UVa 11346 Probability

G - Probability

Time Limit: 1 sec 
Memory Limit: 16MB

Consider rectangular coordinate system and point L(X,Y) which is randomly chosen among all points in the area A which is defined in the following manner: A = {(x,y) | x is from interval [-a;a]; y is from interval [-b;b]}. What is the probability P that the area of a rectangle that is defined by points (0,0) and (X,Y) will be greater than S?

INPUT:

The number of tests N <= 200 is given on the first line of input. Then N lines with one test case on each line follow. The test consists of 3 real numbers a > 0, b > 0 ir S => 0.

OUTPUT:

For each test case you should output one number P and percentage "%" symbol following that number on a single line. P must be rounded to 6 digits after decimal point.

SAMPLE INPUT:

310 5 201 1 12 2 0

SAMPLE OUTPUT:

23.348371%0.000000%100.000000%

#include <cstdio>#include <cmath>double a, b, s;int main(){int t;scanf("%d", &t);int count = 0;while(count < t){scanf("%lf %lf %lf", &a, &b, &s);double result;if(s == 0)result = 100;else if(a*b <= s)result = 0;else{result = (a*b-s*log(a)-s+s*log(s/b))/(a*b)*100;}printf("%.6f%%\n", result);count++;}return 0;}

题目本身不难，首先明确xy = s为一条双曲线，求得双曲线和矩形相交的上方面积即可。

该面积用定积分来求解，用x积分，被积函数为y, 为b-S/x.