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POJ 1003 Hangover&&NYOJ 156 Hangover【数学题】

2024-08-08 04:43:33   218人阅读

计算1+1/2+1/3+++1/n


Hangover
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 104558 Accepted: 50926

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


#include<stdio.h>
int main()
{
	double s,sum;
	int i,t;
	while(scanf("%lf",&s),s)
	{
		for(i=2,sum=0;;i++)
		{
			sum+=1.0/i;
			if(sum>=s)
			{
				t=i;
				break;
			}
		}
		printf("%d card(s)\n",t-1);
	}
	
	return 0;
}



POJ 1003 Hangover&&NYOJ 156 Hangover【数学题】


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