[HDU][3124][Moonmist][最近圆对问题(二分 + 扫描线)]

/*
题目：Moonmist
题目来源：HDU 3124 (2009 Asia Wuhan Regional Contest Online)
题目难度：中等偏难
题目内容或思路：
    最近圆对
    二分 + 扫描线
    一道很不错的题目，不过OJ上数据比较弱，一些有问题的代码也能AC
    解题报告：http://blog.sina.com.cn/s/blog_64675f540100o02x.html
做题日期：2011.3.12
*/
#include <cstdio>
#include <cstdlib>
#include <climits>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <string>
#include <queue>
#include <map>
#include <vector>
#include <bitset>
#include <cmath>
#include <set>
#include <utility>
#include <ctime>
#define sqr(x) ((x)*(x)) 
using namespace std;

const int N = 50010;
const double eps = 1e-8;
int n, lft[N], rht[N];
set<int> s;

struct circle {
    double x, y, r;
}cir[N];

int dcmp(double x) {
    if (x < -eps) return -1; else return x > eps;
}

double dis(circle a, circle b) {
    return sqrt(sqr(a.x - b.x) + sqr(a.y - b.y)) - a.r - b.r;
}

bool cmp(circle a, circle b) {
    return a.y < b.y;
}

bool cmp2(int i, int j) {
    return cir[i].x - cir[i].r < cir[j].x - cir[j].r;
}

bool cmp3(int i, int j) {
    return cir[i].x + cir[i].r < cir[j].x + cir[j].r;
}

bool inter(circle a, circle b, double delta) {
    return dcmp(dis(a, b) - delta * 2) < 0;
}

bool insert(int i, double mid) {
    set<int>::iterator it = s.insert(lft[i]).first;
    if (it != s.begin()) {
        if (inter(cir[*--it], cir[lft[i]], mid))
            return false;
        ++it;
    }
    if (++it != s.end() && inter(cir[*it], cir[lft[i]], mid))
        return false;
    return true;
}

bool remove(int j, double mid) {
    set<int>::iterator it = s.find(rht[j]);
    if (it != s.begin() && it != --s.end()) {
        int a = *--it;  ++it;
        int b = *++it;
        if (inter(cir[a], cir[b], mid))
            return false;
    }
    s.erase(rht[j]);
    return true;
}

bool check(double mid) {
    s.clear();
    for (int i = 0, j = 0; i < n || j < n;) {
        if (j == n) {
            if (!insert(i++, mid)) return false;
        } else if (i == n) {
            if (!remove(j++, mid)) return false;
        } else if (dcmp(cir[lft[i]].x - cir[lft[i]].r - mid
            - cir[rht[j]].x - cir[rht[j]].r - mid) <= 0) {
                if (!insert(i++, mid)) return false;
        } else {
            if (!remove(j++, mid)) return false;
        }
    }
    return true;
}

void solve() {
    scanf("%d", &n);
    for (int i = 0; i < n; ++i) {
        scanf("%lf%lf%lf", &cir[i].x, &cir[i].y, &cir[i].r);
        lft[i] = rht[i] = i;
    }
    sort(cir, cir + n, cmp);
    sort(lft, lft + n, cmp2);
    sort(rht, rht + n, cmp3);
    double mid, low = 0, high = dis(cir[0], cir[1]) / 2;
    while (dcmp(high - low)) {
        mid = (high + low) / 2;
        if (check(mid)) low = mid;
        else high = mid;
    }
    printf("%lf\n", low + high);
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("D:\\in.txt", "r", stdin);
#endif
    int cas;
    scanf("%d", &cas);
    while (cas--) {
        solve();
    }
    return 0;
}