed main() {
   int tc;
   cin >> tc;
   for (int i = 1; i <= tc; ++i) {
      solve(i);
   }

   return EXIT_SUCCESS;
}