网络流之 最大流模版

13 、最大流
	13.1 SAP邻接 矩阵形式
	/*
	* SAP算法（矩阵形式）
	* 结点编号从0开始
	*/
	const int MAXN=1100;
int maze[MAXN][MAXN];
int gap[MAXN],dis[MAXN],pre[MAXN],cur[MAXN];
int sap(int start,int end,int nodenum)
{
	memset(cur,0,sizeof(cur));
	memset(dis,0,sizeof(dis));
	memset(gap,0,sizeof(gap));
	int u=pre[start]=start,maxflow=0,aug=-1;
	gap[0]=nodenum;
	while(dis[start]<nodenum)
	{
loop:
		for(int v=cur[u];v<nodenum;v++)
			if(maze[u][v] && dis[u]==dis[v]+1)
			{
				if(aug==-1 || aug>maze[u][v])aug=maze[u][v];
				pre[v]=u;
				u=cur[u]=v;
				if(v==end)
				{
					maxflow+=aug;
					for(u=pre[u];v!=start;v=u,u=pre[u])
					{
						maze[u][v]-=aug;
						maze[v][u]+=aug;
					}
					aug=-1;
				}
				goto loop;
			}
			int mindis=nodenum-1;
			for(int v=0;v<nodenum;v++)
				if(maze[u][v]&&mindis>dis[v])
				{
					cur[u]=v;
					mindis=dis[v];
				}
				if((--gap[dis[u]])==0)break;
				gap[dis[u]=mindis+1]++;
				u=pre[u];
	}
	return maxflow;
}

13.2 SAP邻接矩阵形式 2
	保留原矩阵，可用于多次使最大流
	/*
	* SAP邻接矩阵形式
	* 点的编号从0开始
	* 增加个flow数组，保留原矩阵maze,可用于多次使用最大流
	*/
	const int MAXN=1100;
int maze[MAXN][MAXN];
int gap[MAXN],dis[MAXN],pre[MAXN],cur[MAXN];
int flow[MAXN][MAXN];//存最大流的容量
int sap(int start,int end,int nodenum)
{
	memset(cur,0,sizeof(cur));
	memset(dis,0,sizeof(dis));
	memset(gap,0,sizeof(gap));
	98 / 152 ACM模板 kuangbin
		memset(flow,0,sizeof(flow));
	int u=pre[start]=start,maxflow=0,aug=-1;
	gap[0]=nodenum;
	while(dis[start]<nodenum)
	{
loop:
		for(int v=cur[u];v<nodenum;v++)
			if(maze[u][v]-flow[u][v] && dis[u]==dis[v]+1)
			{
				if(aug==-1 || aug>maze[u][v]-flow[u][v])aug=maze[u][v]-flow[u][v];
				pre[v]=u;
				u=cur[u]=v;
				if(v==end)
				{
					maxflow+=aug;
					for(u=pre[u];v!=start;v=u,u=pre[u])
					{
						flow[u][v]+=aug;
						flow[v][u]-=aug;
					}
					aug=-1;
				}
				goto loop;
			}
			int mindis=nodenum-1;
			for(int v=0;v<nodenum;v++)
				if(maze[u][v]-flow[u][v]&&mindis>dis[v])
				{
					cur[u]=v;
					mindis=dis[v];
				}
				if((--gap[dis[u]])==0)break;
				gap[dis[u]=mindis+1]++;
				u=pre[u];
	}
	return maxflow;
}

