Various distances

AtCoder

IDabc180_b

Time2000ms

Memory256MB

Difficulty—

Given is a point $(x_1,\ldots,x_N)$ in an $N$\-dimensional space. Find the Manhattan distance, Euclidian distance, and Chebyshev distance between this point and the origin. Here, each of them is defined as follows: * The Manhattan distance: $|x_1|+\ldots+|x_N|$ * The Euclidian distance: $\sqrt{|x_1|^2+\ldots+|x_N|^2}$ * The Chebyshev distance: $\max(|x_1|,\ldots,|x_N|)$ ## Constraints * $1 \leq N \leq 10^5$ * $-10^5 \leq x_i \leq 10^5$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $\ldots$ $x_N$ [samples]

Samples

Input #1

2
2 -1

Output #1

3
2.236067977499790
2

Each of the distances is computed as follows:

*   The Manhattan distance: $|2|+|-1|=3$
*   The Euclidian distance: $\sqrt{|2|^2+|-1|^2}=2.236067977499789696\ldots$
*   The Chebyshev distance: $\max(|2|,|-1|)=2$

Input #2

10
3 -1 -4 1 -5 9 2 -6 5 -3

Output #2

39
14.387494569938159
9

API Response (JSON)

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      "content": "Given is a point $(x_1,\\ldots,x_N)$ in an $N$\\-dimensional space.\nFind the Manhattan distance, Euclidian distance, and Chebyshev distance between this point and the origin. Here, each of them is defin...",
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