Poj1003

一、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.

二、问题分析

这道题就是题目难点，其他的也没什么难的了。题意呢就是，求1/2 + 1/3 + 1/4 + ... + 1/(n + 1)<input的最大的n.起初想着用调和级数来Log(n)+C-1(C为欧拉常数)求这个式子的，后来发现不太精确。所以就这能暴力求解了，反正也是很简单。要注意的就是，除法的精度在久1/n时，要用1.0/n这样编译器才知道是浮点运算。最后将结果减1既得所求。