13.3 ISAPSAPSAP邻接表形式
	const int MAXN = 100010;//点数的最大值
const int MAXM = 400010;//边数的最大值
const int INF = 0x3f3f3f3f;
struct Edge
{
	int to,next,cap,flow;
}edge[MAXM];//注意是MAXM
int tol;
int head[MAXN];
int gap[MAXN],dep[MAXN],pre[MAXN],cur[MAXN];
void init()
{
	tol = 0;
	memset(head,-1,sizeof(head));
}
//加边，单向图三个参数，双向图四个参数
void addedge(int u,int v,int w,int rw=0)
{
	edge[tol].to = v;edge[tol].cap = w;edge[tol].next = head[u];
	edge[tol].flow = 0;head[u] = tol++;
	edge[tol].to = u;edge[tol].cap = rw;edge[tol].next = head[v];
	edge[tol].flow = 0;head[v]=tol++;
}
//输入参数：起点、终点、点的总数
//点的编号没有影响，只要输入点的总数
int sap(int start,int end,int N)
{
	memset(gap,0,sizeof(gap));
	memset(dep,0,sizeof(dep));
	memcpy(cur,head,sizeof(head));
	int u = start;
	pre[u] = -1;
	gap[0] = N;
	int ans = 0;
	while(dep[start] < N)
	{
		if(u == end)
		{
			int Min = INF;
			for(int i = pre[u];i != -1; i = pre[edge[i^1].to])
				if(Min > edge[i].cap - edge[i].flow)
					Min = edge[i].cap - edge[i].flow;
			for(int i = pre[u];i != -1; i = pre[edge[i^1].to])
			{
				edge[i].flow += Min;
				edge[i^1].flow -= Min;
			}
			u = start;
			ans += Min;
			continue;
		}
		bool flag = false;
		int v;
		for(int i = cur[u]; i != -1;i = edge[i].next)
		{
			v = edge[i].to;
			if(edge[i].cap - edge[i].flow && dep[v]+1 == dep[u])
			{
				flag = true;
				cur[u] = pre[v] = i;
				break;
			}
		}
		if(flag)
		{
			u = v;
			continue;
		}
		int Min = N;
		for(int i = head[u]; i != -1;i = edge[i].next)
			if(edge[i].cap - edge[i].flow && dep[edge[i].to] < Min)
			{
				Min = dep[edge[i].to];
				cur[u] = i;
			}
			gap[dep[u]]--;
			if(!gap[dep[u]])return ans;
			dep[u] = Min+1;
			gap[dep[u]]++;
			if(u != start) u = edge[pre[u]^1].to;
	}
	return ans;
}

ISAP13.4  ISAP+bfs +bfs+bfs初始化 +栈优化
	const int MAXN = 100010;//点数的最大值
const int MAXM = 400010;//边数的最大值
const int INF = 0x3f3f3f3f;
struct Edge
{
	int to,next,cap,flow;
}edge[MAXM];//注意是MAXM
int tol;
int head[MAXN];
int gap[MAXN],dep[MAXN],cur[MAXN];
void init()
{
	tol = 0;
	memset(head,-1,sizeof(head));
}
void addedge(int u,int v,int w,int rw = 0)
{
	edge[tol].to = v; edge[tol].cap = w; edge[tol].flow = 0;
	edge[tol].next = head[u]; head[u] = tol++;
	edge[tol].to = u; edge[tol].cap = rw; edge[tol].flow = 0;
	edge[tol].next = head[v]; head[v] = tol++;
}
int Q[MAXN];
void BFS(int start,int end)
{
	memset(dep,-1,sizeof(dep));
	memset(gap,0,sizeof(gap));
	gap[0] = 1;
	int front = 0, rear = 0;
	dep[end] = 0;
	Q[rear++] = end;
	while(front != rear)
	{
		int u = Q[front++];
		for(int i = head[u]; i != -1; i = edge[i].next)
		{
			int v = edge[i].to;
			if(dep[v] != -1)continue;
			Q[rear++] = v;
			dep[v] = dep[u] + 1;
			gap[dep[v]]++;
		}
	}
}
int S[MAXN];
int sap(int start,int end,int N)
{
	BFS(start,end);
	memcpy(cur,head,sizeof(head));
	int top = 0;
	int u = start;
	int ans = 0;
	while(dep[start] < N)
	{
		if(u == end)
		{
			int Min = INF;
			int inser;
			for(int i = 0;i < top;i++)
				if(Min > edge[S[i]].cap - edge[S[i]].flow)
				{
					Min = edge[S[i]].cap - edge[S[i]].flow;
					inser = i;
				}
				for(int i = 0;i < top;i++)
				{
					edge[S[i]].flow += Min;
					edge[S[i]^1].flow -= Min;
				}
				ans += Min;
				top = inser;
				u = edge[S[top]^1].to;
				continue;
		}
		bool flag = false;
		int v;
		for(int i = cur[u]; i != -1; i = edge[i].next)
		{
			v = edge[i].to;
			if(edge[i].cap - edge[i].flow && dep[v]+1 == dep[u])
			{
				flag = true;
				cur[u] = i;
				break;
			}
		}
		if(flag)
		{
			S[top++] = cur[u];
			u = v;
			continue;
		}
		int Min = N;
		for(int i = head[u]; i != -1; i = edge[i].next)
			if(edge[i].cap - edge[i].flow && dep[edge[i].to] < Min)
			{
				Min = dep[edge[i].to];
				cur[u] = i;
			}
			gap[dep[u]]--;
			if(!gap[dep[u]])return ans;
			dep[u] = Min + 1;
			gap[dep[u]]++;
			if(u != start)u = edge[S[--top]^1].to;
	}
	return ans;
}