正题

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题目大意

有n个点，给出坐标，选择所有距离在k之内的边要求联通所有点，求最小的k。

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解题思路

垃圾解法

用二分答案然后加并查集求是否联通。
时间复杂度：$O(mlogn)$

正解

按距离排序，然后连边到所有岛都联通为止。
时间复杂度：$O(mlogm)$

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垃圾解法的代码

#include<cstdio>
#include<algorithm>
#include<cmath>
using namespace std;
struct node{int from,to;double w;
}a[1000001];
int n,dx[1001],dy[1001],dr[1001],father[1001],s,tot;
double dis(double x1,double y1,double x2,double y2)
{return sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
}//求距离
bool cmp(node xxx,node yxx)//排序
{return xxx.w<yxx.w;}
int find(int x)//并查集
{return father[x]==x?x:father[x]=find(father[x]);}
void unionn(int x,int y)//并查集
{int fa=find(x),fb=find(y);if (fa==fb) return;else{if (fa<fb) father[fb]=fa;else father[fa]=fb;s--;}
}
bool check(double ll){//判断可否联通for (int i=1;i<=n;i++)father[i]=i;s=n;for (int i=1;i<=tot;i++)if(ll<a[i].w) return false;else{unionn(a[i].from,a[i].to);if (s==1) return true;}return false;
}
int main()
{scanf("%d",&n);for (int i=1;i<=n;i++)scanf("%d%d%d",&dx[i],&dy[i],&dr[i]);for (int i=1;i<n;i++)for (int j=i+1;j<=n;j++){a[++tot].from=i;a[tot].to=j;double lw=dis(dx[i],dy[i],dx[j],dy[j])-dr[i]-dr[j];a[tot].w=lw;if (a[tot].w<0) a[tot].w=0;//输入}sort(a+1,a+1+tot,cmp);int l=1,r=2000,mid;while (l<=r)//二分{mid=(l+r)/2;if (check((double)mid)) r=mid-1;else l=mid+1;}printf("%d",l);
}

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对拍

数据生成

#include<cstdio>
#include<cstdlib>
#include<ctime>
#define random(x) rand()*rand()%x+1
using namespace std;
int n,m;
int main()
{freopen("air.in","w",stdout);srand((unsigned)time(0));n=random(1000);//n=1000;printf("%d\n",n);for (int i=1;i<=n;i++){printf("%d %d %d\n",random(1000),random(1000),random(5));}
}

判断加对拍

#include<cstdio>
#include<cstdlib>
#include<ctime>
#include<cmath>
using namespace std;
int n,dx[1001],dy[1001],dr[1001],father[1001],s,l;
bool ok;
double dis(double x1,double y1,double x2,double y2)
{return sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
}
int find(int x)
{return father[x]==x?x:father[x]=find(father[x]);}
void unionn(int x,int y)
{int fa=find(x),fb=find(y);if (fa==fb) return;else{if (fa<fb) father[fb]=fa;else father[fa]=fb;s--;}
}
int main()
{for (int ti=1;ti<=10000;ti++){system("airdata.exe");double st=clock();system("air.exe");double ed=clock();if (ed-st>1000){printf("TLE");break;}freopen("air.in","r",stdin);scanf("%d",&n);for (int i=1;i<=n;i++)scanf("%d%d%d",&dx[i],&dy[i],&dr[i]);fclose(stdin);freopen("air.out","r",stdin);scanf("%d",&l);s=n;ok=false;for (int i=1;i<=n;i++)father[i]=i;for (int i=1;i<=n;i++){for (int j=1;j<=n;j++){double lw=dis(dx[i],dy[i],dx[j],dy[j])-dr[i]-dr[j];if (lw<=l){unionn(i,j);}if (s==1) ok=true;}if (s==1) ok=true;}if (s!=1){printf("WA");break;}fclose(stdin);printf("AC point:%d time:0.%0.lf\n",ti,ed-st);}
}