1003 Hangover

最新推荐文章于 2024-12-10 18:38:12 发布

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#初等数学

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本文探讨了如何使用一定数量的卡片实现最大化的悬空距离。通过数学公式计算不同卡片堆叠时的最大悬空长度，并提供了算法实现，以确定达到特定悬空长度所需的最小卡片数。

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.
这里写图片描述

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)

Source

Mid-Central USA 2001

#include<iostream>

using namespace std;

int main()
{
    double c;
    while (cin >> c&&c)
    {
        int n;
        double sum = 0;
        for (int n = 1;; n++)
        {
            sum += 1.0 / (n + 1);
            if (sum >= c)
            {
                cout << n << " card(s)" << endl;
                break;
            }
        }
    }

    return 0;
}