HDU 1056 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)
  
  

Mid-Central USA 2001

#include<iostream>
using namespace std;
int main()
{
    double target,num,sum;
    while(cin>>target&&target!=0.00)
     {
         sum = 0.0f;
         num = 2;
        while(sum<target)
         {
             sum += 1.0/num;
             num++;
         }
         cout<<num-2<<" card(s)"<<endl;
     }
    return 0;
}