poj 2926 Requirements(最大哈密顿距离，二进制）

Requirements

Time Limit: 5000MS		Memory Limit: 65536K
Total Submissions: 3998		Accepted: 1356

Description

An undergraduate student, realizing that he needs to do research to improve his chances of being accepted to graduate school, decided that it is now time to do some independent research. Of course, he has decided to do research in the most important domain: the requirements he must fulfill to graduate from his undergraduate university. First, he discovered (to his surprise) that he has to fulfill 5 distinct requirements: the general institute requirement, the writing requirement, the science requirement, the foreign-language requirement, and the field-of-specialization requirement. Formally, a requirement is a fixed number of classes that he has to take during his undergraduate years. Thus, for example, the foreign language requirement specifies that the student has to take 4 classes to fulfill this requirement: French I, French II, French III, and French IV. Having analyzed the immense multitude of the classes that need to be taken to fulfill the different requirements, our student became a little depressed about his undergraduate university: there are so many classes to take…

Dejected, the student began studying the requirements of other universities that he might have chosen after high school. He found that, in fact, other universities had exactly the same 5 requirements as his own university. The only difference was that different universities had different number of classes to be satisfied in each of the five requirement.

Still, it appeared that universities have pretty similar requirements (all of them require a lot of classes), so he hypothesized that no two universities are very dissimilar in their requirements. He defined the dissimilarity of two universities X and Y as |x₁ − y₁| + |x₂ − y₂| + |x₃ − y₃| + |x₄ − y₄| + |x₅ − y₅|, where an x_i (y_i) is the number of classes in the requirement i of university X (Y) multiplied by an appropriate factor that measures hardness of the corresponding requirement at the corresponding university.

Input

The first line of the input file contains an integer N (1 ≤ N ≤ 100 000), the number of considered universities. The following N lines each describe the requirements of a university. A university X is described by the five non-negative real numbers x₁ x₂ x₃ x₄ x₅.

Output

On a single line, print the dissimilarity value of the two most dissimilar universities. Your answer should be rounded to exactly two decimal places.

Sample Input

3
2 5 6 2 1.5
1.2 3 2 5 4
7 5 3 2 5

Sample Output

12.80

给n个5维坐标点，求它们的最大哈密顿距离，即 |x₁ − y₁| + |x₂ − y₂| + |x₃ − y₃| + |x₄ − y₄| + |x₅ − y₅|最大。

先把问题退化一下，一维不能说明问题，选个二维的吧，a(x1,y1),b(x2,y2), ab点的最大距离有四种情况，(x1-x2) + (y1-y2), (x1-x2) + (y2-y1), (x2-x1) + (y1-y2), (x2-x1) + (y2-y1)

转化一下，将a，b的坐标分开，即为(x1+y1) - (x2+y2), (x1-y1) -(x2-y2), (-x1+y1) - (-x2+y2), (-x1-y1) - (-x2-y2)

通过观察发现，"-"号左右两边的符号完全相同，这样就可以把这两个点分开了，只需要找到(x1+y1)，(x1-y1)，(-x1+y1) ，(-x1-y1)的最大值和(x2+y2)，(x2-y2)，(-x2+y2)，(-x2-y2)的最小值就行，由于"+","-"可以用二进制表示，那么5维的所有"+","-"就可以用0~(1<<5)的数表示了。

代码：

#include 
#include 
#include 
#include 
using namespace std;
const int maxn=100000+1000;
const int inf=1000000000;
double a[maxn][5];
int main()
{
    int n;
    while(~scanf("%d",&n))
    {
        for(int i=0;imaxi)
                maxi=t;
                if(t