BZOJ 1690
假设求出∑a/∑b>L
L∑b-∑a<0 => ∑(Lb-a)<0即可说明有比L优的解
可以二分L，∑(Lb-a)<0可以通过Dfs_Spfa找负环
1 #include <cstdio> 2 #include <cstring> 3 using namespace std; 4 const int Maxn=2010; 5 const double eps=1e-3; 6 struct EDGE 7 { 8 int next,to,t; 9 double w; 10 }edge[Maxn<<3]; 11 int head[Maxn],m,n,f[Maxn],u,v,w,cnt; 12 double dis[Maxn]; 13 bool flag,vis[Maxn]; 14 inline void Add(int u,int v,int t) 15 {edge[cnt].next=head[u];edge[cnt].to=v;edge[cnt].t=t;head[u]=cnt++;} 16 void Build(double p) 17 { 18 for (int i=1;i<=n;i++) 19 for (int j=head[i];j!=-1;j=edge[j].next) 20 edge[j].w=(double)(edge[j].t)*p-(double)f[edge[j].to]; 21 } 22 void Spfa(int u) 23 { 24 vis[u]=true; 25 for (int i=head[u];i!=-1;i=edge[i].next) 26 if (dis[edge[i].to]>dis[u]+edge[i].w) 27 { 28 if (vis[edge[i].to]) {flag=true; return;} 29 dis[edge[i].to]=dis[u]+edge[i].w; 30 Spfa(edge[i].to); 31 } 32 vis[u]=false; 33 } 34 inline bool Check() 35 { 36 memset(vis,false,sizeof(vis)); 37 memset(dis,0,sizeof(dis)); 38 flag=false; 39 for (int i=1;i<=n;i++) 40 { 41 Spfa(i); if (flag) return true; 42 } 43 return false; 44 } 45 int main() 46 { 47 scanf("%d%d",&n,&m); 48 for (int i=1;i<=n;i++) scanf("%d",&f[i]); 49 memset(head,-1,sizeof(head)); 50 for (int i=1;i<=m;i++) 51 { 52 scanf("%d%d%d",&u,&v,&w); 53 Add(u,v,w); 54 } 55 double l=0,r=10000; 56 while (r-l>eps) 57 { 58 double mid=(l+r)/2; 59 Build(mid); 60 if (Check()) l=mid; else r=mid; 61 } 62 printf("%.2lf",l); 63 return 0; 64 }
BZOJ 1486
同理可得
1 #include <cstdio> 2 #include <cstring> 3 using namespace std; 4 const int Maxn=10010; 5 const double eps=1e-9; 6 struct EDGE 7 { 8 int next,to,t; 9 double w; 10 }edge[Maxn<<3]; 11 int head[Maxn],m,n,u,v,w,cnt; 12 double dis[Maxn]; 13 bool flag,vis[Maxn]; 14 inline void Add(int u,int v,int t) 15 {edge[cnt].next=head[u];edge[cnt].to=v;edge[cnt].t=t;head[u]=cnt++;} 16 void Build(double p) 17 { 18 for (int i=1;i<=n;i++) 19 for (int j=head[i];j!=-1;j=edge[j].next) 20 edge[j].w=(double)edge[j].t-p; 21 } 22 void Spfa(int u) 23 { 24 vis[u]=true; 25 for (int i=head[u];i!=-1;i=edge[i].next) 26 if (dis[edge[i].to]>dis[u]+edge[i].w) 27 { 28 if (vis[edge[i].to]) {flag=true; return;} 29 dis[edge[i].to]=dis[u]+edge[i].w; 30 Spfa(edge[i].to); 31 } 32 vis[u]=false; 33 } 34 inline bool Check() 35 { 36 memset(vis,false,sizeof(vis)); 37 memset(dis,0,sizeof(dis)); 38 flag=false; 39 for (int i=1;i<=n;i++) 40 { 41 Spfa(i); if (flag) return true; 42 } 43 return false; 44 } 45 int main() 46 { 47 48 scanf("%d%d",&n,&m); 49 memset(head,-1,sizeof(head)); 50 for (int i=1;i<=m;i++) 51 { 52 scanf("%d%d%d",&u,&v,&w); 53 Add(u,v,w); 54 } 55 double l=-10000000,r=10000000; 56 while (r-l>eps) 57 { 58 double mid=(l+r)/2; 59 Build(mid); 60 if (Check()) r=mid;else l=mid; 61 } 62 printf("%.8lf ",l); 63 return 0; 64 }