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上下界网络流模板

分类: IT文章 • 2025-01-23 21:08:01

无源汇上下界可行流

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<string>
  4 #include<cstring>
  5 #include<cmath>
  6 #include<algorithm>
  7 #include<queue>
  8 #include<stack>
  9 #include<set>
 10 #include<bitset>
 11 #include<vector>
 12 #include<cstdlib>
 13 #define QAQ int
 14 #define TAT long long
 15 #define OwO bool
 16 #define ORZ double
 17 #define F(i,j,n) for(QAQ i=j;i<=n;++i)
 18 #define E(i,j,n) for(QAQ i=j;i>=n;--i)
 19 #define MES(i,j) memset(i,j,sizeof(i))
 20 #define MEC(i,j) memcpy(i,j,sizeof(j))
 21 
 22 using namespace std;
 23 const QAQ N=305,M=30000;
 24 
 25 QAQ n,m,s,t;
 26 struct Link{
 27     QAQ to,last,val,id;
 28 }a[M];
 29 QAQ head[N],js=1;
 30 QAQ dis[N],use[N],ans[M];
 31 QAQ low[M],flow[N];
 32 OwO vis[N];
 33 queue<QAQ> q;
 34 
 35 void add(QAQ x,QAQ y,QAQ z,QAQ p){
 36     a[++js].to=y;a[js].id=p;a[js].val=z;
 37     a[js].last=head[x];head[x]=js;
 38 }
 39 
 40 OwO bfs(){
 41     F(i,s,t) dis[i]=vis[i]=0;
 42     dis[s]=vis[s]=1;
 43     q.push(s);
 44     while(!q.empty()){
 45         QAQ x=q.front();q.pop();
 46         for(QAQ i=head[x];i;i=a[i].last) if(a[i].val&&!vis[a[i].to]){
 47             vis[a[i].to]=1;
 48             dis[a[i].to]=dis[x]+1;
 49             q.push(a[i].to);
 50         }
 51     }
 52     return vis[t];
 53 }
 54 
 55 QAQ dfs(QAQ x,QAQ want){
 56     if(x==t||!want) return want;
 57     QAQ f=0,ans=0;
 58     for(QAQ i=use[x];i;i=a[i].last) if(dis[a[i].to]==dis[x]+1){
 59         f=dfs(a[i].to,min(a[i].val,want));
 60         if(!f) continue;
 61         ans+=f;
 62         want-=f;
 63         a[i].val-=f;
 64         a[i^1].val+=f;
 65         if(!want) break;
 66         use[x]=i;
 67     }
 68     if(!ans) dis[x]=-1;
 69     return ans;
 70 }
 71 
 72 QAQ dinic(){
 73     QAQ ans=0;
 74     while(bfs()){
 75         MEC(use,head);
 76         ans+=dfs(s,1e9);
 77     }
 78     return ans;
 79 }
 80 
 81 QAQ main(){
 82     scanf("%d%d",&n,&m);
 83     s=0;t=n+1;
 84     F(i,1,m){
 85         QAQ u,v,w;
 86         scanf("%d%d%d%d",&u,&v,&low[i],&w);
 87         add(u,v,w-low[i],i);
 88         add(v,u,0,i);
 89         flow[v]+=low[i];
 90         flow[u]-=low[i];
 91     }
 92     QAQ sum=0;
 93     F(i,1,n) if(flow[i]<0){
 94         add(i,t,-flow[i],0);
 95         add(t,i,0,0);
 96     }
 97     else {
 98         sum+=flow[i];
 99         add(s,i,flow[i],0);
100         add(i,s,0,0);
101     }
102     if(dinic()==sum){
103         printf("YES
");
104         F(x,1,n) for(QAQ i=head[x];i;i=a[i].last) if(a[i].id==0||i%2==0) continue;
105         else {
106             ans[a[i].id]=a[i].val+low[a[i].id];
107         }
108         F(i,1,m) printf("%d
",ans[i]);
109     }
110     else printf("NO
");
111     return 0;
112 }
View Code

