2018.11.06-知识回顾

1.最小圆覆盖

#include<bits/stdc++.h>
#define il inline
#define D double
#define _(d) while(d(isdigit(ch=getchar())))
using namespace std;
const int N=5e5+5;struct node{D x,y;}a[N],o;D r;int n;
il int read(){int x,f=1;char ch;_(!)ch=='-'?f=-1:f;x=ch-48;_()x=x*10+ch-48;return f*x;}
il D dis(node a,node b){return sqrt((a.y-b.y)*(a.y-b.y)+(a.x-b.x)*(a.x-b.x));}
il void makecir(node a,node b,node c){
    D x1,y1,c1,x2,y2,c2;
    x1=2*(b.x-a.x);y1=2*(b.y-a.y);
    c1=b.x*b.x+b.y*b.y-a.x*a.x-a.y*a.y;
    x2=2*(c.x-a.x);y2=2*(c.y-a.y);
    c2=c.x*c.x+c.y*c.y-a.x*a.x-a.y*a.y;
    o.x=(y1*c2-y2*c1)/(y1*x2-y2*x1);
    o.y=(x2*c1-x1*c2)/(y1*x2-y2*x1);
    r=dis(o,a);
}
int main()
{
    n=read();for(int i=1;i<=n;i++)scanf("%lf%lf",&a[i].x,&a[i].y);
    random_shuffle(a+1,a+n+1);o=a[1];r=0;
    for(int i=2;i<=n;i++)if(dis(o,a[i])>r){
        o=a[i];r=0;
        for(int j=1;j<=i-1;j++)if(dis(o,a[j])>r){
            o.x=(a[i].x+a[j].x)/2.0;
            o.y=(a[i].y+a[j].y)/2.0;
            r=dis(o,a[j]);
            for(int k=1;k<=j-1;k++)if(dis(o,a[k])>r)makecir(a[i],a[j],a[k]);
        }
    }
    printf("%.10lf\n%.10lf %.10lf\n",r,o.x,o.y);
  return 0;
}

2.网络流

（小M的作物）

#include<bits/stdc++.h>
#define _(d) while(d(isdigit(ch=getchar())))
#define il inline
using namespace std;
const int N=3005,M=5e6+5,inf=2e9;int a[N],b[N],n,m,s,t,head[N],cnt=1,k[N],ans,res,d[N],ne[M],to[M],v[M];queue<int> q;
il int read(){int x,f=1;char ch;_(!)ch=='-'?f=-1:f;x=ch-48;_()x=x*10+ch-48;return f*x;}
il void insert(int x,int y,int z){ne[++cnt]=head[x];head[x]=cnt;to[cnt]=y;v[cnt]=z;}
il void add(int u,int v,int w){insert(u,v,w);insert(v,u,0);}
il bool bfs(){
    memset(d,-1,sizeof(d));q.push(s);d[s]=1;
    while(!q.empty()){
        int x=q.front();q.pop();
        for(int i=head[x];i;i=ne[i]){
            if(!v[i]||d[to[i]]!=-1)continue;
            q.push(to[i]);d[to[i]]=d[x]+1;
        }
    }
    return d[t]!=-1;
}
int dfs(int x,int f){
    if(x==t)return f;int w,used=0;
    for(int i=head[x];i;i=ne[i]){
        if(d[x]+1!=d[to[i]]||(!v[i]))continue;
        w=f-used;w=dfs(to[i],min(w,v[i]));
        v[i]-=w;v[i^1]+=w;used+=w;if(used==f)return used;
    }
    if(!used)d[x]=-1;return used;
}
il void dinic(){while(bfs()){res+=dfs(s,inf);}}
int main()
{
  n=read();for(int i=1;i<=n;i++)a[i]=read(),ans+=a[i];
    for(int i=1;i<=n;i++)b[i]=read(),ans+=b[i];m=read();t=n+2*m+1;
  for(int i=1;i<=n;i++)add(s,i,a[i]),add(i,t,b[i]);
  for(int i=1;i<=m;i++){
    int kk=read();int c1=read(),c2=read();ans+=c1+c2;add(s,n+i,c1);add(n+m+i,t,c2);
        for(int j=1;j<=kk;j++){int k=read();add(n+i,k,inf);add(k,n+m+i,inf);}
    }
    dinic();printf("%d\n",ans-res);
  return 0;
}

 3.STL牛逼

nth_element(a+1,a+1+m,a+n+1,greater<int>());

取出前m大的数字（前m大内是乱序）期望效率O(n)牛逼！！

 4.爬树缩点

il void work(int x,int y,int z){
    x=getf(x);y=getf(y);
    while(x^y){
        if(d[x]<d[y])swap(x,y);
        res[x]=z;x=f[x]=getf(fa[x]);
    }
}//f[]是并查集的爸爸，fa[]是原树上爸爸