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 JAVA (judge verdict: Runtime Error)

import java.util.Scanner;

class Main{
        public static void main(String[] args){
    	Scanner scan = new Scanner(System.in);
    	int n;
    	int[] Vec_x;
    	int[] Vec_y;
    	double[] D = new double[3];
    	double D_Max = 0.0;
    	
    	n = scan.nextInt();
    	Vec_x = new int[n];
    	Vec_y = new int[n];
    	
    	for(int i = 0; i < n; i++){
    		Vec_x[i] = scan.nextInt();
    	}
    	for(int i = 0; i < n; i++){
    		Vec_y[i] = scan.nextInt();
    	}
    	
    	//p = 1
    	for(int i = 0; i < n; i++){
    		D[0] += Math.abs(Vec_x[i] - Vec_y[i]); 
    	}
    	System.out.println(String.format("%.6f", D[0]));
    	
    	//p = 2
    	for(int i = 0; i < n; i++){
    		D[1] += Math.pow(Math.abs(Vec_x[i] - Vec_y[i]), 2); 
    	}
    	D[1] = Math.pow(D[1], 1.0/2.0);
    	System.out.println(String.format("%.6f", D[1]));
    	//p = 3
    	for(int i = 0; i < n; i++){
    		D[2] += Math.pow(Math.abs(Vec_x[i] - Vec_y[i]), 3); 
    	}
    	D[2] = Math.pow(D[2], 1.0/3.0);
    	System.out.println(String.format("%.6f", D[2]));
    	
    	D_Max = Math.abs(Vec_x[0] - Vec_y[0]);
    	if(D_Max < Math.abs(Vec_x[1] - Vec_y[1])) {
    		D_Max = Math.abs(Vec_x[1] - Vec_y[1]);
    	}
    	if(Math.abs(Vec_x[1] - Vec_y[1]) < Math.abs(Vec_x[2] - Vec_y[2])) {
    		D_Max = Math.abs(Vec_x[2] - Vec_y[2]);
    	}
    	System.out.println(String.format("%.6f", D_Max));
     }
}