This one was too good a question for me. i did something couldn't pass out. I have joined topcoder for practice - all people out there help me improve.....
Fly Swatter
Problem

What are your chances of hitting a fly with a tennis racquet?

To start with, ignore the racquet's handle. Assume the racquet is a perfect ring, of outer radius R and thickness t (so the inner radius of the ring is R−t).

The ring is covered with horizontal and vertical strings. Each string is a cylinder of radius r. Each string is a chord of the ring (a straight line connecting two points of the circle). There is a gap of length g between neighbouring strings. The strings are symmetric with respect to the center of the racquet i.e. there is a pair of strings whose centers meet at the center of the ring.

The fly is a sphere of radius f. Assume that the racquet is moving in a straight line perpendicular to the plane of the ring. Assume also that the fly's center is inside the outer radius of the racquet and is equally likely to be anywhere within that radius. Any overlap between the fly and the racquet (the ring or a string) counts as a hit.

Input

One line containing an integer N, the number of test cases in the input file.

The next N lines will each contain the numbers f, R, t, r and g separated by exactly one space. Also the numbers will have at most 6 digits after the decimal point.

Output

N lines, each of the form "Case #k: P", where k is the number of the test case and P is the probability of hitting the fly with a piece of the racquet.

Answers with a relative or absolute error of at most 10-6 will be considered correct.

Limits

f, R, t, r and g will be positive and smaller or equal to 10000.

t < style="font-weight:bold;">Nothing to speak man here is what rem wrote:

#include <map>
#include <set>
#include <cmath>
#include <queue>
#include <vector>
#include <string>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cassert>
#include <numeric>
#include <algorithm>
#include <iostream>
#include <sstream>
#include <ctime>
using namespace std;

typedef long long int64;
typedef vector<int> vi;
typedef vector<string> vs;
typedef vector<double> vd;

#define _CRT_SECURE_NO_WARNINGS
#define For(i,a,b) for (int i(a),_b(b); i <= _b; ++i)
#define Ford(i,a,b) for (int i(a),_b(b); i >= _b; --i)
#define Rep(i,n) for (int i(0),_n(n); i < _n; ++i)
#define Repd(i,n) for (int i((n)-1); i >= 0; --i)
#define Fill(a,c) memset(&a, c, sizeof(a))
#define MP(x, y) make_pair((x), (y))
#define All(v) (v).begin(), (v).end()

template<typename T, typename S> T cast(S s) {
   stringstream ss;
   ss << s;
   T res;
   ss >> res;
   return res;
}

template<typename T> inline T sqr(T a) { return a*a; }
template<typename T> inline int Size(const T& c) { return (int)c.size(); }
template<typename T> inline void checkMin(T& a, T b) { if (b < a) a = b; }
template<typename T> inline void checkMax(T& a, T b) { if (b > a) a = b; }

const double pi = 2*acos(0.0);
const double eps = 1e-9;

double asin2(double x) {
   double res = asin(max(-1.0, min(1.0, x)));
   assert(-pi/2 <= res && res <= pi/2);
   return res;
}

double inters(double x1, double y1, double x2, double y2, double r) {
   assert(x1 <= x2 && y1 <= y2);
   assert(sqrt(sqr(x1)+sqr(y1)) <= r);
   if (sqrt(sqr(x2)+sqr(y2)) <= r)
       return (x2-x1)*(y2-y1);
   vector<double> xs;
   xs.push_back(x1);
   xs.push_back(x2);   
   double x = sqrt(sqr(r)-sqr(y1));
   if (y1 < r && x1 < x && x < x2)
       xs.push_back(x);
   x = sqrt(sqr(r)-sqr(y2));
   if (y2 < r && x1 < x && x < x2)
       xs.push_back(x);
   if (x1 < r && r < x2)
       xs.push_back(r);
   sort(All(xs));
   double res = 0;
   Rep(i, Size(xs)-1) {
       double x1 = xs[i], x2 = xs[i+1];
       if (x1 > r-eps)
           break;
       double s1 = y1*(x2-x1), s2 = y2*(x2-x1);
       double s4 = (0.5*x2*sqrt(sqr(r)-sqr(x2))+0.5*sqr(r)*asin2(x2/r))-(0.5*x1*sqrt(sqr(r)-sqr(x1))+0.5*sqr(r)*asin2(x1/r));
       double s3 = -s4;
       res += max(0.0, min(s2, s4)-max(s1, s3));
   }
   assert(res <= (x2-x1)*(y2-y1));
   return res;
}

int main() {
   freopen("input.txt", "rt", stdin);
   freopen("output.txt", "wt", stdout);

   int t;
   scanf("%d", &t);
   For(test, 1, t) {
       double f, R, t, r, g;
       scanf("%lf%lf%lf%lf%lf", &f, &R, &t, &r, &g);
       double sum = 0;
       if (g > 2*f) {
           double x = r;
           while (x+f < R-t-f) {
               double y = r;
               while (sqrt(sqr(x+f)+sqr(y+f)) < R-t-f) {
                   sum += inters(x+f, y+f, x+g-f, y+g-f, R-t-f);
                   y += 2*r+g;
               }
               x += 2*r+g;
           }
       }
       printf("Case #%d: %.6lf\n", test, (pi*sqr(R)-4*sum)/(pi*sqr(R)));
   }

   exit(0);
}