hdu 5241 Friends（数学或者乱搞）

Problem Description
Mike has many friends. Here are nine of them: Alice, Bob, Carol, Dave, Eve, Frank, Gloria, Henry and Irene.

Mike is so skillful that he can master n languages (aka. programming languages).

His nine friends are all weaker than he. The sets they can master are all subsets of Mike’s languages.

But the relations between the nine friends is very complex. Here are some clues.

1. Alice is a nice girl, so her subset is a superset of Bob’s.
2. Bob is a naughty boy, so his subset is a superset of Carol’s.
3. Dave is a handsome boy, so his subset is a superset of Eve’s.
4. Eve is an evil girl, so her subset is a superset of Frank’s.
5. Gloria is a cute girl, so her subset is a superset of Henry’s.
6. Henry is a tall boy, so his subset is a superset of Irene’s.
7. Alice is a nice girl, so her subset is a superset of Eve’s.
8. Eve is an evil girl, so her subset is a superset of Carol’s.
9. Dave is a handsome boy, so his subset is a superset of Gloria’s.
10. Gloria is a cute girl, so her subset is a superset of Frank’s.
11. Gloria is a cute girl, so her subset is a superset of Bob’s.

Now Mike wants to know, how many situations there might be.

Input
The first line contains an integer T(T20) denoting the number of test cases.

For each test case, the first line contains an integer n(0n3000), denoting the number of languages.

Output
For each test case, output ”Case #t:” to represent this is the t-th case. And then output the answer.

Sample Input
2 0 2

Sample Output
Case #1: 1 Case #2: 1024

Source

（图片来源xpchf）

BZOJ 2456: mode（乱搞，附java快速读入模板）

Output

一行一个正整数表示那个众数。

5
3 2 3 1 3

3

HINT

100%的数据，n<=500000，数列中每个数<=maxlongint。

zju2132 The Most Frequent Number

Java 牛顿迭代法求大数开方

$\sqrt a$可以看成$x^{2}-a=0$的一个正根。然后运用牛顿迭代法求解：$x_n_+_1=x_n-$$\frac{f_{x_n}}{f_{x_n}'}$。那么最后得到这个式子：$\frac{(x_n+\frac{a}{x_n})}{2}$