题目

英语翻译
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.
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.
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)

提问时间：2020-10-15

答案

你能走多远堆卡片悬垂桌子?如果你有一个卡,你可以创建一个最大悬垂半卡的长度.(我们这里假设这些开关卡必须垂直于表.)与两张卡片上,你能做的不止是一个底部悬垂半卡的长度,以及一个悬垂桌子边的底部有三分之一的一张卡片,总长度的最大宽度1 / 2 + 2 / 1 / 3 = 1卡长度.一般来说,你可以使护士卡悬垂1 / 2 + 1 / 3 + 1 / 4 +…+ 1 /(n + 1)卡长度