poj 3714 raid

摘要: 平面最近点对

二分的思想
区域按x从大到小等分成两块s1,s2
最小距离点对的两个点有三种情况,都在s1;都在s2;一个在s1,一个在s2
都在同一区域的则递归地找
当左边界等于右边界,即只有一个点,返回inf
只有两个点,直接返回距离
比较两区域最小值大小,取小者为md

不在同一区域,则将距分界线x向距离md以内的点找出
并按y大小排序
对这些点,依次与其后6个点求距离,更新md(至于这里为什么是对其后6个点求距离就够了,需要额外证明,这里略去,这里对y向距离小于md的求距离也一样的)

Raid

Time Limit: 5000MS		Memory Limit: 65536K
Total Submissions: 7877		Accepted: 2353

Description

After successive failures in the battles against the Union, the Empire retreated to its last stronghold. Depending on its powerful defense system, the Empire repelled the six waves of Union's attack. After several sleepless nights of thinking, Arthur, General of the Union, noticed that the only weakness of the defense system was its energy supply. The system was charged by N nuclear power stations and breaking down any of them would disable the system.

The general soon started a raid to the stations by N special agents who were paradroped into the stronghold. Unfortunately they failed to land at the expected positions due to the attack by the Empire Air Force. As an experienced general, Arthur soon realized that he needed to rearrange the plan. The first thing he wants to know now is that which agent is the nearest to any power station. Could you, the chief officer, help the general to calculate the minimum distance between an agent and a station?

Input

The first line is a integer T representing the number of test cases.
Each test case begins with an integer N (1 ≤ N ≤ 100000).
The next N lines describe the positions of the stations. Each line consists of two integers X (0 ≤ X ≤ 1000000000) and Y (0 ≤ Y ≤ 1000000000) indicating the positions of the station.
The next following N lines describe the positions of the agents. Each line consists of two integers X (0 ≤ X ≤ 1000000000) and Y (0 ≤ Y ≤ 1000000000) indicating the positions of the agent. 　

Output

For each test case output the minimum distance with precision of three decimal placed in a separate line.

Sample Input

2
4
0 0
0 1
1 0
1 1
2 2
2 3
3 2
3 3
4
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0

Sample Output

1.414
0.000

Source

POJ Founder Monthly Contest – 2008.12.28, Dagger

/*=============================================================================
#     FileName: min_dist.cpp
#         Desc: poj 3714
#       Author: zhuting
#        Email: cnjs.zhuting@gmail.com
#     HomePage: my.oschina.net/locusxt
#      Version: 0.0.1
#    CreatTime: 2013-12-02 19:01:32
#   LastChange: 2013-12-02 21:06:34
#      History: 补注释
=============================================================================*/

/*
* 据说直接用int记点是过不了的
* 所以用double或者long long
*/
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#define maxn 200005
using namespace std;

const double inf = 1e100;

class point
{
public:
double x;
double y;
bool flag;/*标志阵营*/
};
point poi[maxn];

int ordy[maxn] = {0};/*按y的顺序排序,一开始数组开在里面,一直re= =*/

bool cmpx(point a, point b)/*点按x排序*/
{
return a.x < b.x;
}

bool cmpy(int a, int b)
{
return poi[a].y < poi[b].y;
}

double dist(int a, int b)/*计算两点距离,当属于同阵营则距离无限大*/
{
if (poi[a].flag == poi[b].flag)
return inf;

double ax = poi[a].x;
double ay = poi[a].y;
double bx = poi[b].x;
double by = poi[b].y;
return sqrt((ax - bx) * (ax - bx) + (ay - by) * (ay - by));
}

/*
* 二分的思想
* 区域按x从大到小等分成两块s1,s2
* 最小距离点对的两个点有三种情况,都在s1;都在s2;一个在s1,一个在s2
* 都在同一区域的则递归地找
* 当左边界等于右边界,即只有一个点,返回inf
* 只有两个点,直接返回距离
* 比较两区域最小值大小,取小者为md
*
* 不在同一区域,则将距分界线x向距离md以内的点找出
* 并按y大小排序
* 对这些点,依次与其后6个点求距离,更新md(至于这里为什么是对其后6个点求距离就够了,需要额外证明,这里略去,这里对y向距离小于md的求距离也一样的)
*
* 最后返回md
*/

double min_dist(point* p, int left, int right)
{
double md = inf;
if (left == right)
return md;
if (left + 1 == right)
return dist(left, right);
int mid = (left + right) >> 1;
double l_md = min_dist(p, left, mid);
double r_md = min_dist(p, mid + 1, right);
if (l_md < r_md) md = l_md;
else md = r_md;

int cur = 0;

for (int i = mid; i >= left; --i)
{
if (p[mid].x - p[i].x <= md)
ordy[cur++] = i;
else break;
}
for (int i = mid + 1; i <= right; ++i)
{
if (p[i].x - p[mid].x <= md)
ordy[cur++] = i;
else break;
}

sort(ordy, ordy + cur, cmpy);
for (int i = 0; i < cur; ++i)
for (int j = i + 1; j <= i + 6; ++j)
{
if (j >= cur) break;
if (p[ordy[j]].y - p[ordy[i]].y >= md)
break;
double tmp = dist(ordy[i], ordy[j]);
if (tmp < md)
md =tmp;
}
return md;
}

int main()
{
int t = 0, n = 0;
scanf("%d", &t);
while(t--)
{
scanf("%d", &n);
for (int i = 0; i < n; ++i)
{
scanf ("%lf%lf", &poi[i].x, &poi[i].y);
poi[i].flag = 1;
}
for (int i = n; i < 2 * n ; ++i)
{
scanf ("%lf%lf", &poi[i].x, &poi[i].y);
poi[i].flag = 0;
}

sort(poi, poi + 2 * n, cmpx);
double ans = min_dist(poi, 0, 2 * n - 1);

printf("%.3lf\n", ans);

}
return 0;
}