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199.java
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199.java
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public class Main {
public static void main(String[] args) {
long startTime = System.nanoTime();
int size = 10;
double k1 = 1; // choose curvature 1 for the 3 equal circles
double k0 = k1 * (3 - 2 * Math.sqrt(3)); // get curvature of the outer
// circle
double a0 = 1 / (k0 * k0); // area of outer circle
double a1 = 3 / (k1 * k1); // area of 3 inner circles
a1 += 3 * getArea(k0, k1, k1, size); // fill three outer gaps
a1 += getArea(k1, k1, k1, size); // fill centre gap
System.out.println("Answer: "
+ String.format("%.6g%n", ((a0 - a1) / a0))); // report
// resulting
// fraction
long endTime = System.nanoTime();
System.out.printf("Total Time: %.6f seconds\n",
((endTime - startTime) / 1000000000.0));
}
static double getArea(double k1, double k2, double k3, int depth) {
if (depth == 0)
return 0.0;
// calculate circle curvature of inside circle
double k4 = k1 + k2 + k3 + 2 * Math.sqrt(k1 * k2 + k2 * k3 + k3 * k1);
double a = 1 / (k4 * k4); // circle area
a += getArea(k1, k2, k4, depth - 1); // add areas if inbetween fillings
a += getArea(k2, k3, k4, depth - 1);
a += getArea(k3, k1, k4, depth - 1);
return a;
}
}