POJ 1607

Deck

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 7686		Accepted: 3356

Description

A single playing card can be placed on a table, carefully, so that the short edges of the card are parallel to the table's edge, and half the length of the card hangs over the edge of the table. If the card hung any further out, with its center of gravity off
the table, it would fall off the table and flutter to the floor. The same reasoning applies if the card were placed on another card, rather than on a table. 

Two playing cards can be arranged, carefully, with short edges parallel to table edges, to extend 3/4 of a card length beyond the edge of the table. The top card hangs half a card length past the edge of the bottom card. The bottom card hangs with only 1/4
of its length past the table's edge. The center of gravity of the two cards combined lies just over the edge of the table. 

Three playing cards can be arranged, with short edges parallel to table edges, and each card touching at most one other card, to extend 11/12 of a card length beyond the edge of the table. The top two cards extend 3/4 of a card length beyond the edge of the
bottom card, and the bottom card extends only 1/6 over the table's edge; the center of gravity of the three cards lines over the edges of the table. 

If you keep stacking cards so that the edges are aligned and every card has at most one card above it and one below it, how far out can 4 cards extend over the table's edge? Or 52 cards? Or 1000 cards? Or 99999? 

Input

Input contains several nonnegative integers, one to a line. No integer exceeds 99999.
Output

The standard output will contain, on successful completion of the program, a heading: 

Cards Overhang 

(that's two spaces between the words) and, following, a line for each input integer giving the length of the longest overhang achievable with the given number of cards, measured in cardlengths, and rounded to the nearest thousandth. The length must be expressed
with at least one digit before the decimal point and exactly three digits after it. The number of cards is right-justified in column 5, and the decimal points for the lengths lie in column 12.
Sample Input

1
2
3
4
30

Sample Output

Cards  Overhang
1     0.500
2     0.750
3     0.917
4     1.042
30     1.997

Source

South Central USA 1998
1Y直接秒。http://www.guokr.com/article/4437/

#include <cstdio>
#include <cmath>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <map>
#include <string>
#include <stack>
#include <cctype>
#include <vector>
#include <queue>
#include <set>
#include <utility>
#include <cassert>

using namespace std;
///#define Online_Judge
#define outstars cout << "***********************" << endl;
#define clr(a,b) memset(a,b,sizeof(a))
#define lson l , mid  , rt << 1
#define rson mid + 1 , r , rt << 1 | 1

#define mk make_pair
#define FOR(i , x , n) for(int i = (x) ; i < (n) ; i++)
#define FORR(i , x , n) for(int i = (x) ; i <= (n) ; i++)
#define REP(i , x , n) for(int i = (x) ; i > (n) ; i--)
#define REPP(i ,x , n) for(int i = (x) ; i >= (n) ; i--)
const int MAXN = 400000 + 150;
const int sigma_size = 26;
const long long LLMAX = 0x7fffffffffffffffLL;
const long long LLMIN = 0x8000000000000000LL;
const int INF = 0x7fffffff;
const int IMIN = 0x80000000;
#define eps 1e-4
const int MOD = (int)1e9 + 7;
typedef long long LL;
const double PI = acos(-1.0);
typedef double D;
typedef pair<int , int> pi;
///#pragma comment(linker, "/STACK:102400000,102400000")

int main()
{
int n;
double ans;
printf("Cards  Overhang\n");
while(~scanf("%d" , &n))
{
ans = 0.0;
FORR(i , 1 , n)
{
ans += 1.0 / (2 * i);
//            cout << ans << endl;
}
printf("%5d     %.3lf\n" , n , ans);
}
return 0;
}