2013
11-08

# 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.

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.

1.00
3.71
0.04
5.19
0.00


3 card(s)
61 card(s)
1 card(s)
273 card(s)

import java.util.*;

public class Main {

public static void main(String[] args) {
Scanner cin = new Scanner(System.in);
String str;
int maxCardNum = 0;

while(cin.hasNext())
{
str = cin.nextLine();
if(str.equals("0.00"))
break;

float len = Float.valueOf(str).floatValue();

maxCardNum = getCardNum(len);
System.out.println(maxCardNum + " card(s)");
}

}

private static int getCardNum(float len)
{
float value = 0;
int index = 2;

while (value < len)
{
value += 1.0/index;
index++;
}

return index-2;
}

}

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