poj2926(曼哈顿距离)

Requirements

Time Limit: 5000MS		Memory Limit: 65536K
Total Submissions: 4312		Accepted: 1504

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

题意：计算五维空间中点的最大曼哈顿距离。

思路：

以二维平面为例：

设距离最远的两点为 i, j，可知所求的最大距离必定有以下四种形式之一：

(xi-xj)+(yi-yj), (xj-xi)+(yi-yj), (xi-xj)+(yj-yi), (xj-xi)+(yj-yi) 变形一下，把相同点的坐标放到一起，

即 (xi+yi)-(xj+yj), (-xi+yi)-(-xj+yj), (xi-yi)-(xj-yj), (-xi-yi)-(-xj-yj)，可以发现即去绝对值之后把同一点的坐标放在一起，对应坐标符号相同。

假如我们用 0 表示负号，用 1 表示正号，那么 (xi+yi) 可以表示为 11。

那么要表示一个维数为 dem 的所有状态，只需要用 0 ~ (2^dem-1) 的所有二进制就可以了。

于是只要对所有的点 (xi,yi)，依次计算出 (xi+yi), (xi-yi), (-xi+yi), (-xi-yi)这四种形式，然后把每个点i算出来的这四种情况的最大值、最小值分别记录（更新）到数组 max[] 和 min[] 中，然后枚举每一种去绝对值的组合，组合后的最大值即为 answer。

来源：传送门

代码：

#include
#include
#include
#include
#define inf 1e100
using namespace std;
double p[100005][5];
int main()
{
	int n;
	while(~scanf("%d",&n))
	{
		memset(p,0,sizeof(p));
		for(int i=0;i>k)&1)res+=p[i][k];
					else res-=p[i][k];
				}
				maxx=max(maxx,res);
				minx=min(minx,res);
			}
			ans=max(ans,maxx-minx);
		}
		printf("%.2lf\n",ans);
	}
}