HANGOVER - Hangover


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.

Input:
1.00
3.71
0.04
5.19
0.00
Output:
3 card(s)
61 card(s)
1 card(s)
273 card(s)

hide comments
lmalvi: 2019-07-05 19:50:29

https://codechefforbeginners.blogspot.com/2019/07/hangover-hangover-math-how-far-can-you.html

blackfly19: 2019-06-18 10:42:12

2nd AC
No loop required!!

Nitin: 2019-06-04 21:30:27

I forgot to put card(s) in output and it took me 15 mins and a WA to realize that

albertark1589: 2019-05-13 23:14:53

Last edit: 2019-05-13 23:18:54
mgroovyank: 2019-04-19 10:06:23

Really easy. Don't forget printing "card(s)"

manyu2: 2019-03-29 12:46:55

easy AC in one go!!

rahul11197: 2019-03-17 12:41:08

ac in 10

sahilsinghss: 2019-03-14 23:30:43

Wohoo! my 50th

tanav_shah1: 2019-02-06 20:56:05

Very Easy, AC in one go!!

pasari: 2019-01-24 09:38:10

Can someone resolve TLE in java. I've declared all variables as float still it is giving TLE


Added by:Wanderley Guimarăes
Date:2006-06-09
Time limit:0.213s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM Mid Central Regionals 2001