最大流：SAP+GAP模版

#include

#include

#include

#define MAXN 205

#define MAXM 410

#define INT_MAX 0x7fffffff

using namespace std;

int n,m;

struct node
{
int c,next,to;
} edge[MAXM];
int cnt,head[MAXN];

void addedge(int from,int to,int c)//这里存的还是一条有向边

{
edge[cnt].to=to;
edge[cnt].c=c;
edge[cnt].next=head[from]; head[from]=cnt++;
edge[cnt].to=from;
edge[cnt].c=0;     edge[cnt].next=head[to];
head[to]=cnt++;

}

int gap[MAXN],h[MAXN],curedges[MAXN],pre[MAXN];

int start,end;

int SAP_GAP()

{
start=1;
end=n;

//gap;  h：距离标号数组；curedges：当前弧数组；pre前驱数组

int cur_flow,flow_ans=0,u,tmp,neck,i;// 初始化最大0

memset(h,0,sizeof(h));

memset(gap,0,sizeof(gap));

memset(pre,-1,sizeof(pre));

for(i=1; i<=n; i++)
curedges[i]=head[i];//初始化当前弧为第一条邻接边

gap[0]=n;
u=start;

while(h[start]<</span>n)

{   if(u==end)

{   cur_flow=INT_MAX;

for(i=start; i!=end; i=edge[curedges[i]].to)

{   if(cur_flow>edge[curedges[i]].c)

{   neck=i;
cur_flow=edge[curedges[i]].c;
}

}       //增广成功，寻找瓶颈边

for(i=start; i!=end; i=edge[curedges[i]].to)

{  tmp=curedges[i];

edge[tmp].c-=cur_flow;
edge[tmp^1].c=cur_flow;

}

flow_ans+=cur_flow;
u=neck;

}

for(i=curedges[u]; i!=-1; i=edge[i].next)

if(edge[i].c&&h[u]==h[edge[i].to]+1)
break;  //寻找可行弧

if(i!=-1)       //找到可行弧

{   curedges[u]=i;
pre[edge[i].to]=u;
u=edge[i].to;
}

else            //未找到可行弧

{   gap[h[u]]--;

if(gap[h[u]]==0)   break;  //GAP优化

curedges[u]=head[u];

for(tmp=n,i=head[u]; i!=-1; i=edge[i].next)

if(edge[i].c)
tmp=min(tmp,h[edge[i].to]);

h[u]=tmp+1;

++gap[h[u]];

if(u!=start) u=pre[u];

}

}

return flow_ans;

}

void init()

{   int from,to,c;
cnt=0;

memset(head,-1,sizeof(head));

for(int i=0; i<</span>m; i++)

{   scanf("%d%d%d",&from,&to,&c);
addedge(from,to,c);
}

}

int main()

{
//freopen("in.txt","r",stdin);

while(~scanf("%d%d",&m,&n))

{  init();

printf("%d\n",SAP_GAP());

}

return 0;

}

code2：链式前向星(2)

#include

#include

#include

#define inf 0x7fffffff

using namespace std;

const int N=205;

const int M=500;//边是双向存的（注意不是无向）要开正常的2倍大

struct Edge{int v,next,w;} edge[M];int head[N],cnt,n,m,s=1;

int pre[N],cur[N],dis[N],gap[N];

void addedge(int u,int v,int w)//这里存的还是一条有向边

{  edge[cnt].v=v;edge[cnt].w=w;

edge[cnt].next=head[u];head[u]=cnt++;

edge[cnt].v=u;edge[cnt].w=0;

edge[cnt].next=head[v];head[v]=cnt++;

}

int sap()

{  int flow=0,aug=inf,u;bool flag;

memset(pre,-1,sizeof(pre));memset(dis,0,sizeof(dis));

memset(gap,0,sizeof(gap));

for(int i=1; i<=n; i++)

cur[i]=head[i];

gap[s]=n;   //初始化时全部处于gap[s]

u=pre[s]=s;

while(dis[s]<</span>n)

{   flag=0;

for(int &j=cur[u]; j!=-1; j=edge[j].next)

{  int v=edge[j].v;

if(edge[j].w>0&&dis[u]==dis[v]+1)

{flag=1;

if(edge[j].w<</span>aug) aug=edge[j].w;

pre[v]=u;u=v;

if(u==n)    //如果到达end

{   flow+=aug;

while(u!=s)

{   u=pre[u];

edge[cur[u]].w-=aug;

edge[cur[u]^1].w+=aug;//异或是找与其配对的边

}

aug=inf;

}

break;

}

}

if(flag)                      //未找到可行边

continue;

int mindis=n;

for(int j=head[u]; j!=-1; j=edge[j].next)

{    int v=edge[j].v;

if(edge[j].w>0&&dis[v]<</span>mindis)

{  mindis=dis[v];cur[u]=j;}

}

if((--gap[dis[u]])==0)break;

dis[u]=mindis+1;

gap[dis[u]]++;

u=pre[u];

}

return flow;

}

void init()

{   int from,to,c;cnt=0;

memset(head,-1,sizeof(head));

for(int i=0;i<</span>m;i++)

{  scanf("%d%d%d",&from,&to,&c);addedge(from,to,c);}

}

int main()

{   while(~scanf("%d%d",&m,&n))

{

init();

printf("%d\n",sap());

}

return 0;

}

code3：邻接矩阵

#include

#include

#include

#define M 205

using namespace std;

const int inf=~0U>>1;

int n,nb,nc,m;

int gap[M],flow[M][M],dist[M],cur[M];int pre[M];int source,end,s,t;

int sap()

{s=source;t=end;

memset(cur,0,sizeof(cur));memset(dist,0,sizeof(dist));  memset(gap,0,sizeof(gap));

int u=pre[s]=s,maxflow=0,aug=inf;

gap[0]=n;

while(dist[s]<</span>n)

{

loop:

for(int v=cur[u];v<=n;v++)

{  if(flow[u][v]&&dist[u]==dist[v]+1)

{

cur[u]=v;aug=min(aug,flow[u][v]);

pre[v]=u;u=v;

if(v==t)

{    maxflow+=aug;

for(u=pre[u];v!=s;v=u,u=pre[u])

flow[u][v]-=aug,flow[v][u]+=aug;

aug=inf;

}

goto loop;

}

}

int mind=n;

for(int v=1;v<=n;v++)

if(flow[u][v]&&(mind>dist[v]))

{cur[u]=v;mind=dist[v];}

if((--gap[dist[u]])==0) break;

gap[dist[u]=mind+1]++;

u=pre[u];

}

return maxflow;

}

void init()

{        int from,to,c;

memset(flow,0,sizeof(flow));//没加这个 wa了4次

for(int i=0;i<</span>m;i++)

{scanf("%d%d%d",&from,&to,&c);flow[from][to]+=c;}

source=1;end=n;

}

int main()

{int x,y,c;

while(~scanf("%d%d",&m,&n))

{

init();

printf("%d\n",sap());

}

return 0;

}