AcWing 119 袭击 (平面最近点对)

题目链接：https://www.acwing.com/problem/content/121/

经典问题，平面最近点对，使用分治来解决
把所有点按横坐标排序，分治求解距离
合并时将两边的最近点对距离也比较一下

属于不同集合的点比较距离时判断一下即可

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<cmath>
#include<stack>
#include<queue>
using namespace std;
typedef long long ll;

const int maxn = 200010;
const double INF = 2 << 28;

int T, n, tot;

struct Point{
	double x, y;
}p[maxn], tmp[maxn];

bool cmp(Point a, Point b){
	return a.x < b.x;
}

double calc(Point a, Point b){
	double X = (a.x - b.x);
	double Y = (a.y - b.y);
	return sqrt(X * X + Y * Y);
}

double Merge(int L, int R){
	double dis = INF;
	if(L == R){
		return dis;
	}
	if(L + 1 == R){
		return calc(p[L], p[R]);
	}
	int mid = (L + R) >> 1;
	double d1 = Merge(L, mid);
	double d2 = Merge(mid + 1, R);
	dis = min(d1, d2);
	
	int cnt = 0;
	for(int i=L; i <= R; ++i){
		if(fabs(p[i].x - p[mid].x) < dis){
			tmp[++cnt] = p[i];
		}
	}
	
	sort(tmp + 1, tmp + 1 + cnt, cmp);
	
	for(int i = 1;i <= cnt; ++i){
		for(int j = 1;j < i; ++j){
			dis = min(dis, calc(tmp[i], tmp[j]));
		}
	}
	return dis;
}

ll read(){ ll s=0,f=1; char ch=getchar(); while(ch<'0' || ch>'9'){ if(ch=='-') f=-1; ch=getchar(); } while(ch>='0' && ch<='9'){ s=s*10+ch-'0'; ch=getchar(); } return s*f; }

int main(){
		n = read(); tot = 0;
		for(int i=1;i<=n;++i){
			++tot;
			scanf("%lf %lf",&p[tot].x, &p[tot].y);
		}
		
		sort(p + 1, p + 1 + tot, cmp);
		
		printf("%.4lf\n",Merge(1,tot));
	return 0;
}