[蓝书/Ch5] The K-League UVALive - 2531 最大流/公平分配问题

题目链接

首先算出i在剩下比赛中全部获胜,看剩下的是否互相牵制,这样就转化成了公平分配问题的模型.

#include<bits/stdc++.h>

using namespace std;
typedef long long ll;
const int maxn = 1000 + 10;
const int INF = 1000000000;

struct Edge {
  int from, to, cap, flow;
};

bool operator < (const Edge& a, const Edge& b) {
  return a.from < b.from || (a.from == b.from && a.to < b.to);
}

struct Dinic {
  int n, m, s, t;
  vector<Edge> edges;    // 边数的两倍
  vector<int> G[maxn];   // 邻接表，G[i][j]表示结点i的第j条边在e数组中的序号
  bool vis[maxn];         // BFS使用
  int d[maxn];           // 从起点到i的距离
  int cur[maxn];        // 当前弧指针

  void ClearAll(int n) {
    for(int i = 0; i < n; i++) G[i].clear();
    edges.clear();
  }

  void ClearFlow() {
    for(int i = 0; i < edges.size(); i++) edges[i].flow = 0;
  }

  void AddEdge(int from, int to, int cap) {
    edges.push_back((Edge){from, to, cap, 0});
    edges.push_back((Edge){to, from, 0, 0});
    m = edges.size();
    G[from].push_back(m-2);
    G[to].push_back(m-1);
  }

  bool BFS() {
    memset(vis, 0, sizeof(vis));
    queue<int> Q;
    Q.push(s);
    vis[s] = 1;
    d[s] = 0;
    while(!Q.empty()) {
      int x = Q.front(); Q.pop();
      for(int i = 0; i < G[x].size(); i++) {
        Edge& e = edges[G[x][i]];
        if(!vis[e.to] && e.cap > e.flow) {
          vis[e.to] = 1;
          d[e.to] = d[x] + 1;
          Q.push(e.to);
        }
      }
    }
    return vis[t];
  }

  int DFS(int x, int a) {
    if(x == t || a == 0) return a;
    int flow = 0, f;
    for(int& i = cur[x]; i < G[x].size(); i++) {
      Edge& e = edges[G[x][i]];
      if(d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap-e.flow))) > 0) {
        e.flow += f;
        edges[G[x][i]^1].flow -= f;
        flow += f;
        a -= f;
        if(a == 0) break;
      }
    }
    return flow;
  }

  int Maxflow(int s, int t) {
    this->s = s; this->t = t;
    int flow = 0;
    while(BFS()) {
      memset(cur, 0, sizeof(cur));
      flow += DFS(s, INF);
    }
    return flow;
  }

  vector<int> Mincut() { // call this after maxflow
    vector<int> ans;
    for(int i = 0; i < edges.size(); i++) {
      Edge& e = edges[i];
      if(vis[e.from] && !vis[e.to] && e.cap > 0) ans.push_back(i);
    }
    return ans;
  }

  void Reduce() {
    for(int i = 0; i < edges.size(); i++) edges[i].cap -= edges[i].flow;
  }
};

Dinic g;

int n;
int T;
int w[100];
int d[100];
int a[100][100];
inline int getnum(int x,int y)
{
    return n+(x-1)*n+y;
}
vector<int> ans;
int main()
{
//    freopen("data.txt","r",stdin);
    ios_base::sync_with_stdio(false);
    cin >> T;
    while(T--)
    {
        ans.clear();
        cin >> n;
        for(int i=1;i<=n;i++)
        {
            cin >> w[i]>>d[i];
        }

        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=n;j++)
            {
                cin >> a[i][j];
            }
        }

        int s = 0;
        int t = n*n+n+1;
        for(int i=1;i<=n;i++)
        {
            int total = w[i];
            for(int j=1;j<=n;j++)
            {
                total += a[i][j];
            }
            g.ClearAll(t+5);
            int sum = 0;
            for(int j=1;j<=n;j++)
            {
                for(int jj=1;jj<j;jj++)
                {
                    if(j==i||jj==i) continue;
                    int num = getnum(j,jj);
                    sum += a[j][jj];
                    g.AddEdge(s,num,a[j][jj]);
                    g.AddEdge(num,j,INF);
                    g.AddEdge(num,jj,INF);
                }
            }
//            cout <<total<<"&&"<<endl;
            int f= 0;
            for(int j=1;j<=n;j++)
            {
                if(w[j]>total)
                {
                    f = 1;
                    break;
                }
                if(j==i) continue;
                g.AddEdge(j,t,total-w[j]);
            }

            if(f)
            {
                continue;
            }

            if(g.Maxflow(s,t)==sum)
            {
                ans.push_back(i);
            }
        }
        for(int i=0;i<ans.size();i++)
        {
            cout << ans[i];
            if(i!=ans.size()-1)
                cout <<" ";
        }
        cout << endl;


    }
    return 0;
}