有源汇有上下界最大流

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<string>
  4 #include<cstring>
  5 #include<cmath>
  6 #include<algorithm>
  7 #include<queue>
  8 #include<stack>
  9 #include<set>
 10 #include<bitset>
 11 #include<vector>
 12 #include<cstdlib>
 13 #define QAQ int
 14 #define TAT long long
 15 #define OwO bool
 16 #define ORZ double
 17 #define F(i,j,n) for(QAQ i=j;i<=n;++i)
 18 #define E(i,j,n) for(QAQ i=j;i>=n;--i)
 19 #define MES(i,j) memset(i,j,sizeof(i))
 20 #define MEC(i,j) memcpy(i,j,sizeof(j))
 21 
 22 using namespace std;
 23 const QAQ N=405,M=30000;
 24 
 25 QAQ n,m,s,t,ss,tt;
 26 struct Link{
 27     QAQ to,last,val,id;
 28 }a[M];
 29 QAQ head[N],js=1;
 30 QAQ dis[N],use[N],ans[M];
 31 QAQ low[M],flow[N];
 32 OwO vis[N];
 33 queue<QAQ> q;
 34 
 35 void add(QAQ x,QAQ y,QAQ z,QAQ p){
 36     a[++js].to=y;a[js].id=p;a[js].val=z;
 37     a[js].last=head[x];head[x]=js;
 38 }
 39 
 40 OwO bfs(){
 41     F(i,0,n+1) dis[i]=vis[i]=0;
 42     dis[ss]=vis[ss]=1;
 43     q.push(ss);
 44     while(!q.empty()){
 45         QAQ x=q.front();q.pop();
 46         for(QAQ i=head[x];i;i=a[i].last) if(a[i].val&&!vis[a[i].to]){
 47             vis[a[i].to]=1;
 48             dis[a[i].to]=dis[x]+1;
 49             q.push(a[i].to);
 50         }
 51     }
 52     return vis[tt];
 53 }
 54 
 55 QAQ dfs(QAQ x,QAQ want){
 56     if(x==tt||!want) return want;
 57     QAQ f=0,ans=0;
 58     for(QAQ i=use[x];i;i=a[i].last) if(dis[a[i].to]==dis[x]+1){
 59         f=dfs(a[i].to,min(a[i].val,want));
 60         if(!f) continue;
 61         ans+=f;
 62         want-=f;
 63         a[i].val-=f;
 64         a[i^1].val+=f;
 65         if(!want) break;
 66         use[x]=i;
 67     }
 68     if(!ans) dis[x]=-1;
 69     return ans;
 70 }
 71 
 72 QAQ dinic(){
 73     QAQ ans=0;
 74     while(bfs()){
 75         MEC(use,head);
 76         ans+=dfs(ss,1e9);
 77     }
 78     return ans;
 79 }
 80 
 81 QAQ main(){
 82     scanf("%d%d%d%d",&n,&m,&s,&t);
 83     ss=0;tt=n+1;
 84     F(i,1,m){
 85         QAQ u,v,w;
 86         scanf("%d%d%d%d",&u,&v,&low[i],&w);
 87         add(u,v,w-low[i],i);
 88         add(v,u,0,i);
 89         flow[v]+=low[i];
 90         flow[u]-=low[i];
 91     }
 92     QAQ sum=0;
 93     F(i,1,n) if(flow[i]<0){
 94         add(i,tt,-flow[i],0);
 95         add(tt,i,0,0);
 96     }
 97     else {
 98         sum+=flow[i];
 99         add(ss,i,flow[i],0);
100         add(i,ss,0,0);
101     }
102     add(t,s,1e9,0);
103     if(dinic()==sum){
104         sum=a[head[t]^1].val;
105         F(i,2,js) if(!a[i].id) a[i].val=0;
106         head[ss]=head[tt]=0;
107         ss=s;tt=t;
108         printf("%d
",sum+dinic());
109     }
110     else printf("please go home to sleep
");
111     return 0;
112 }
View Code

