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有上下界的可行流

study from :

https://www.luogu.org/blog/top-oier/qian-tan-you-shang-xia-jie-di-wang-lao-liu

网络流

每次都要对dep数组进行初始化。

dfs函数的优化：如果TLE，尝试使用一下。

loj

https://loj.ac/problem/115

115

  1 #include <cstdio>
  2 #include <cstdlib>
  3 #include <cmath>
  4 #include <cstring>
  5 #include <string>
  6 #include <algorithm>
  7 #include <set>
  8 #include <map>
  9 #include <queue>
 10 #include <iostream>
 11 using namespace std;
 12 
 13 #define ll long long
 14 
 15 const int maxn=2e2+10;
 16 const int maxm=10201;
 17 const int inf=1e9;
 18 const double eps=1e-8;
 19 
 20 struct node
 21 {
 22     int d,len;
 23     node *to,*opp;
 24 }*e[maxn],*b[maxm];
 25 
 26 int dif[maxn],dep[maxn],q[maxn],n,low[maxm],ss,tt,st,en;
 27 
 28 void addedge(int x,int y,int z)
 29 {
 30     node *p1,*p2;
 31     p1=new node();
 32     p2=new node();
 33 
 34     p1->d=y;
 35     p1->len=z;
 36     p1->to=e[x];
 37     p1->opp=p2;
 38     e[x]=p1;
 39 
 40     p2->d=x;
 41     p2->len=0;
 42     p2->to=e[y];
 43     p2->opp=p1;
 44     e[y]=p2;
 45 }
 46 
 47 void addedge_1(int x,int y,int z,int i)
 48 {
 49     node *p1,*p2;
 50     p1=new node();
 51     p2=new node();
 52 
 53     p1->d=y;
 54     p1->len=z;
 55     p1->to=e[x];
 56     p1->opp=p2;
 57     e[x]=p1;
 58 
 59     p2->d=x;
 60     p2->len=0;
 61     p2->to=e[y];
 62     p2->opp=p1;
 63     e[y]=p2;
 64 
 65     b[i]=p2;
 66 }
 67 
 68 bool bfs()
 69 {
 70     node *p;
 71     int head=0,tail=1,d,dd;
 72     memset(dep,0,sizeof(dep));
 73     dep[st]=1;
 74     q[1]=st;
 75     while (head<tail)
 76     {
 77         head++;
 78         d=q[head];
 79         p=e[d];
 80         while (p)
 81         {
 82             dd=p->d;
 83             if (!dep[dd] && p->len)
 84             {
 85                 q[++tail]=dd;
 86                 dep[dd]=dep[d]+1;
 87             }
 88             p=p->to;
 89         }
 90     }
 91     if (dep[en])
 92         return 1;
 93     return 0;
 94 }
 95 
 96 int dfs(int d,int add)
 97 {
 98     if (!add || d==en)
 99         return add;
100     int totr=0,r,dd;
101     node *p=e[d];
102     while (p)
103     {
104         dd=p->d;
105         if (dep[dd]==dep[d]+1 && (r=dfs(dd,min(add,p->len)))>0)
106         {
107             totr+=r;
108             add-=r;
109             p->len-=r;
110             p->opp->len+=r;
111         }
112         p=p->to;
113     }
114     return totr;
115 }
116 
117 int main()
118 {
119     int m,x,y,u,v,tot=0,sum=0,i;
120     scanf("%d%d",&n,&m);
121     ss=0,tt=n+1;
122     st=ss,en=tt;
123     for (i=1;i<=m;i++)
124     {
125         scanf("%d%d%d%d",&x,&y,&u,&v);
126         low[i]=u;
127         dif[x]-=u,dif[y]+=u;
128         addedge_1(x,y,v-u,i);
129     }
130     for (i=1;i<=n;i++)
131         if (dif[i]>0)
132         {
133             addedge(ss,i,dif[i]);
134             tot+=dif[i];
135         }
136         else
137             addedge(i,tt,-dif[i]);
138 
139     while (bfs())
140         sum+=dfs(st,inf);
141     if (sum==tot)
142     {
143         printf("YES
");
144         for (i=1;i<=m;i++)
145             printf("%d
",low[i]+b[i]->len);
146     }
147     else
148         printf("NO");
149     return 0;
150 }
151 /*
152 
153 */

