Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

Distance II

Your task is to calculate the distance between two $n$ dimensional vectors $x = \{x_1, x_2, ..., x_n\}$ and $y = \{y_1, y_2, ..., y_n\}$.

The Minkowski's distance defined below is a metric which is a generalization of both the Manhattan distance and the Euclidean distance.

\[
D_{xy} = (\sum_{i=1}^n |x_i - y_i|^p)^{\frac{1}{p}}
\]

It can be the Manhattan distance

\[
D_{xy} = |x_1 - y_1| + |x_2 - y_2| + ... + |x_n - y_n|
\]

where $p = 1 $.

It can be the Euclidean distance

\[
D_{xy} = \sqrt{(|x_1 - y_1|)^{2} + (|x_2 - y_2|)^{2} + ... + (|x_n - y_n|)^{2}}
\]

where $p = 2 $.

Also, it can be the Chebyshev distance

\[
D_{xy} = max_{i=1}^n (|x_i - y_i|)
\]

where $p = \infty$

Write a program which reads two $n$ dimensional vectors $x$ and $y$, and calculates Minkowski's distance where $p = 1, 2, 3, \infty$ respectively.

Input

In the first line, an integer $n$ is given. In the second and third line, $x = \{x_1, x_2, ... x_n\}$ and $y = \{y_1, y_2, ... y_n\}$ are given respectively. The elements in $x$ and $y$ are given in integers.

Output

Print the distance where $p = 1, 2, 3$ and $\infty$ in a line respectively.
The output should not contain an absolute error greater than 10-5.

Constraints

$1 \leq n \leq 100$

$0 \leq x_i, y_i \leq 1000$

Sample Input

3
1 2 3
2 0 4

Sample Output

4.000000
2.449490
2.154435
2.000000

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{   
    static void Main(string[] args)
    {
        int n = int.Parse(Console.ReadLine());
        string[] strx = Console.ReadLine().Split(' ');
        string[] stry = Console.ReadLine().Split(' ');
        double[] datax = new double[n];
        double[] datay = new double[n];
        double[] dis = new double[n];
        double p1 = 0;
        double p2 = 0;
        double p3 = 0;
        double nugen = 0;      

        for(int i = 0; i < n; i++)
        {
            datax[i] = double.Parse(strx[i]);
            datay[i] = double.Parse(stry[i]);
            double s = datax[i] - datay[i];
            dis[i] = s > 0 ? s : -s;
        }

        double p2sum = 0;
        double p3sum = 0;
        for(int i = 0; i < n; i++)
        {
            p1 += dis[i];
            p2sum += Math.Pow(dis[i], 2);
            p3sum += Math.Pow(dis[i], 3);
        }
        p2 = Math.Sqrt(p2sum);
        p3 = Math.Pow(p3sum, 1.0 / 3.0);
        nugen = dis.Max();

        Console.WriteLine(string.Format("{0:f6}\n{1:f6}\n{2:f6}\n{3:f6}", p1, p2, p3, nugen));

    }
}