网络流做题记录
大网络流时代！！！
最大流
经典入门题目，对于每个左侧点建立与右侧点边权为1的边
建立超级源点连左侧，超级汇点连右侧，直接跑最大流
Code：
#include<bits/stdc++.h>
#define int long long
#define INF 0x3f3f3f3f
using namespace std;
const int M=2e5+110;
inline int read(){
int sum=0,k=1;char c=getchar();
while(c>'9'||c<'0'){if(c=='-')k=-1;c=getchar();
}while(c>='0'&&c<='9'){sum=sum*10+c-48;c=getchar();
}return sum*k;
}
int Head[M],Tot=1;
struct Line_Node{
int Next,To,Val;
}Ed[M];
inline void Adde(int u,int v,int w){
Ed[++Tot]={Head[u],v,w};
Head[u]=Tot;
}
int n,m,s,t,cur[M];
int Deep[M];bool vis[M];
inline bool bfs(){
for(int i=0;i<=n+1;i++)
Deep[i]=INF,vis[i]=false,cur[i]=Head[i];
Deep[s]=true,vis[s]=true;
queue<int>q;q.push(s);
while(!q.empty()){
int u=q.front();
q.pop();vis[u]=false;
for(int i=Head[u];i;i=Ed[i].Next){
int v=Ed[i].To,w=Ed[i].Val;
if(Deep[u]+1<Deep[v]&&w!=false){
Deep[v]=Deep[u]+1;
if(vis[v]==false){
vis[v]=true;q.push(v);
}
}
}
}if(Deep[t]==INF) return false;
else return true;
}
inline int dfs(int u,int mi){
int mm=0;
if(u==t) return mi;
for(int i=cur[u];i;i=Ed[i].Next){
cur[u]=i;
int v=Ed[i].To,w=Ed[i].Val;
if(Deep[u]+1==Deep[v]&&w!=false){
mm=dfs(v,min(w,mi));
if(mm!=false){
Ed[i].Val-=mm;
Ed[i^1].Val+=mm;
return mm;
}
}
}return false;
}
inline int Dinic(){
int ans=0,res=0;
while(bfs())
while(res=dfs(s,INF))
ans+=res;
return ans;
}
signed main(){
m=read(),n=read();
s=0,t=n+1;//超级源点与超级汇点
while(1){
int u=read(),v=read();
if(u==v&&u==-1) break;
Adde(u,v,1);Adde(v,u,0);
}//正常建边
//各个点与源点,汇点连边
for(int i=1;i<=m;i++) Adde(s,i,1),Adde(i,s,0);
for(int i=m+1;i<=n;i++) Adde(i,t,1),Adde(t,i,0);
cout<<Dinic()<<endl;
for(int i=2;i<=Tot;i+=2){
if(Ed[i].To==s||Ed[i^1].To==s)
continue;
if(Ed[i].To==t||Ed[i^1].To==t)
continue;
if(Ed[i^1].Val!=false)//当正反边存在边权时,为流经点
cout<<Ed[i^1].To<<" "<<Ed[i].To<<endl;
}
return 0;
}
二分图思想，把每个单位与每个桌子连流量为1的边，源点与单位连人数边，桌子与汇点连容量边
暴力枚举方案数
Code:
#include<bits/stdc++.h>
#define INF 0x3f3f3f3f
#define int long long
using namespace std;
const int M=2e5+110;
inline int read(){
int sum=0,k=1;char c=getchar();
while(c>'9'||c<'0'){if(c=='-')k=-1;c=getchar();
}while(c>='0'&&c<='9'){sum=sum*10+c-48;c=getchar();
}return sum*k;
}
struct Line_Node{
int Next,To,Val;
}Ed[M];
int Head[M],Tot=1;
inline void Adde(int u,int v,int w){
Ed[++Tot]={Head[u],v,w};
Head[u]=Tot;
}
int n,m,s,t,sum,cur[M];
int Deep[M];bool vis[M];
inline bool bfs(){
for(int i=0;i<=n+m+1;i++)
Deep[i]=INF,vis[i]=false,cur[i]=Head[i];
Deep[s]=0,vis[s]=true;
queue<int>q;q.push(s);
while(!q.empty()){
int u=q.front();
q.pop();vis[u]=false;
for(int i=Head[u];i;i=Ed[i].Next){
int v=Ed[i].To,w=Ed[i].Val;
if(Deep[v]>Deep[u]+1&&w!=false){
Deep[v]=Deep[u]+1;
if(vis[v]==false){
q.push(v);
vis[v]=true;
}
}
}
}if(Deep[t]!=INF&&Deep[t]!=0) return true;
else return false;
}
inline int dfs(int u,int mi){
int mm=0;
if(u==t) return mi;
for(int i=cur[u];i;i=Ed[i].Next){
cur[u]=i;
int v=Ed[i].To,w=Ed[i].Val;
if(Deep[v]==Deep[u]+1&&w!=false){
mm=dfs(v,min(w,mi));
if(mm!=false){
Ed[i].Val-=mm;
Ed[i^1].Val+=mm;
return mm;
}
}
}return false;
}
inline int Dinic(){
int ans=0,res=0;
