Hangover

冷不防 2022-05-25 13:10 32阅读 0赞

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.

![hangover.jpg][]

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)

代码：

#include<stdio.h>
    int main()
    {
    int i,j,n,m,k,t;
    double a,b,c,d;
    while(scanf("%lf",&a)&&a)
    {
    b=0;
    for(i=0;b<a;i++)
    {
    b+=1.0*1/(i+2);
    }
    printf("%d card(s)\n",i);
    }
    }

[hangover.jpg]: /images/20220525/0be089bbf9474fe793e1d3ee1191016d.png