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最新推荐文章于 2024-06-06 09:06:09 发布

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最新推荐文章于 2024-06-06 09:06:09 发布

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本文介绍了一个有趣的数学问题：如何计算使卡片从桌面悬空特定距离所需的最少卡片数量。通过逐步累加1/2, 1/3, ... 直到总和超过目标长度，文章提供了一段Java代码实现这一计算。

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Description

How far can you make a stack of cards overhang a table? If you have one card, you can create a maximum overhang of half a card length. (We're assuming that the cards must be perpendicular to the table.) With two cards you can make the top card overhang the bottom one by half a card length, and the bottom one overhang the table by a third of a card length, for a total maximum overhang of 1/2 + 1/3 = 5/6 card lengths. In general you can make n cards overhang by 1/2 + 1/3 + 1/4 + ... + 1/(n + 1) card lengths, where the top card overhangs the second by 1/2, the second overhangs tha third by 1/3, the third overhangs the fourth by 1/4, etc., and the bottom card overhangs the table by 1/(n + 1). This is illustrated in the figure below.

Input

The input consists of one or more test cases, followed by a line containing the number 0.00 that signals the end of the input. Each test case is a single line containing a positive floating-point number c whose value is at least 0.01 and at most 5.20; c will contain exactly three digits.

Output

For each test case, output the minimum number of cards necessary to achieve an overhang of at least c card lengths. Use the exact output format shown in the examples.

Sample Input

1.00
3.71
0.04
5.19
0.00

Sample Output

3 card(s)
61 card(s)
1 card(s)
273 card(s)

就是计算1/2+1/3+...+1/n大于某个数的题目

import java.util.Scanner;


public class Main {

	public static int calCount(double length){
		int count = 1;
		double sum = 0;
		while(true){
			sum += 1.0/(count+1);//此处一开始设置成1耽误了好久
			if(sum > length){
				break;
			}
			count++;
		}
		return count;
	}
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		while(sc.hasNext()){
			double length = sc.nextDouble();
			if(length == 0.00)
				break;
			int num = calCount(length);
			System.out.println(num + " card(s)");
		}
	}

}