cylinder.java

Ulm大学2007年竞赛题和解题报告

// Author: Adrian Kuegel

import java.io.*;
import java.util.*;
import java.text.*;

public class cylinder {
	static double get_volume(double r, double h) {
		return r*r*Math.PI*h;
	}
	public static void main(String [] args) throws Exception {
		Scanner in = new Scanner(new File("cylinder.in"));
		DecimalFormat df = new DecimalFormat("0.000",new DecimalFormatSymbols(Locale.US));
		while(true) {
			int w = in.nextInt();
			int h = in.nextInt();
			if (w == 0 && h == 0)
				break;
			// first case: use w as height of cylinder
			// in this case, we want to maximize the radius of the circle
			// r <= w/2 && 2*r*PI <= h-2*r -> r <= min(w/2, h/(2*PI+2))
			double r1 = Math.min(w/2.0, h/(Math.PI*2+2));
			double res = get_volume(r1, w);

			// second case:
			// use h-2*r as height of cylinder
			// r <= w/2 && 2*r*PI <= w -> r <= w / (2*PI)
			double r2 = w / Math.PI / 2;
			// maximize r*r*PI*(h-2*r), subject to 0 <= r <= r2
			// 2*r*PI*h - 6*r*r*PI = 0
			// 2*h = 6*r -> r = h/3
			// since we know w <= h, r2 <= h / (2*PI) <= h / 3
			// it follows the maximum occurs at r2
			res = Math.max(res, get_volume(r2, h-2*r2));
			System.out.println(df.format(res));
		}
	}
}