POJ 1273 Drainage Ditches

Drainage Ditches

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 52160		Accepted: 19830

Description

Every time it rains on Farmer John's fields, a pond forms over Bessie's favorite clover patch. This means that the clover is covered by water for awhile and takes quite a long time to regrow. Thus, Farmer John has built a set of drainage ditches so that Bessie's clover patch is never covered in water. Instead, the water is drained to a nearby stream. Being an ace engineer, Farmer John has also installed regulators at the beginning of each ditch, so he can control at what rate water flows into that ditch.
Farmer John knows not only how many gallons of water each ditch can transport per minute but also the exact layout of the ditches, which feed out of the pond and into each other and stream in a potentially complex network.
Given all this information, determine the maximum rate at which water can be transported out of the pond and into the stream. For any given ditch, water flows in only one direction, but there might be a way that water can flow in a circle.

Input

The input includes several cases. For each case, the first line contains two space-separated integers, N (0 <= N <= 200) and M (2 <= M <= 200). N is the number of ditches that Farmer John has dug. M is the number of intersections points for those ditches. Intersection 1 is the pond. Intersection point M is the stream. Each of the following N lines contains three integers, Si, Ei, and Ci. Si and Ei (1 <= Si, Ei <= M) designate the intersections between which this ditch flows. Water will flow through this ditch from Si to Ei. Ci (0 <= Ci <= 10,000,000) is the maximum rate at which water will flow through the ditch.

Output

For each case, output a single integer, the maximum rate at which water may emptied from the pond.

Sample Input

Sample Output

Source

USACO 93

最基本的网络流问题，今天学习了一下网络流，就先写了这道，直接套Ford-Fulkerson算法模板即可

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<vector>
 4 #include<cstring>
 5 #include<algorithm>
 6 #define INF 0x7fffffff
 7 #define MAX_V 210
 8 
 9 using namespace std;
10 
11 struct edge
12 {
13     int to;
14     int cap;
15     int rev;
16 };
17 
18 int m,n;
19 bool used[MAX_V];
20 vector<edge> G[MAX_V];
21 
22 void add_edge(int _from,int _to,int _cap)
23 {
24     edge temp;
25     temp.to=_to;
26     temp.cap=_cap;
27     temp.rev=G[_to].size();
28     G[_from].push_back(temp);
29     temp.to=_from;
30     temp.cap=0;
31     temp.rev=G[_from].size()-1;
32     G[_to].push_back(temp);
33 }
34 
35 int dfs(int v,int t,int f)
36 {
37     if(v==t)
38         return f;
39 
40     used[v]=true;
41     for(int i=0;i<G[v].size();i++)
42     {
43         edge &e=G[v][i];
44         if(!used[e.to]&&e.cap>0)
45         {
46             int d=dfs(e.to,t,min(f,e.cap));
47             if(d>0)
48             {
49                 e.cap-=d;
50                 G[e.to][e.rev].cap+=d;
51                 return d;
52             }
53         }
54     }
55 
56     return 0;
57 }
58 
59 int max_flow(int s,int t)
60 {
61     int flow=0;
62     while(true)
63     {
64         memset(used,false,sizeof(used));
65         int f=dfs(s,t,INF);
66         if(f==0)
67             return flow;
68         flow+=f;
69     }
70 }
71 
72 int main()
73 {
74     while(scanf("%d %d",&n,&m)==2)
75     {
76         for(int i=1;i<=m;i++)
77             G[i].clear();
78 
79         int s,e,c;
80         for(int i=1;i<=n;i++)
81         {
82             scanf("%d %d %d",&s,&e,&c);
83             add_edge(s,e,c);
84         }
85         printf("%d
",max_flow(1,m));
86     }
87 
88     return 0;
89 }

[C++]

下面是用Dinic算法模板写的，与上面的相比速度要快一点

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<vector>
  4 #include<cstring>
  5 #include<algorithm>
  6 #include<queue>
  7 #define INF 0x7fffffff
  8 #define MAX_V 210
  9 
 10 using namespace std;
 11 
 12 struct edge
 13 {
 14     int to;
 15     int cap;
 16     int rev;
 17 };
 18 
 19 int m,n;
 20 int iter[MAX_V];
 21 int level[MAX_V];
 22 vector<edge> G[MAX_V];
 23 
 24 void add_edge(int _from,int _to,int _cap)
 25 {
 26     edge temp;
 27     temp.to=_to;
 28     temp.cap=_cap;
 29     temp.rev=G[_to].size();
 30     G[_from].push_back(temp);
 31     temp.to=_from;
 32     temp.cap=0;
 33     temp.rev=G[_from].size()-1;
 34     G[_to].push_back(temp);
 35 }
 36 
 37 void bfs(int s)
 38 {
 39     memset(level,-1,sizeof(level));
 40     queue<int> que;
 41     level[s]=0;
 42     que.push(s);
 43     while(!que.empty())
 44     {
 45         int v=que.front();
 46         que.pop();
 47         for(int i=0;i<G[v].size();i++)
 48         {
 49             edge &e=G[v][i];
 50             if(e.cap>0&&level[e.to]<0)
 51             {
 52                 level[e.to]=level[v]+1;
 53                 que.push(e.to);
 54             }
 55         }
 56     }
 57 }
 58 
 59 int dfs(int v,int t,int f)
 60 {
 61     if(v==t)
 62         return f;
 63 
 64     for(int &i=iter[v];i<G[v].size();i++)
 65     {
 66         edge &e=G[v][i];
 67         if(e.cap>0&&level[v]<level[e.to])
 68         {
 69             int d=dfs(e.to,t,min(f,e.cap));
 70             if(d>0)
 71             {
 72                 e.cap-=d;
 73                 G[e.to][e.rev].cap+=d;
 74                 return d;
 75             }
 76         }
 77     }
 78 
 79     return 0;
 80 }
 81 
 82 
 83 int max_flow(int s,int t)
 84 {
 85     int flow=0;
 86 
 87     while(true)
 88     {
 89         bfs(s);
 90         if(level[t]<0)
 91             return flow;
 92         memset(iter,0,sizeof(iter));
 93         int f;
 94         while((f=dfs(s,t,INF))>0)
 95             flow+=f;
 96     }
 97 }
 98 
 99 
100 int main()
101 {
102     while(scanf("%d %d",&n,&m)==2)
103     {
104         for(int i=1;i<=m;i++)
105             G[i].clear();
106 
107         int s,e,c;
108         for(int i=1;i<=n;i++)
109         {
110             scanf("%d %d %d",&s,&e,&c);
111             add_edge(s,e,c);
112         }
113         printf("%d
",max_flow(1,m));
114     }
115 
116     return 0;
117 }

[C++]