hdu 2289 Cup

The WHU ACM Team has a big cup, with which every member drinks water. Now, we know the volume of the water in the cup, can you tell us it height? 

The radius of the cup's top and bottom circle is known, the cup's height is also known.

InputThe input consists of several test cases. The first line of input contains an integer T, indicating the num of test cases. 
Each test case is on a single line, and it consists of four floating point numbers: r, R, H, V, representing the bottom radius, the top radius, the height and the volume of the hot water. 

Technical Specification 

1. T ≤ 20. 
2. 1 ≤ r, R, H ≤ 100; 0 ≤ V ≤ 1000,000,000. 
3. r ≤ R. 
4. r, R, H, V are separated by ONE whitespace. 
5. There is NO empty line between two neighboring cases. 

OutputFor each test case, output the height of hot water on a single line. Please round it to six fractional digits.Sample Input

1
100 100 100 3141562

Sample Output

99.999024

解题思路：
推公式然后二分暴搜

实现代码：

#include <stdio.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <string>
#include <math.h>
#include <stdlib.h>
#include <bitset>
using namespace std;

#define rep(i,a,b) for (int i=(a),_ed=(b);i<=_ed;i++)
#define per(i,a,b) for (int i=(b),_ed=(a);i>=_ed;i--)
#define pb push_back
#define mp make_pair
const int inf_int = 2e9;
const long long inf_ll = 2e18;
#define inf_add 0x3f3f3f3f
#define mod 1000000007
#define LL long long
#define ULL unsigned long long
#define MS0(X) memset((X), 0, sizeof((X)))
#define SelfType int
SelfType Gcd(SelfType p,SelfType q){return q==0?p:Gcd(q,p%q);}
SelfType Pow(SelfType p,SelfType q){SelfType ans=1;while(q){if(q&1)ans=ans*p;p=p*p;q>>=1;}return ans;}
#define Sd(X) int (X); scanf("%d", &X)
#define Sdd(X, Y) int X, Y; scanf("%d%d", &X, &Y)
#define Sddd(X, Y, Z) int X, Y, Z; scanf("%d%d%d", &X, &Y, &Z)
#define reunique(v) v.resize(std::unique(v.begin(), v.end()) - v.begin())
#define all(a) a.begin(), a.end()
#define   mem(x,v)      memset(x,v,sizeof(x))
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef vector<int> vi;
typedef vector<long long> vll;
#define PI acos(-1.0)
#define exp 1e-9
double fuck(double r,double R,double h,double H)
{
    double u = h/H*(R-r) + r;
    return PI/3*(r*r+r*u+u*u)*h;
}
int main()
{
    int t;
    double r,R,H,V,mid,v,right,left;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%lf%lf%lf%lf",&r,&R,&H,&V);
        left=0;
        right=100;
        while(right-left>exp)
        {
            mid=(right+left)/2;
            v=fuck(r,R,mid,H);
            if(fabs(v-V)<=exp)
                break;
            else if(v>V)
                right=mid-exp;
            else
                left=mid+exp;
        }
        printf("%.6lf\n",mid);
    }
    return 0;
}