4.2.2 - The Perfect Stall.cpp

/*
ID: nathan.18
TASK: stall4
LANG: C++11
*/

#include <iostream>
#include <string>
#include <utility>
#include <sstream>
#include <algorithm>
#include <stack>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <bitset>
#include <cmath>
#include <cstring>
#include <iomanip>
#include <fstream>
#include <cassert>
#include <unordered_set>

using namespace std;

#define FOR(i, a, b) for (int i=a; i<(b); i++)
#define F0R(i, a) for (int i=0; i<(a); i++)
#define F0R1(i, a) for (int i=1; i<=(a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define F0Rd1(i, a) for (int i=a; i>0; i--)
#define SORT(vec) sort(vec.begin(), vec.end())

#define INF 1000000010
#define LL_INF 4500000000000000000
#define LSOne(S) (S & (-S))
#define EPS 1e-9
#define pA first
#define pB second
#define mp make_pair
#define pb push_back
#define PI acos(-1.0)
#define ll long long
#define MOD (int)(2e+9+11)
#define SET(vec, val, size) for (int i = 0; i < size; i++) vec[i] = val;
#define SET2D(arr, val, dim1, dim2) F0R(i, dim1) F0R(j, dim2) arr[i][j] = val;
#define SET3D(arr, val, dim1, dim2, dim3) F0R(i, dim1) F0R(j, dim2) F0R(k, dim3) arr[i][j][k] = val;
#define SET4D(arr, val, dim1, dim2, dim3, dim4) F0R(i, dim1) F0R(j, dim2) F0R(k, dim3) F0R(l, dim4) arr[i][j][k][l] = val;
#define READGRID(arr, dim) F0R(i, dim) F0R(j, dim) cin >> arr[i][j];
typedef pair<int, int> ii;
typedef pair<ii, int> iii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<iii> viii;
typedef vector<ll> vl;

#define MAX_V 500

int res[MAX_V][MAX_V], mf, f, s, t;                          // global variables
vi p;

void augment(int v, int minEdge) {     // traverse BFS spanning tree from s to t
    if (v == s) { f = minEdge; return; }  // record minEdge in a global variable f
    else if (p[v] != -1) { augment(p[v], min(minEdge, res[p[v]][v])); // recursive
        res[p[v]][v] -= f; res[v][p[v]] += f; }       // update
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);

    freopen("stall4.in", "r", stdin);
    freopen("stall4.out", "w", stdout);

    int n, m; cin >> n >> m;
    s = 0, t = 470;

    memset(res, 0, sizeof res);
    F0R(i, n) {
        int x; cin >> x;
        F0R(j, x) {
            int y; cin >> y;
            res[i+1][y+220] = 1;
        }
        res[s][i+1] = 1;
    }
    F0R1(i, m) {
        res[i+220][t] = 1;
    }


    mf = 0;                                              // mf stands for max_flow
    while (true) {           // O(VE^2) (actually O(V^3E) Edmonds Karp's algorithm
        f = 0;
        // run BFS, compare with the original BFS shown in Section 4.2.2
        vi dist(MAX_V, INF); dist[s] = 0; queue<int> q; q.push(s);
        p.assign(MAX_V, -1);           // record the BFS spanning tree, from s to t!
        while (!q.empty()) {
            int u = q.front(); q.pop();
            if (u == t) break;      // immediately stop BFS if we already reach sink t
            for (int v = 0; v < MAX_V; v++)                 // note: this part is slow
                if (res[u][v] > 0 && dist[v] == INF)
                    dist[v] = dist[u] + 1, q.push(v), p[v] = u;
        }
        augment(t, INF);     // find the min edge weight `f' along this path, if any
        if (f == 0) break;      // we cannot send any more flow (`f' = 0), terminate
        mf += f;                 // we can still send a flow, increase the max flow!
    }

    cout << mf << endl;

    return 0;
}