最近点对算法模板

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#include<algorithm> using namespace std; #define maxs 200005 struct Point {     double x,y; }point[maxs]; int y_sort[maxs]; int cmpx(Point a,Point b)//按照x对这些点从小到大排序 {     return a.x<b.x; } int cmpy(int a,int b)//对最近点算法中的y_sort数组排序 {     return point[a].y<point[b].y; } double dis(Point a,Point b) {     return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y)); } /*     最近点对算法,在point[first]--point[last]个点中寻找一个最短距离     使用该算法前先对这些点排序     sort(point,point+n,cmpx); */ double findMin(int first, int last) {     if((last-first)==1)         return dis(point[first],point[last]);     else if(last-first==2)     {         double d1 = dis(point[first],point[first+1]);         double d2 = dis(point[first],point[first+2]);         double d3 = dis(point[first+1],point[first+2]);         return min(min(d1,d2),d3);     }     //二分     int mid = (first+last)/2;     double min_dist = min(findMin(first,mid),findMin(mid+1,last));     if(min_dist==0)         return 0;     int y_end = 0;     for(int i=mid;point[mid].x-point[i].x<min_dist&&i>=first;i--)         y_sort[y_end++]=i;     for(int i=mid+1;point[i].x-point[mid+1].x<min_dist&&i<=last;i++)         y_sort[y_end++]=i;     sort(y_sort,y_sort+y_end,cmpy);     for(int i=0;i<y_end;i++)         for(int j=i+1;j<y_end&&(point[y_sort[j]].y-point[y_sort[i]].y)<min_dist;j++)             min_dist=min(min_dist,dis(point[y_sort[i]],point[y_sort[j]]));     return min_dist;   }

 

 

poj3714

题目大意：

有若干车站和加油站，求车站和加油站的最小距离.

思路：

求最近点对,注意的是需要对车站和加油站分类，同类的话就初始化为INF

这样就不会找到相同类间的距离了,从而只会得到车站和加油站的最小距离

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#include <iostream> #include<cstdio> #include<cmath> #include<algorithm> using namespace std; #define maxs 200005 #define INF 1e100 struct Point {     double x,y;     bool flag; }point[maxs]; int y_sort[maxs]; int cmpx(Point a,Point b)//按照x对这些点从小到大排序 {     return a.x<b.x; } int cmpy(int a,int b)//对最近点算法中的y_sort数组排序 {     return point[a].y<point[b].y; } double dis(Point a,Point b) {     if(a.flag!=b.flag)         return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));     return INF;//是同一类，初始化为无穷大,这样最近点对算法就不会找同类的最短距离 } /*     最近点对算法,在point[first]--point[last]个点中寻找一个最短距离     使用该算法前先对这些点排序     sort(point,point+n,cmpx); */ double findMin(int first, int last) {     if((last-first)==1)         return dis(point[first],point[last]);     else if(last-first==2)     {         double d1 = dis(point[first],point[first+1]);         double d2 = dis(point[first],point[first+2]);         double d3 = dis(point[first+1],point[first+2]);         return min(min(d1,d2),d3);     }     //二分     int mid = (first+last)/2;     double min_dist = min(findMin(first,mid),findMin(mid+1,last));     if(min_dist==0)         return 0;     int y_end = 0;     for(int i=mid;point[mid].x-point[i].x<min_dist&&i>=first;i--)         y_sort[y_end++]=i;     for(int i=mid+1;point[i].x-point[mid+1].x<min_dist&&i<=last;i++)         y_sort[y_end++]=i;     sort(y_sort,y_sort+y_end,cmpy);     for(int i=0;i<y_end;i++)         for(int j=i+1;j<y_end&&(point[y_sort[j]].y-point[y_sort[i]].y)<min_dist;j++)             min_dist=min(min_dist,dis(point[y_sort[i]],point[y_sort[j]]));     return min_dist;   } int main() {     //freopen("in.txt","r",stdin);     int T,n;     cin>>T;     while(T--)     {         scanf("%d",&n);         for(int i=0;i<n;i++)         {             scanf("%lf%lf",&point[i].x,&point[i].y);             point[i].flag=true;         }         for(int i=n;i<2*n;i++)         {             scanf("%lf%lf",&point[i].x,&point[i].y);             point[i].flag=false;         }         n=2*n;         sort(point,point+n,cmpx);//排序         double ans = findMin(0,n-1);         printf("%0.3f\n",ans);     }     return 0; }