while(bfs()){
while(res=dfs(s,INF)){
ans+=res;
}
}
return ans;
}
int r[M],c[M];
signed main(){
scanf("%lld%lld",&m,&n);
s=0,t=m+n+1;//关键在于建图
for(int i=1;i<=m;i++){
scanf("%lld",&r[i]);
Adde(s,i,r[i]);
Adde(i,s,0);
sum+=r[i];
}
for(int i=1;i<=n;i++){
scanf("%lld",&c[i]);
Adde(i+m,t,c[i]);
Adde(t,i+m,0);
}
for(int i=1;i<=m;i++)
for(int j=1;j<=n;j++)
Adde(i,j+m,1),Adde(j+m,i,0);
int maxx=Dinic();
if(sum==maxx) cout<<1<<endl;
else{
cout<<0<<endl;
return 0;
}
for(int i=1;i<=m;i++){
for(int j=Head[i];j;j=Ed[j].Next){
int v=Ed[j].To,w=Ed[j].Val;
if(v>m&&w==false&&v<t)
printf("%lld ",v-m);
}
cout<<'\n';
}
return 0;
}
每个点拆成入点和出点，入点连超级原点，出点连超级汇点，跑Dinic，输出暴力的小trick
#include<bits/stdc++.h>
#define INF 0x3f3f3f3f
#define int long long
using namespace std;
const int M=2e5+110;
inline int read(){
int sum=0,k=1;char c=getchar();
while(c>'9'||c<'0'){if(c=='-')k=-1;c=getchar();
}while(c>='0'&&c<='9'){sum=sum*10+c-48;c=getchar();
}return sum*k;
}
int Head[M],Tot=1;
struct Line_Node{
int Next,To,Val;
}Ed[M];
inline void Adde(int u,int v,int w){
Ed[++Tot]={Head[u],v,w};
Head[u]=Tot;
}
int n,m,s,t,cur[M];
int Deep[M];bool vis[M];
inline bool bfs(){
for(int i=0;i<=n*2+1;i++)
Deep[i]=INF,vis[i]=false,cur[i]=Head[i];
Deep[s]=0,vis[s]=true;
queue<int>q;q.push(s);
while(!q.empty()){
int u=q.front();
q.pop();vis[u]=false;
for(int i=Head[u];i;i=Ed[i].Next){
int v=Ed[i].To,w=Ed[i].Val;
// cout<<"u:"<<u<<" v:"<<v<<" w:"<<w<<" Deep[u]:"<<Deep[u]<<" Deep[v]:"<<Deep[v]<<endl;
if(Deep[v]>Deep[u]+1&&w!=false){
Deep[v]=Deep[u]+1;
if(vis[v]==false){
vis[v]=true,q.push(v);
}
}
}
}if(Deep[t]==INF) return false;
else return true;
}
int tt[M],ff[M];
inline int dfs(int u,int mi){
// cout<<"u:"<<u<<" mi:"<<mi<<endl;
int mm=0;
if(u==t) return mi;
for(int i=cur[u];i;i=Ed[i].Next){
cur[u]=i;
int v=Ed[i].To,w=Ed[i].Val;
// cout<<"v:"<<v<<" w:"<<w<<" Deep[u]:"<<Deep[u]<<" Deep[v]:"<<Deep[v]<<endl;
if(Deep[v]==Deep[u]+1&&w!=false){
mm=dfs(v,min(w,mi));
if(mm!=false){
tt[u]=v;
if(u!=s) ff[v-n]=true;
Ed[i].Val-=mm;
Ed[i^1].Val+=mm;
return mm;
}
}
}return false;
}
inline int Dinic(){
int ans=0,res=0;
while(bfs()){
while(res=dfs(s,INF)){
// cout<<res<<endl;
ans+=res;
}
}
for(int i=1;i<=n;i++)
if(!ff[i]){
int u=i;
cout<<u<<" ";
while(tt[u]&&tt[u]!=t){
cout<<tt[u]-n<<" ";
u=tt[u]-n;
}
cout<<endl;
}
return ans;
}
int in[M],out[M];
bool chr[M];
inline void pr(int u){
if(chr[u]) return ;
chr[u]=1;
// printf("%lld ",u);
for(int i=Head[u];i;i=Ed[i].Next){
int v=Ed[i].To,w=Ed[i^1].Val;
if(v==s||v==t) continue;
if(w!=false) return void(pr(v));
}
}
signed main(){
n=read(),m=read();
// cout<<" n:"<<n<<" m:"<<m<<endl;
s=0,t=n*2+1;
for(int i=1;i<=n;i++)
Adde(s,i,1),Adde(i+n,t,1),
Adde(i,s,0),Adde(t,i+n,0);
for(int i=1;i<=m;i++){
int u=read(),v=read();
Adde(u,v+n,1),Adde(v+n,u,0);
}
int maxx=Dinic();
// for(int i=Head[0];i;i=Ed[i].Next){
// int v=Ed[i].To,w=Ed[i^1].Val;
// if(w!=false){
// pr(v);
// cout<<'\n';
// }
// }
cout<<n-maxx<<endl;
return 0;
}
/*
1 4 7 10 11
2 5 8
3 6 9
*/
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