紫书 习题 11-9 UVa 12549 （二分图最小点覆盖）

用到了二分图的一些性质， 最大匹配数=最小点覆盖

 貌似在白书上有讲

还不是很懂， 自己看着别人的博客用网络流写了一遍

反正以后学白书应该会系统学二分图的，紫书上没讲深。

目前就这样吧。

#include<cstdio>
#include<vector>
#include<cstring>
#include<queue>
#include<algorithm>
#define REP(i, a, b) for(int i = (a); i < (b); i++)
using namespace std;

const int MAXN = 21234;
const int MAXM = 112;
struct Edge{ int from, to, cap, flow; };
vector<Edge> edges;
vector<int> g[MAXN];
int cur[MAXN], h[MAXN];
int n, m, s, t;
int map[MAXM][MAXM], c[MAXM][MAXM], r[MAXM][MAXM];

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

bool bfs()
{
	queue<int> q;
	q.push(s);
	memset(h, 0, sizeof(h));
	h[s] = 1;
	
	while(!q.empty())
	{
		int x = q.front(); q.pop();
		REP(i, 0, g[x].size())
		{
			Edge& e = edges[g[x][i]];
			if(e.cap > e.flow && !h[e.to])
			{
				h[e.to] = h[x] + 1;
				q.push(e.to);
			}
		}
	}
	
	return h[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(h[x] + 1 == h[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;
			if((a -= f) == 0) break;
		}
	}
	return flow;
}

int maxflow()
{
	int flow = 0;
	while(bfs())
	{
		memset(cur, 0, sizeof(cur));
		flow += dfs(s, 1e9);
	}
	return flow;
}

void make_edges()
{
	int cnt = 0, tmp;
	REP(i, 0, n)
	{
		bool ok = true;
		REP(j, 0, m)
		{
			if(map[i][j] == 1)
			{
				if(ok) cnt++;
				r[i][j] = cnt;
				ok = false;
			}
			else if(map[i][j] == 2) ok = true;
		}
	}
	tmp = cnt;
	
	REP(j, 0, m)
	{
		bool ok = true;
		REP(i, 0, n)
		{
			if(map[i][j] == 1)
			{
				if(ok) cnt++;
				c[i][j] = cnt;
				ok = false;
			}
			else if(map[i][j] == 2) ok = true;
		}
	}
	
	REP(i, 1, cnt + 5) g[i].clear();
	s = cnt + 3, t = s + 1;
	REP(i, 1, tmp + 1) AddEdge(s, i, 1);
	REP(i, tmp + 1, cnt + 1) AddEdge(i, t, 1);
	REP(i, 0, n)
		REP(j, 0, m)
			if(map[i][j] == 1)
				AddEdge(r[i][j], c[i][j], 1);
}

int main()
{
	int T;
	scanf("%d", &T);
	
	while(T--)
	{
		scanf("%d%d", &n, &m);
		edges.clear();
		memset(map, 0, sizeof(map));
		memset(c, 0, sizeof(c));
		memset(r, 0, sizeof(r));
		
		int tmp, x, y;
		scanf("%d", &tmp);
		while(tmp--)
		{
			scanf("%d%d", &x, &y); 
			x--; y--;
			map[x][y] = 1;
		}
		scanf("%d", &tmp);
		while(tmp--)
		{
			scanf("%d%d", &x, &y);
			x--; y--;
			map[x][y] = 2;
		}
		
		make_edges();
		printf("%d
", maxflow());
	}

	return 0;
}