116

  1 #include <cstdio>
  2 #include <cstdlib>
  3 #include <cmath>
  4 #include <cstring>
  5 #include <string>
  6 #include <algorithm>
  7 #include <set>
  8 #include <map>
  9 #include <queue>
 10 #include <iostream>
 11 using namespace std;
 12 
 13 #define ll long long
 14 
 15 const int maxn=2e2+10;
 16 const int maxm=1e4;
 17 const int inf=1e9;
 18 const double eps=1e-8;
 19 
 20 struct node
 21 {
 22     int d,len;
 23     node *to,*opp;
 24 }*e[maxn];
 25 
 26 int dif[maxn],dep[maxn],q[maxn],n,low[maxm],ss,tt,st,en;
 27 
 28 void addedge(int x,int y,int z)
 29 {
 30     node *p1,*p2;
 31     p1=new node();
 32     p2=new node();
 33 
 34     p1->d=y;
 35     p1->len=z;
 36     p1->to=e[x];
 37     p1->opp=p2;
 38     e[x]=p1;
 39 
 40     p2->d=x;
 41     p2->len=0;
 42     p2->to=e[y];
 43     p2->opp=p1;
 44     e[y]=p2;
 45 }
 46 
 47 bool bfs()
 48 {
 49     node *p;
 50     int head=0,tail=1,d,dd;
 51     memset(dep,0,sizeof(dep));
 52     dep[st]=1;
 53     q[1]=st;
 54     while (head<tail)
 55     {
 56         head++;
 57         d=q[head];
 58         p=e[d];
 59         while (p)
 60         {
 61             dd=p->d;
 62             if (!dep[dd] && p->len)
 63             {
 64                 q[++tail]=dd;
 65                 dep[dd]=dep[d]+1;
 66             }
 67             p=p->to;
 68         }
 69     }
 70     if (dep[en])
 71         return 1;
 72     return 0;
 73 }
 74 
 75 int dfs(int d,int add)
 76 {
 77     if (!add || d==en)
 78         return add;
 79     int totr=0,r,dd;
 80     node *p=e[d];
 81     while (p)
 82     {
 83         dd=p->d;
 84         if (dep[dd]==dep[d]+1 && (r=dfs(dd,min(add,p->len)))>0)
 85         {
 86             totr+=r;
 87             add-=r;
 88             p->len-=r;
 89             p->opp->len+=r;
 90         }
 91         p=p->to;
 92     }
 93     return totr;
 94 }
 95 
 96 int main()
 97 {
 98     int m,s,t,x,y,u,v,tot=0,sum=0,i;
 99     scanf("%d%d%d%d",&n,&m,&s,&t);
100     ss=0,tt=n+1;
101     for (i=1;i<=m;i++)
102     {
103         scanf("%d%d%d%d",&x,&y,&u,&v);
104         dif[x]-=u,dif[y]+=u;
105         addedge(x,y,v-u);
106     }
107     for (i=1;i<=n;i++)
108         if (dif[i]>0)
109         {
110             tot+=dif[i];
111             addedge(ss,i,dif[i]);
112         }
113         else
114             addedge(i,tt,-dif[i]);
115     addedge(t,s,inf);
116 
117     st=ss,en=tt;
118     while (bfs())
119         sum+=dfs(st,inf);
120     if (sum==tot)
121     {
122         sum=0;
123         st=s,en=t;
124         while (bfs())
125             sum+=dfs(st,inf);
126         printf("%d",sum);
127     }
128     else
129         printf("please go home to sleep");
130     return 0;
131 }
132 /*
133 
134 */

