HDU 3605 —— Escape 状态压缩+最大流

原题：http://acm.hdu.edu.cn/showproblem.php?pid=3605

#include<cstdio>
#include<cstring>
#include<string>
#include<queue>
#include<cmath>
#include<vector>
#include<algorithm>
#define inf 1e9
using namespace std;
const int maxn = 1500;
const int maxm = 15000;
int n, m;
int num_nodes;
int can[15];
int tmp[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))
	{
		memset(tmp, 0, sizeof tmp);
		for(int i = 0;i<n;i++)
		{
			int k = 0;
			for(int j = 0;j<m;j++)
			{
				int x;
				scanf("%d", &x);
				if(x)	k |= 1<<j;
			}
			tmp[k]++;
		}
		for(int i = 0;i<m;i++)	scanf("%d", &can[i]);
		int s = 0, t = (1<<m)+m+1;
		num_nodes = t+1;
		init();
		for(int i = 0;i<(1<<m);i++)
		{
			if(tmp[i])
			add(s, i+1, tmp[i]);
		}
		for(int i = 0;i<m;i++)
			add((1<<m)+i+1, t, can[i]);
		for(int i = 0;i<(1<<m);i++)
		{
			for(int j = 0;j<m;j++)
			{
				if(i & (1<<j))
				add(i+1, (1<<m)+j+1, tmp[i]);
			}
		}
		int flow = Maxflow(s, t);
		if(flow == n)	printf("YES\n");
		else	printf("NO\n");
	}
	return 0;
}