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Light Bulb 三分入门题

2015-08-16 21:13 120 查看
                      Light Bulb

分析:求出公式,发现在给定范围内是凸函数。三分求最值。

/********************************
please don't hack me!! /(ToT)/~~
__------__
/~          ~\
|    //^\\//^\|
/~~\  ||  T| |T|:~\
| |6   ||___|_|_||:|
\__.  /      o  \/'
|   (       O   )
/~~~~\    `\  \         /
| |~~\ |     )  ~------~`\
/' |  | |   /     ____ /~~~)\
(_/'   | | |     /'    |    ( |
| | |     \    /   __)/ \
\  \ \      \/    /' \   `\
\  \|\        /   | |\___|
\ |  \____/     | |
/^~>  \        _/ <
|  |         \       \
|  | \        \        \
-^-\  \       |        )
`\_______/^\______/
************************************/

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <cstdlib>
#include <sstream>
using namespace std;
typedef long long LL;
const LL INF = 0x5fffffff;
const double EXP = 1E-8;
const LL MOD = (LL)1E9+7;
const int MS = 1005;

double H, h, D;

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

int main() {
int T;
scanf("%d",&T);
while (T--) {
scanf("%lf%lf%lf",&H,&h,&D);
double l = 0;
double r = h * D / H;
while ((r - l) >= EXP) {
double mid = (l + r) / 2;
double mmid = (mid + r) / 2;
if (fun(mid) > fun(mmid))
r = mmid;
else
l = mid;
}
printf("%.3lf\n",fun(l));
}
return 0;
}
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