POJ - 1003 Hangover
2014-06-02 18:47
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[align=center]Hangover[/align]
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.
![](http://poj.org/images/1003/hangover.jpg)
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
Sample Output
Source
Mid-Central USA 2001
思路:sum = 1/2 + 1/3 + 1/4 + ...+ 1/(n+1) ,直到sum >= c;
Time Limit: 1000MS | Memory Limit: 10000K | |
Total Submissions: 99582 | Accepted: 48278 |
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.
![](http://poj.org/images/1003/hangover.jpg)
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
思路:sum = 1/2 + 1/3 + 1/4 + ...+ 1/(n+1) ,直到sum >= c;
#include "iostream" #include "cstdio" #include "cstring" #include "cmath" #include "algorithm" using namespace std; int main() { //freopen("in.txt", "r", stdin); int i, j; float c; while(scanf("%f", &c) == 1 && c != 0.00) { float sum = 0.00; for(i = 2; i; i++) { sum += 1.0/i; if(sum >= c) { cout<<i-1<<" card(s)"<<endl; break; } } } return 0; }
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