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USACO 4.2 Drainage Ditches(网络流模板题)

2024-09-01 08:02:31   217人阅读

Drainage Ditches
Hal Burch

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. Note however, that there can be more than one ditch between two intersections.

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.

PROGRAM NAME: ditch

INPUT FORMAT

Line 1: 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.
Line 2..N+1: Each of 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.

SAMPLE INPUT (file ditch.in)

5 4
1 2 40
1 4 20
2 4 20
2 3 30
3 4 10

OUTPUT FORMAT

One line with a single integer, the maximum rate at which water may emptied from the pond.

SAMPLE OUTPUT (file ditch.out)

50
————————————————————————————————————————————————
它有个俗名叫草地排水
 1 /*
 2 ID:ivorysi
 3 PROG:ditch
 4 LANG:C++
 5 */
 6 #include <iostream>
 7 #include <cstdio>
 8 #include <cstring>
 9 #include <queue>
10 #include <set>
11 #include <vector>
12 #define inf 0x7fffffff
13 #define ivorysi
14 #define siji(i,x,y) for(int i=x;i<=y;++i)
15 #define gongzi(j,x,y) for(int j=x;j>=y;--j)
16 #define xiaosiji(i,x,y) for(int i=x;i<y;++i)
17 #define sigongzi(j,x,y) for(int j=x;j>y;--j)
18 using namespace std;
19 struct node {
20     int to,next,val;
21 }edge[505];
22 int head[305],sum=1;
23 void add(int u,int v,int c) {
24     edge[++sum].to=v;
25     edge[sum].next=head[u];
26     edge[sum].val=c;
27     head[u]=sum;
28 }
29 void AddTwoWays(int u,int v,int c) {
30     add(u,v,c);
31     add(v,u,0);//反向边
32 }
33 int n,m,dis[305],gap[305],ans;
34 int sap(int u,int aug){//O（玄学）
35     if(u==m) return aug;
36     int dmin=m-1,flow=0,v,t;
37 
38     for(int i=head[u];i;i=edge[i].next) {
39         v=edge[i].to;
40         if(edge[i].val>0) {//只有还能流动的地方才能分层
41             if(dis[u]==dis[v]+1) {
42                 t=sap(v,min(aug-flow,edge[i].val));//限制流量不超过该点流量和边的限制
43                 edge[i].val-=t;
44                 edge[i^1].val+=t;
45                 flow+=t;
46                 if(aug==flow) return flow;//流尽
47                 if(dis[1]>=m) return flow;//搜索已在某处达到结束条件
48             }
49             dmin=min(dmin,dis[v]);
50         }
51     }
52     if(!flow) {
53         --gap[dis[u]];
54         if(gap[dis[u]]==0) dis[1]=m;//出现断层说明无法再流
55         dis[u]=dmin+1;//分层
56         ++gap[dis[u]];
57     }
58     return flow;
59 }
60 int main(int argc, char const *argv[])
61 {
62 #ifdef ivorysi
63     freopen("ditch.in","r",stdin);
64     freopen("ditch.out","w",stdout);
65 #else
66     freopen("f1.in","r",stdin);
67 #endif    
68     scanf("%d%d",&n,&m);
69     int u,v,c;
70     siji(i,1,n) {
71         scanf("%d%d%d",&u,&v,&c);
72         AddTwoWays(u,v,c);
73     }
74     while(dis[1]<m) {ans+=sap(1,inf);}
75     printf("%d\n",ans);
76     return 0;
77 }

 

 

USACO 4.2 Drainage Ditches(网络流模板题)


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