ZOJ 3203 Light Bulb 三分

最简单的三分题，期末考完先做一道练练手

就是这么一个图，告诉你H h D，问你L最长是多少，假设人到灯的距离是X，那么容易得到

L = H-D/x*(H-h)+D-x,求个导很容易发现是一个关于x 的凸性函数，就可以三分啦

要注意的是三分的时候的精度eps，这题要求得是1e-9才能A，1e-8都WA，真是囧

#include <cstdio>
#include <sstream>
#include <fstream>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <map>
#include <cctype>
#include <ctime>
#include <set>
#include <climits>
#include <vector>
#include <queue>
#include <stack>
#include <cstdlib>
#include <cmath>
#include <string>
#include <list>

#define INPUT_FILE "in.txt"
#define OUTPUT_FILE "out.txt"

using namespace std;

typedef long long LL;
const int INF = INT_MAX / 2;
const double eps = 1e-9;

void setfile() {
    freopen(INPUT_FILE,"r",stdin);
    freopen(OUTPUT_FILE,"w",stdout);
}

double f(double H,double h,double D,double x) {
    return H - D / x * (H - h) + D - x;
}


//三分搜索
double tsearch(double H,double h,double D) {
    double l = D * (H - h) / H,r = D,mid,midr;
    while(fabs(l - r) > eps) {
        mid = (l + r) / 2;
        midr = (mid + r) / 2;
        if(f(H,h,D,mid) > f(H,h,D,midr)) {
            r = midr;
        } else l = mid;
    }
    return f(H,h,D,l);
}

int main() {
    int T; scanf("%d",&T);
    double H,h,D;
    for(int kase = 1;kase <= T;kase++) {
        scanf("%lf%lf%lf",&H,&h,&D);
        printf("%.3f\n",tsearch(H,h,D));
    }
    return 0;
}