有源汇有上下界最小流 

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<string>
  4 #include<cstring>
  5 #include<cmath>
  6 #include<algorithm>
  7 #include<queue>
  8 #include<stack>
  9 #include<set>
 10 #include<bitset>
 11 #include<vector>
 12 #include<cstdlib>
 13 #define QAQ int
 14 #define TAT long long
 15 #define OwO bool
 16 #define ORZ double
 17 #define F(i,j,n) for(QAQ i=j;i<=n;++i)
 18 #define E(i,j,n) for(QAQ i=j;i>=n;--i)
 19 #define MES(i,j) memset(i,j,sizeof(i))
 20 #define MEC(i,j) memcpy(i,j,sizeof(j))
 21 
 22 using namespace std;
 23 const QAQ N=70000,M=2000000;
 24 
 25 QAQ n,m,s,t,ss,tt;
 26 struct Link{
 27     QAQ to,last,val,id;
 28 }a[M];
 29 QAQ head[N],js=1;
 30 QAQ dis[N],use[N],ans[M];
 31 QAQ low[M],flow[N];
 32 OwO vis[N];
 33 queue<QAQ> q;
 34 
 35 inline void read(int &x){
 36     int f = 0, ch = 0; x = 0;
 37     for(; !isdigit(ch); ch = getchar()) if(ch == '-') f = 1;
 38     for(; isdigit(ch); ch = getchar()) x = x * 10 + ch - '0';
 39     if(f) x = -x;
 40 }
 41 
 42 void add(QAQ x,QAQ y,QAQ z,QAQ p){
 43     a[++js].to=y;a[js].id=p;a[js].val=z;
 44     a[js].last=head[x];head[x]=js;
 45 }
 46 
 47 OwO bfs(){
 48     F(i,0,n+1) dis[i]=vis[i]=0;
 49     dis[ss]=vis[ss]=1;
 50     q.push(ss);
 51     while(!q.empty()){
 52         QAQ x=q.front();q.pop();
 53         for(QAQ i=head[x];i;i=a[i].last) if(a[i].val&&!vis[a[i].to]){
 54             vis[a[i].to]=1;
 55             dis[a[i].to]=dis[x]+1;
 56             q.push(a[i].to);
 57         }
 58     }
 59     return vis[tt];
 60 }
 61 
 62 QAQ dfs(QAQ x,QAQ want){
 63     if(x==tt||!want) return want;
 64     QAQ f=0,ans=0;
 65     for(QAQ i=use[x];i;i=a[i].last) if(dis[a[i].to]==dis[x]+1){
 66         f=dfs(a[i].to,min(a[i].val,want));
 67         if(!f) continue;
 68         ans+=f;
 69         want-=f;
 70         a[i].val-=f;
 71         a[i^1].val+=f;
 72         if(!want) break;
 73         use[x]=i;
 74     }
 75     if(!ans) dis[x]=-1;
 76     return ans;
 77 }
 78 
 79 QAQ dinic(){
 80     QAQ ans=0;
 81     while(bfs()){
 82         F(i,0,n+1) use[i]=head[i];
 83         ans+=dfs(ss,2e9);
 84     }
 85     return ans;
 86 }
 87 
 88 QAQ main(){
 89 //    freopen("8.in","r",stdin);
 90     read(n);read(m);read(s);read(t);
 91 //    scanf("%d%d%d%d",&n,&m,&s,&t);
 92     ss=0;tt=n+1;
 93     F(i,1,m){
 94         QAQ u,v,w;
 95         read(u);read(v);read(low[i]);read(w);
 96 //        scanf("%d%d%d%d",&u,&v,&low[i],&w);
 97         add(u,v,w-low[i],i);
 98         add(v,u,0,i);
 99         flow[v]+=low[i];
100         flow[u]-=low[i];
101     }
102     QAQ sum=0;
103     F(i,1,n) if(flow[i]<0){
104         add(i,tt,-flow[i],0);
105         add(tt,i,0,0);
106     }
107     else {
108         sum+=flow[i];
109         add(ss,i,flow[i],0);
110         add(i,ss,0,0);
111     }
112     add(t,s,2e9,0);
113     if(dinic()==sum){
114         sum=a[head[t]^1].val;
115         F(i,2,js) if(!a[i].id) a[i].val=0;
116         head[ss]=head[tt]=0;
117         ss=t;tt=s;
118         printf("%d
",sum-dinic());
119     }
120     else printf("please go home to sleep
");
121     return 0;
122 }
View Code

