Problem:
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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 JAVA (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        List<Integer> xi = new ArrayList<>();
        List<Integer> yi = new ArrayList<>();
        double D1 = 0;
        double D2 = 0;
        double D3 = 0;
        double D4 = 0;
        int k = 0;
        int n = sc.nextInt();
        for (int i = 0; i < n; i++) {
            int x = sc.nextInt();
            xi.add(x);
        }
        for (int i = 0; i < n; i++) {
            int y = sc.nextInt();
            yi.add(y);
        }
        for (int i = 0; i < n; i++) {
            k = Math.abs(xi.get(i) - yi.get(i));
            D1 += k;
            D2 += Math.pow(k,2);
            D3 += Math.pow(k,3);
            if(D4 < k)
                D4 = k;
        }
        System.out.println(D1);
         System.out.println(Math.sqrt(D2));
          System.out.println(Math.cbrt(D3));
           System.out.println(D4);
    }
}