POJ 1459 —— Power Network

原题：http://poj.org/problem?id=1459

题意：一共有n个结点，在这些结点中有 np 个是发电站，有 nc 个是用户，给出m条线路所能运输的电量，以及每个发电站输出的电量、每个用户能接收的电量；

问用户所能接收的最大电量；

思路：因为是多源多汇，所以我们建立一个超级源点 s = n 和一个超级汇点 t = n+1；

建立 s 到发电站的的边，容量就是发电站输出的电量；

建立用户到 t 的边，容量就是用户所能接收的电量；

剩下的 m 条边直接建边即可；

#include<cstdio>
#include<cstring>
#include<string>
#include<queue>
#include<vector>
#include<algorithm>
#define inf 0x3f3f3f3f
using namespace std;
const int maxn = 1e5+5;
int n, np, nc, m;
int num_nodes;

struct Edge
{
	int from, to, flow, cap;
}edge[maxn*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], front[maxn], cur[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<n+2;i++)	G[i].clear();
	edgenum = 0;
	memset(deep, 0, sizeof deep);
}

int main()
{
	while(~scanf("%d%d%d%d", &n, &np, &nc, &m))
	{
		init();
		while(m--)
		{
			int u, v, c;
			scanf(" (%d,%d)%d", &u, &v, &c);
			add(u, v, c);
		}
		int s = n, t = n+1;
		while(np--)
		{
			int v, c;
			scanf(" (%d)%d", &v, &c);
			add(s, v, c);
		}
		while(nc--)
		{
			int u, c;
			scanf(" (%d)%d", &u, &c);
			add(u, t, c);
		}
		num_nodes = n+2;
		int flow = Maxflow(s, t);
		printf("%d\n", flow);
	}
	return 0;
}