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.NoSuchElementException;
import java.util.Scanner;
import java.util.stream.Stream;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        try {
            int n = Integer.parseInt(sc.nextLine());
            if (n > 100 || n < 1) {
                throw new IllegalTestCaseException();
            }
            double[] xs = Stream.of(sc.nextLine().split(" "))
                    .mapToDouble(Double::parseDouble)
                    .toArray();
            double[] ys = Stream.of(sc.nextLine().split(" "))
                    .mapToDouble(Double::parseDouble)
                    .toArray();
            if (n != xs.length || n != ys.length) {
                throw new IllegalTestCaseException();
            }
            double d1 = minkowskiDistance(n, xs, ys, 1);
            double d2 = minkowskiDistance(n, xs, ys, 2);
            double d3 = minkowskiDistance(n, xs, ys, 3);
            double di = minkowskiDistance(n, xs, ys, -1);
            System.out.printf("%.8f\n%.8f\n%.8f\n%.8f\n", d1, d2, d3, di);
        } catch (IllegalTestCaseException
                | NumberFormatException
                | NoSuchElementException e) {
            System.out.println(e);
        }
    }

    /**
     * @param p
     *   if p is -1, it means p is infinity.
     */
    private static double minkowskiDistance(int n, double[] xs, double[] ys, double p) {
        if (p == -1) {
            double max = -1;
            for (int i = 0; i < n; i++) {
                max = Double.max(Math.abs(xs[i] - ys[i]), max);
            }
            return max;
        }
        double summation = 0;
        for (int i = 0; i < n; i++) {
            summation += Math.pow(Math.abs(xs[i] - ys[i]), p);
        }
        summation = Math.pow(summation, 1 / p);
        return summation;
    }

    private static class IllegalTestCaseException extends RuntimeException {
        IllegalTestCaseException() {
            super("Illegal condition.");
        }
    }
}