117

那个博客里解1的方法好像不对

dfs函数的两个优化，不知道是否真的有用。。。

95分，loj的第8个数据，dfs函数执行了很长时间。

看了一下其它代码，感觉是因为存储方式不一样，所以过了，感觉靠脸。。。

应该还有更好的优化方法，待学。

data 链接: https://pan.baidu.com/s/1BoxoTiTgYCaXcZcRisJz5Q 提取码: d3ip

  1 #include <cstdio>
  2 #include <cstdlib>
  3 #include <cmath>
  4 #include <cstring>
  5 #include <string>
  6 #include <algorithm>
  7 #include <set>
  8 #include <map>
  9 #include <queue>
 10 #include <iostream>
 11 using namespace std;
 12 
 13 #define ll long long
 14 
 15 const int maxn=50003+10;
 16 const int maxm=125003+10;
 17 const ll inf=1e18;
 18 const double eps=1e-8;
 19 
 20 struct node
 21 {
 22     int d;
 23     ll len;
 24     node *to,*opp;
 25 }*e[maxn];
 26 
 27 ll dif[maxn],z=0;
 28 int dep[maxn],q[maxn],n,ss,tt,st,en;
 29 
 30 void addedge(int x,int y,ll z)
 31 {
 32     node *p1,*p2;
 33     p1=new node();
 34     p2=new node();
 35 
 36     p1->d=y;
 37     p1->len=z;
 38     p1->to=e[x];
 39     p1->opp=p2;
 40     e[x]=p1;
 41 
 42     p2->d=x;
 43     p2->len=0;
 44     p2->to=e[y];
 45     p2->opp=p1;
 46     e[y]=p2;
 47 }
 48 
 49 bool bfs()
 50 {
 51     node *p;
 52     int head=0,tail=1,d,dd;
 53     memset(dep,0,sizeof(dep));
 54     dep[st]=1;
 55     q[1]=st;
 56     while (head<tail)
 57     {
 58         head++;
 59         d=q[head];
 60         p=e[d];
 61         while (p)
 62         {
 63             dd=p->d;
 64             if (!dep[dd] && p->len)
 65             {
 66                 q[++tail]=dd;
 67                 dep[dd]=dep[d]+1;
 68 //                if (dd==en)
 69 //                    return 1;
 70             }
 71             p=p->to;
 72         }
 73     }
 74 //    if (dep[en])
 75 //        return 1;
 76     return 0;
 77 }
 78 
 79 ll dfs(int d,ll add)
 80 {
 81     z++;
 82     if (!add || d==en)
 83         return add;
 84     int dd;
 85     ll totr=0,r;
 86     node *p=e[d];
 87     while (p)
 88     {
 89         dd=p->d;
 90         if (dep[dd]==dep[d]+1 && (r=dfs(dd,min(add,p->len)))>0)
 91         {
 92             totr+=r;
 93             add-=r;
 94             p->len-=r;
 95             p->opp->len+=r;
 96             if (totr==add)
 97                 return totr;
 98         }
 99         p=p->to;
100     }
101     if (!totr)
102         dep[d]=-1;
103     return totr;
104 }
105 
106 int main()
107 {
108     int m,s,t,x,y,i;
109     ll u,v;
110     ll tot=0,sum=0;
111     scanf("%d%d%d%d",&n,&m,&s,&t);
112     ss=0,tt=n+1;
113     for (i=1;i<=m;i++)
114     {
115         scanf("%d%d%lld%lld",&x,&y,&u,&v);
116         dif[x]-=u,dif[y]+=u;
117         addedge(x,y,v-u);
118     }
119     for (i=1;i<=n;i++)
120         if (dif[i]>0)
121         {
122             tot+=dif[i];
123             addedge(ss,i,dif[i]);
124         }
125         else
126             addedge(i,tt,-dif[i]);
127 
128     st=ss,en=tt;
129     while (bfs())
130         sum+=dfs(st,inf);
131 
132     addedge(t,s,inf);
133     while (bfs())
134         sum+=dfs(st,inf);
135 
136     printf("z=%lld
",z);
137 
138     if (sum==tot)
139         printf("%lld",e[s]->len);
140     else
141         printf("please go home to sleep");
142     return 0;
143 }
144 /*
145 
146 */

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原文地址：https://www.cnblogs.com/cmyg/p/10692584.html