Cup
Time Limit: 3000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 6684 Accepted Submission(s): 2062
Problem Description
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.
Input
The 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.
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.
Output
For 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
题目大意：给出一个杯子的上下半径r,R，杯子的高度H，装入V升水，求水的高度
思路：二分或数学方法
二分
1 #include <stdio.h> 2 #include <math.h> 3 double r, R, H, V; 4 #define PI 3.1415926535897932 5 double vv(double h) 6 { 7 double x=r+(R-r)*h/H; 8 return (PI*h*(x*x+r*x+r*r)/3.0); 9 } 10 double f(double z, double y) 11 { 12 double mid; 13 while((y-z)>1e-10) 14 { 15 mid=(z+y)/2.0; 16 if(vv(mid)<V) 17 z=mid; 18 else 19 y=mid; 20 } 21 return mid; 22 } 23 int main() 24 { 25 int a; 26 scanf("%d", &a); 27 while(a--) 28 { 29 scanf("%lf%lf%lf%lf", &r, &R, &H, &V); 30 printf("%lf ", f(0,H)); 31 } 32 return 0; 33 }