有源汇上下界费用流([AHOI2014/JSOI2014]支线剧情)

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<string>
  4 #include<cstring>
  5 #include<cmath>
  6 #include<algorithm>
  7 #include<queue>
  8 #include<stack>
  9 #include<set>
 10 #include<bitset>
 11 #include<sstream>
 12 #include<cstdlib>
 13 #define QAQ int
 14 #define TAT long long
 15 #define OwO bool
 16 #define ORZ double
 17 #define Ug unsigned
 18 #define F(i,j,n) for(QAQ i=j;i<=n;++i)
 19 #define E(i,j,n) for(QAQ i=j;i>=n;--i)
 20 #define MES(i,j) memset(i,j,sizeof(i))
 21 #define MEC(i,j) memcpy(i,j,sizeof(j))
 22 
 23 using namespace std;
 24 const QAQ N=505,M=5000000;
 25 const QAQ oo=1e8;
 26 
 27 QAQ n,m,s,t;
 28 struct Link{
 29     QAQ to,last,rem,val,from;
 30 }a[M];
 31 QAQ head[N],js=1,ans;
 32 QAQ dis[N];
 33 OwO vis[N];
 34 queue<QAQ> q;
 35 
 36 void add(QAQ x,QAQ y,QAQ z,QAQ w){
 37     a[++js].from=x;a[js].to=y;
 38     a[js].rem=z;a[js].val=w;
 39     a[js].last=head[x];head[x]=js;
 40 }
 41 
 42 void Insert(QAQ x,QAQ y,QAQ z,QAQ w){
 43     add(x,y,z,w);add(y,x,0,-w);
 44 }
 45 
 46 OwO spfa(QAQ s,QAQ t){
 47     F(i,s,t) dis[i]=oo,vis[i]=0;
 48     dis[t]=0;vis[t]=1;
 49     q.push(t);
 50     while(!q.empty()){
 51         QAQ x=q.front();q.pop();vis[x]=0;
 52         for(QAQ i=head[x];i;i=a[i].last) if(a[i^1].rem&&dis[a[i].to]>dis[x]-a[i].val){
 53             dis[a[i].to]=dis[x]-a[i].val;
 54             if(!vis[a[i].to]) vis[a[i].to]=1,q.push(a[i].to);
 55         }
 56     }
 57     return dis[s]<oo;
 58 }
 59 
 60 QAQ dfs(QAQ x,QAQ want){
 61     if(x==t||!want) {
 62 //        vis[x]=1;
 63         return want;
 64     }
 65     QAQ f=0;
 66     vis[x]=1;
 67     for(QAQ i=head[x];i;i=a[i].last) if(!vis[a[i].to]&&a[i].rem&&dis[a[i].to]==dis[x]-a[i].val){
 68         QAQ d=dfs(a[i].to,min(want-f,a[i].rem));
 69         if(d){
 70             ans+=d*a[i].val;
 71             a[i].rem-=d;
 72             a[i^1].rem+=d;
 73             f+=d;
 74         }
 75         if(f==want) break;
 76     }
 77     vis[x]=0;
 78     return f;
 79 }
 80 
 81 void zkw(){
 82 //    QAQ ans=0;
 83     while(spfa(s,t)){
 84         vis[t]=1;
 85         while(vis[t]){
 86             MES(vis,0);
 87             dfs(s,oo);
 88         }
 89     }
 90 //    return ans;
 91 }
 92 
 93 
 94 QAQ main(){
 95     scanf("%d",&n);
 96     s=0;t=n+1;
 97     F(i,1,n){
 98         QAQ k;
 99         scanf("%d",&k);
100         if(k) Insert(i,t,k,0);
101         if(i!=1) Insert(i,1,oo,0);
102         while(k--){
103             QAQ v,w;
104             scanf("%d%d",&v,&w);
105             Insert(s,v,1,w);
106             Insert(i,v,oo,w);
107         }
108     }
109     zkw();
110     printf("%d
",ans);
111     return 0;
112 }
View Code

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