POJ 1149 PIGS 最大流建图

最新推荐文章于 2021-05-02 21:17:07 发布

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本文讨论了如何通过构建网络流模型来解决PIGS问题，并特别强调了合并节点和边的重要性。通过实例和代码实现，展示了网络流在实际问题解决中的应用。

思路见 PKU 1149，PIGS，构造网络流模型时，要注意合并节点和边

又是大神带我飞。。。

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;

#define REP( i, a, b ) for( int i = a; i < b; i++ )
#define FOR( i, a, b ) for( int i = a; i <= b; i++ )
#define CLR( a, x ) memset( a, x, sizeof a )
#define CPY( a, x ) memcpy( a, x, sizeof a )

const int maxn = 100 + 10;
const int maxm = 1000 + 10;
const int maxe = 10000 + 10;
const int INF = 1e9;

struct Edge{
          int v, c, f;
          int next;
          Edge() {}
          Edge(int v, int c, int f, int next) : v(v), c(c), f(f), next(next) {}
};
struct ISAP{
          int n, s, t;
          int num[maxn], cur[maxn], d[maxn], p[maxn];
          int Head[maxn], cntE;
          int Q[maxn], head, tail;
          Edge edge[maxe];
          void Init(int n){
                    this -> n = n;
                    cntE = 0;
                    CLR(Head, -1);
          }
          void Add(int u, int v, int c){
                    edge[cntE] = Edge(v, c, 0, Head[u]);
                    Head[u] = cntE++;
                    edge[cntE] = Edge(u, 0, 0, Head[v]);
                    Head[v] = cntE++;
          }
          void Bfs(){
                    CLR(d, -1);
                    CLR(num, 0);
                    d[t] = 0;
                    head = tail = 0;
                    Q[tail++] = t;
                    num[0] = 1;
                    while(head != tail){
                              int u = Q[head++];
                              for(int i = Head[u]; ~i; i = edge[i].next){
                                        Edge &e = edge[i];
                                        if(~d[e.v]) continue;
                                        d[e.v] = d[u] + 1;
                                        Q[tail++] = e.v;
                                        num[d[e.v]] ++;
                              }
                    }
          }
          int Maxflow(int s, int t){
                    this -> s = s;
                    this -> t = t;
                    CPY(cur, Head);
                    Bfs();
                    int u = p[s] = s, flow = 0;
                    while(d[s] < n){
                              if(u == t){
                                        int f = INF, neck;
                                        for(int i = s; i != t; i = edge[cur[i]].v){
                                                  if(f > edge[cur[i]].c - edge[cur[i]].f){
                                                            f = edge[cur[i]].c - edge[cur[i]].f;
                                                            neck = i;
                                                  }
                                        }
                                        for(int i = s; i != t; i = edge[cur[i]].v){
                                                  edge[cur[i]].f += f;
                                                  edge[cur[i]^1].f -= f;
                                        }
                                        flow += f;
                                        u = neck;
                              }
                              int ok = 0;
                              for(int i = cur[u]; ~i; i = edge[i].next){
                                        Edge &e = edge[i];
                                        if(e.c > e.f && d[e.v] + 1 == d[u]){
                                                  ok = 1;
                                                  cur[u] = i;
                                                  p[e.v] = u;
                                                  u = e.v;
                                                  break;
                                        }
                              }
                              if(!ok){
                                        int m = n - 1;
                                        if(--num[d[u]] == 0) break;
                                        for(int i = Head[u]; ~i; i = edge[i].next){
                                                  Edge &e = edge[i];
                                                  if(e.c - e.f > 0 && m > d[e.v]){
                                                            cur[u] = i;
                                                            m = d[e.v];
                                                  }
                                        }
                                        ++num[d[u] = m + 1];
                                        u = p[u];
                              }
                    }
                    return flow;
          }

}solver;

int S, T, n, m, num[maxm], buy[maxn];
vector<int> pig_houses[maxm];

void input(){
          FOR(i, 1, m) scanf("%d", &num[i]), pig_houses[i].clear();
          FOR(i, 1, n){
                    int x, house;
                    scanf("%d", &x);
                    while(x--){
                              scanf("%d", &house);
                              pig_houses[house].push_back(i);
                    }
                    scanf("%d", &buy[i]);
          }
}

void solve(){
          S = 0, T = n + 1;
          solver.Init(T + 1);
          FOR(i, 1, m) REP(j, 0, pig_houses[i].size()){
                    if(j == 0) solver.Add(S, pig_houses[i][0], num[i]);
                    else solver.Add(pig_houses[i][j-1], pig_houses[i][j], INF);
          }
          FOR(i, 1, n) solver.Add(i, T, buy[i]);
          printf("%d\n", solver.Maxflow(S, T));
}

int main()
{
          //freopen("in.txt", "r", stdin);
          while(~scanf("%d%d", &m, &n)){
                    input();
                    solve();
          }
          return 0;
}