网络流各种算法模版
以下模版都是以POJ1273为例子。
1，sap+gap优化
时间复杂度分析：n*n*m
可否有重边：可
#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <string.h>
#include<queue>
using namespace std;
#define INF 99999999
const int maxn =1110;
const int maxm =220000;
const int oo = 1<<29;
struct Arclist
{
int cnt, head[maxn], dis[maxn];
int cur[maxn], pre[maxn], gap[maxn], aug[maxn];
struct node
{
int u, v, w, next;
}edge[maxm];
void init()
{
cnt = 0;
memset(head,-1,sizeof(head));
}
void add(int u, int v, int w)
{
// cout<<u<<" "<<v<<" "<<w<<endl;
edge[cnt].u = u;
edge[cnt].v = v;
edge[cnt].w = w;
edge[cnt].next = head[u];
head[u] = cnt++;
edge[cnt].u = v;
edge[cnt].v = u;
edge[cnt].w = 0;
edge[cnt].next = head[v];
head[v] = cnt++;
}
int sap(int s, int e, int n)
{
int max_flow = 0, u = s;
int mindis;
for(int i = 0; i <= n; i++)
{
cur[i] = head[i];
dis[i] = 0;
gap[i] = 0;
}
aug[s] = oo;
pre[s] = -1;
gap[0] = n;
while(dis[s]<n)
{
bool flag = false;
if(u==e)
{
max_flow += aug[e];
for(int v = pre[e]; v != -1; v = pre[v])
{
int id = cur[v];
edge[id].w -= aug[e];
edge[id^1].w += aug[e];
aug[v] -= aug[e];
if(edge[id].w==0) u = v;
}
}
for(int id = cur[u]; id != -1; id = edge[id].next)
{
int v = edge[id].v;
if(edge[id].w>0 && dis[u]==dis[v]+1)
{
flag = true;
pre[v] = u;
cur[u] = id;
aug[v] = std::min(aug[u], edge[id].w);
u = v;
break;
}
}
if(flag==false)
{
if(--gap[dis[u]]==0) break;
mindis = n;
cur[u] = head[u];
for(int id = head[u]; id != -1; id = edge[id].next)
{
int v = edge[id].v;
if(edge[id].w>0 && dis[v]<mindis)
{
mindis = dis[v];
cur[u] = id;
}
}
dis[u] = mindis+1;
++gap[dis[u]];
if(u!=s) u = pre[u];
}
}
return max_flow;
}
}G;
int main()
{
int m,n,u,v,w;
while(~scanf("%d%d",&m,&n))
{
G.init();
while(m--)
{
scanf("%d%d%d",&u,&v,&w);
G.add(u,v,w);
}
cout<<G.sap(1,n,n)<<endl;
}
return 0;
}
2，一般预流推进算法
时间复杂度分析：n*n*m
可否有重边：可
#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <string.h>
#include<queue>
using namespace std;
#define INF 99999999
const int maxn =250;
const int maxm =250;
const int oo = 0x7fffffff;
struct push_relablel//一般预流推进法求最大流，时间复杂度O(n*n*m)
{
int res[maxn][maxn];//残留网络
int h[maxn];//高度
int ef[maxn];//余流
int n;//点数
int max_flow;//最大流
queue<int>que;//活动定点队列
int u,v,p,i;
int vis[maxn];
void init(int x){
n=x;
memset(h,0,sizeof(h));
memset(ef,0,sizeof(ef));
memset(res,0,sizeof(res));
}
void add(int u,int v,int w){
res[u][v]+=w;
}
int ans(int s,int t){
max_flow=0;
h[s]=n;
ef[s]=oo;ef[t]=-oo;
while(!que.empty())que.pop();
que.push(s);
while(!que.empty())
{
u=que.front();
que.pop();
for(i=1;i<=n;i++)
{
v=i;
if(res[u][v]<ef[u])p=res[u][v];
else p=ef[u];
if(p>0&&(u==s||h[u]==h[v]+1))
{
res[u][v]-=p;res[v][u]+=p;
if(v==t)max_flow+=p;
ef[u]-=p;ef[v]+=p;
if(v!=s&&v!=t)que.push(v);
}
}
if(u!=s&&u!=t&&ef[u]>0)
{
h[u]++;
que.push(u);
}
}
return max_flow;
}
}G;
int main()
{
int m,n,u,v,w;
while(~scanf("%d%d",&m,&n))
{
G.init(n);
while(m--)
{
scanf("%d%d%d",&u,&v,&w);
G.add(u,v,w);
}
cout<<G.ans(1,n)<<endl;
}
return 0;
}
3，最高标号预流推进算法
时间复杂度分析：n*n*sqrt（m）
可否有重边：可
#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <string.h>
#include<queue>
using namespace std;
#define INF 99999999
const int maxn =250;
const int maxm =250;
const int oo = 0x7fffffff;
struct list
{
int x;
int h;
bool friend operator <(const list &a,const list &b){
return a.h<b.h;
}
}q;
struct push_relablel//最高标号预流推进算法，时间复杂度O(n*n*sqrt（m）)
{
int res[maxn][maxn];//残留网络
int h[maxn];//高度
int ef[maxn];//余流
int n;//点数
int max_flow;//最大流
// queue<int>que;//活动定点队列
priority_queue<list>que;
int u,v,p,i;
int vis[maxn];
void init(int x){
n=x;
memset(h,0,sizeof(h));
memset(ef,0,sizeof(ef));
memset(res,0,sizeof(res));
}
void add(int u,int v,int w){
res[u][v]+=w;
}
int ans(int s,int t){
max_flow=0;
h[s]=n;
ef[s]=oo;ef[t]=-oo;
while(!que.empty())que.pop();
q.x=s;
q.h=h[s];
que.push(q);
while(!que.empty())
{
q=que.top();
que.pop();
u=q.x;
for(i=1;i<=n;i++)
{
v=i;
if(res[u][v]<ef[u])p=res[u][v];
else p=ef[u];
if(p>0&&(u==s||h[u]==h[v]+1))
{
res[u][v]-=p;res[v][u]+=p;
if(v==t)max_flow+=p;
ef[u]-=p;ef[v]+=p;
if(v!=s&&v!=t)
{
q.x=v;
q.h=h[v];
que.push(q);
}
}
}
if(u!=s&&u!=t&&ef[u]>0)
{
h[u]++;
q.x=u;
q.h=h[u];
que.push(q);
}
}
return max_flow;
}
}G;
int main()
{
int m,n,u,v,w;
while(~scanf("%d%d",&m,&n))
{
G.init(n);
while(m--)
{
scanf("%d%d%d",&u,&v,&w);
G.add(u,v,w);
}
cout<<G.ans(1,n)<<endl;
}
return 0;
}