乱搞/分治最短路线段树Day 10.24

Posted 2020-10-11

1、斜率

可以证明如果两点之间还有一点的话那么原来的两个点连线一定不会是最大斜率

然后我就写了个沙茶分治…………

其实根据上面的推论只用枚举相邻的两个点，扫一遍就可以了

 1 #include <cstdio>
 2 #include <algorithm>
 3 #include <iostream>
 4 using namespace std;
 5 typedef pair<int,int> P;
 6 int n,a,b;
 7 P p[500001];
 8 double ans;
 9 void solve(int l,int r)
10 {
11     if (l>=r) return;
12     int mid=(l+r)/2;
13     for (int i=l;i<=r;i++) if (i!=mid)
14     {
15         ans=max(ans,double(p[mid].second-p[i].second)/(p[mid].first-p[i].first));
16     }
17     solve(l,mid-1);solve(mid+1,r);
18 }
19 int main()
20 {
21     freopen("slope.in","r",stdin);
22     freopen("slope.out","w",stdout); 
23     scanf("%d",&n);
24     for (int i=1;i<=n;i++)
25     {
26         scanf("%d%d",&a,&b);
27         p[i]=P(a,b);
28     }
29     sort(p+1,p+n+1);
30     ans=double(p[2].second-p[1].second)/(p[2].first-p[1].first); 
31     solve(1,n);
32     printf("%.3f",ans);
33 } 

 

2、最优路径

这不就是原来做的过路费吗……

 1 #include <cstdio>
 2 #include <iostream>
 3 #include <queue>
 4 #include <cstring>
 5 #define ll long long
 6 using namespace std;
 7 typedef pair<int,int> P;
 8 struct E{
 9     int next,to,w;
10 }e[250001];
11 priority_queue<P,vector<P>,greater<P> > que;
12 int n,m,a,b,c,sz=0,head[501],v[501],reg[501],f[501];
13 ll w[501][501];
14 void insert(int a,int b,int w)
15 {
16     sz++;
17     e[sz].next=head[a];
18     head[a]=sz;
19     e[sz].to=b;
20     e[sz].w=w;
21 }
22 void dijkstra(int s)
23 {
24     memset(reg,0,sizeof(reg));
25     memset(f,0x7f,sizeof(f));
26     f[s]=1;
27     que.push(P(0,s));
28     while(!que.empty())
29     {
30         int x=que.top().second;que.pop();
31         if (reg[x]) continue;
32         reg[x]=1;
33         for (int i=head[x];i;i=e[i].next)
34         {
35             if (v[e[i].to]<=v[s]&&f[e[i].to]>max(f[x],e[i].w))
36             {
37                 f[e[i].to]=max(f[x],e[i].w);
38                 que.push(P(f[e[i].to],e[i].to));
39             }
40         }
41     }
42     for (int i=1;i<=n;i++)
43         for (int j=1;j<=n;j++)
44             if (reg[i]&&reg[j]) w[i][j]=min(w[i][j],(ll)max(f[i],f[j])*v[s]);
45 }
46 int main()
47 {
48     freopen("path.in","r",stdin);
49     freopen("path.out","w",stdout);
50     ios::sync_with_stdio(false); 
51     memset(w,0x7f,sizeof(w));
52     cin>>n>>m;
53     for (int i=1;i<=n;i++) cin>>v[i];
54     for (int i=1;i<=m;i++)
55     {
56         cin>>a>>b>>c; 
57         insert(a,b,c);insert(b,a,c);
58     }
59     for (int i=1;i<=n;i++) dijkstra(i);
60     for (int i=1;i<=n;i++)
61     {
62         for (int j=1;j<=n;j++)
63         {
64             if (i==j){
65                 cout<<0<<" ";
66             }else{
67                 if (w[i][j]==w[0][0])
68                     cout<<-1<<" ";
69                 else
70                     cout<<w[i][j]<<" ";
71             }
72         }
73         cout<<endl;
74     }
75 } 

3、小G的线段树