POJ1003

Hangover

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 109904		Accepted: 53646

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.

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)

Source

Mid-Central USA 2001

 1 #include <iostream>
 2 using namespace std;
 3 
 4 int main(){
 5     double length;
 6     while(cin>>length,length){
 7         if(length == 0.00)    break;
 8         double num = 1.0;    double sum = 0.0;
 9         while(1){
10             sum = sum + 1.0/(num + 1.0);
11             if(sum >= length)    break;
12             else
13             num+=1.0;
14         }
15         cout<<(int)num<<" card(s)"<<endl;
16     }
17     return 0;
18 }

POJ1003

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