poj 2289 —— Jamie's Contact Groups 二分+最大流

原题：http://poj.org/problem?id=2289

#include<cstdio>
#include<cstring>
#include<string>
#include<queue>
#include<vector>
#include<map>
#include<algorithm>
#define inf 1e9
using namespace std;
const int maxn = 2000;
const int maxm = 510000;
int n, m, num_nodes;
map<string, int>mm;
vector<int>vec[maxn];

struct Edge  
{  
    int from, to, flow, cap;  
}edge[maxm*2];  
  
vector<int>G[maxn]; 
int edgenum;  
void add(int u, int v, int c) 
{  
    edge[edgenum].from = u;  
    edge[edgenum].to = v;  
    edge[edgenum].flow = 0;  
    edge[edgenum].cap = c;  
    edgenum++;  
      
    edge[edgenum].from = v;  
    edge[edgenum].to = u;  
    edge[edgenum].flow = 0;  
    edge[edgenum].cap = 0;  
    edgenum++;  
      
    G[u].push_back(edgenum-2);  
    G[v].push_back(edgenum-1);  
}  
  
int deep[maxn];  
bool vis[maxn];  
void BFS(int s, int t)  
{  
    queue<int>Q;  
    memset(vis, false, sizeof vis);  
    Q.push(t);  
    vis[t] = true;  
    deep[t] = 0;  
    while(!Q.empty())  
    {  
        int now = Q.front();  
        Q.pop();  
        for(int i = 0;i<(int)G[now].size();i++)  
        {  
            int v = edge[G[now][i]].to;  
            if(!vis[v]) 
			{  
                deep[v] = deep[now] + 1;  
                vis[v] = true;  
                Q.push(v);  
            }  
        }  
    }  
}  
  
int gap[maxn]; 
int cur[maxn]; 
int front[maxn];  
int Augment(int s, int t)  
{  
    int minflow = inf;  
    int begin = t;  
    while(begin != s)  
    {  
        Edge& e = edge[front[begin]];  
        minflow = min(minflow, e.cap - e.flow);  
        begin = e.from;  
    }  
      
    begin = t;  
    while(begin != s)  
    {  
        edge[front[begin]].flow += minflow;  
        edge[front[begin]^1].flow -= minflow;  
        begin = edge[front[begin]].from;  
    }  
    return minflow;  
}  
  
int Maxflow(int s, int t)  
{  
    int flow = 0;  
    BFS(s, t);  
    memset(gap, 0, sizeof gap);  
    memset(cur, 0, sizeof cur);  
    for(int i = 0;i<num_nodes;i++)  gap[deep[i]]++;  
    int begin = s;  
    while(deep[s] < num_nodes)  
    {  
        if(begin == t) 
		{  
            flow += Augment(s, t);  
            begin = s;  
        }  
        bool flag = false;  
        for(int i = cur[begin];i<(int)G[begin].size();i++)  
        {  
            Edge& e = edge[G[begin][i]];  
            if(e.cap > e.flow && deep[begin] == deep[e.to] + 1) 
			{  
                front[e.to] = G[begin][i];  
                cur[begin] = i;  
                flag = true;  
                begin = e.to;  
                break;  
            }  
        }  
        if(!flag)  
        {  
            int k = num_nodes-1;  
            for(int i = 0;i<(int)G[begin].size();i++) 
			{  
                Edge& e = edge[G[begin][i]];  
                if(e.cap > e.flow)  
                    k = min(k, deep[e.to]);  
            }  
            if(--gap[deep[begin]] == 0) break; 
            gap[deep[begin] = k+1]++;  
            cur[begin] = 0;  
            if(begin != s)   
                begin = edge[front[begin]].from;   
        }  
    }  
    return flow;  
}  
  
void init() 
{  
    for(int i = 0;i<num_nodes+2;i++) G[i].clear();  
    edgenum = 0;  
    memset(deep, 0, sizeof deep);  
}

int main()
{
	while(~scanf("%d%d", &n, &m))
	{
		if(n == 0 && m == 0)	break;
		mm.clear();
		for(int i = 1;i<=n;i++)	vec[i].clear();
		int cnt = 1;
		char name[20];
		int x;
		for(int i = 1;i<=n;i++)
		{
			scanf("%s", name);
			mm[name] = cnt;
			while(1)
			{
				scanf("%d", &x);
				vec[cnt].push_back(x+n+1);
				char ch = getchar();
				if(ch == '\n')	break;
			}
			cnt++;
		}
		int l = 0, r = n;
		int s = 0, t = n+m+1;
		int ans;
		num_nodes = t+1;
		while(l <= r)
		{
			init();
			int mid = (l+r)/2;
			for(int i = 1;i<=n;i++)
			{
				add(s, i, 1);
				for(int j = 0;j<(int)vec[i].size();j++)
					add(i, vec[i][j], 1);
			}				
			for(int i = n+1;i<=n+m;i++)
				add(i, t, mid);
			int flow = Maxflow(s, t);
			if(flow == n)
			{
				r = mid - 1;
				ans = mid;
			}
			else
				l = mid + 1;
		}
		printf("%d\n", ans);
	}
	return 0;
}