【题解】Luogu P2868 [USACO07DEC] 观光奶牛 Sightseeing Cows 最优比率环

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 namespace gengyf{
 4 #define int long long
 5 #define eps 1e-5
 6 const int maxn=1100;
 7 inline int read(){
 8     int x=0,f=1;char s=getchar();
 9     while(s<'0'||s>'9'){if(s=='-')f=-1;s=getchar();}
10     while(s>='0'&&s<='9'){x=x*10+s-'0';s=getchar();}
11     return f*x;
12 }
13 int n,m;
14 struct edge{
15     int nxt,to,w;
16 }e[5010];
17 int head[maxn],cnt,fun[maxn],vis[maxn],num[maxn];
18 double d[maxn];
19 inline void add(int from,int to,int w){
20     e[++cnt].to=to;e[cnt].w=w;
21     e[cnt].nxt=head[from];head[from]=cnt;
22 }
23 bool check(double mid){
24     queue<int>q;
25     memset(d,0,sizeof(d));
26     for(int i=1;i<=n;i++){
27         q.push(i);vis[i]=num[i]=1;
28     }
29     while(!q.empty()){
30         int x=q.front();q.pop();
31         vis[x]=0;
32         for(int i=head[x];i;i=e[i].nxt){
33             int y=e[i].to;double dis=e[i].w;
34             if(d[y]>d[x]+mid*dis-(double)fun[x]){
35                 d[y]=d[x]+mid*dis-(double)fun[x];
36                 if(!vis[y]){
37                     q.push(y);vis[y]=1;
38                     if(++num[y]>=n)return 0;
39                 }
40             }
41         }
42     }
43     return 1;
44 }
45 int main(){
46     n=read();m=read();
47     for(int i=1;i<=n;i++){
48         fun[i]=read();
49     }
50     for(int i=1;i<=m;i++){
51         int u,v,w;
52         u=read();v=read();w=read();
53         add(u,v,w);
54     }
55     double l=0,r=maxn,mid;
56     while(r-l>eps){
57         mid=(l+r)/2;
58         if(check(mid))r=mid;
59         else l=mid;
60     }
61     printf("%.2lf",l);
62     return 0;
63 }
64 /*
65  accuse  指责
66  acknowledge  承认
67  accustomed  习惯的
68  acquaintance  熟人
69 */
70 }
71 signed main(){
72     gengyf::main();
73     return 0;
74 }