HDU 4280 Island Transport(网络流，SAP）

解题思路：

建模很简单，不过以前一直用dinic，而这个题目数据偏大，用dinic超时了，据说没有可以卡住SAP的网络流，于是搞到了一套SAP的模版，过了，保存一下模版。

#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#pragma comment(linker, "/STACK:1024000000,1024000000")
#define LL long long
using namespace std;

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 Node
{
int from,to,next;
int cap;
}edge[MAXM];
int tol;
int head[MAXN];
int dep[MAXN];
int gap[MAXN];//gap[x]=y :说明残留网络中dep[i]==x的个数为y

int n;//n是总的点的个数，包括源点和汇点

void init()
{
tol=0;
memset(head,-1,sizeof(head));
}

void AddEdge(int u,int v,int w)
{
edge[tol].from=u;
edge[tol].to=v;
edge[tol].cap=w;
edge[tol].next=head[u];
head[u]=tol++;
edge[tol].from=v;
edge[tol].to=u;
edge[tol].cap=0;
edge[tol].next=head[v];
head[v]=tol++;
}
void BFS(int start,int end)
{
memset(dep,-1,sizeof(dep));
memset(gap,0,sizeof(gap));
gap[0]=1;
int que[MAXN];
int front,rear;
front=rear=0;
dep[end]=0;
que[rear++]=end;
while(front!=rear)
{
int u=que[front++];
if(front==MAXN)front=0;
for(int i=head[u];i!=-1;i=edge[i].next)
{
int v=edge[i].to;
if(dep[v]!=-1)continue;
que[rear++]=v;
if(rear==MAXN)rear=0;
dep[v]=dep[u]+1;
++gap[dep[v]];
}
}
}
int SAP(int start,int end)
{
int res=0;
BFS(start,end);
int cur[MAXN];
int S[MAXN];
int top=0;
memcpy(cur,head,sizeof(head));
int u=start;
int i;
while(dep[start]<n)
{
if(u==end)
{
int temp=INF;
int inser;
for(i=0;i<top;i++)
if(temp>edge[S[i]].cap)
{
temp=edge[S[i]].cap;
inser=i;
}
for(i=0;i<top;i++)
{
edge[S[i]].cap-=temp;
edge[S[i]^1].cap+=temp;
}
res+=temp;
top=inser;
u=edge[S[top]].from;
}
if(u!=end&&gap[dep[u]-1]==0)//出现断层，无增广路
break;
for(i=cur[u];i!=-1;i=edge[i].next)
if(edge[i].cap!=0&&dep[u]==dep[edge[i].to]+1)
break;
if(i!=-1)
{
cur[u]=i;
S[top++]=i;
u=edge[i].to;
}
else
{
int min=n;
for(i=head[u];i!=-1;i=edge[i].next)
{
if(edge[i].cap==0)continue;
if(min>dep[edge[i].to])
{
min=dep[edge[i].to];
cur[u]=i;
}
}
--gap[dep[u]];
dep[u]=min+1;
++gap[dep[u]];
if(u!=start)u=edge[S[--top]].from;
}
}
return res;
}

int main()
{
int T,N,M;
scanf("%d", &T);
while(T--)
{
scanf("%d%d", &N, &M);
int Min = 100010;
int Max = -100010;
int u,v,w;
n = N;
init();
int x, y;
int s,t;
for(int i=1;i<=N;i++)
{
scanf("%d%d", &x,&y);
if(x < Min)
{
Min = x;
s = i;
}
if(x > Max)
{
Max = x;
t = i;
}
}
for(int i=1;i<=M;i++)
{
scanf("%d%d%d", &u,&v,&w);
AddEdge(u,v,w);
AddEdge(v,u,w);
}
printf("%d\n", SAP(s,t));
}
return 0;
}