permutations.md

PERMUTATIONS

var	desc
$n$	Range of integers $1, 2, ..., n$

In a range from $1, 2, ..., n$ we have to construct a beautiful permutation meaning no adjacent elements differ by 1.

First we have to consider that when $n = 2$ or $n = 3$ then it's not possible to create a beautiful permutation as the elements will always differ by 1 no matter the combination.

Otherwise all we really have to do is creating two iterators which increase by 2 in each iteration. One iterator should start at 2 and the other one at 1.

Let's say we have an iterator over the range (2..=n) where $n = 5$ and we increment by 2 in each iteration:

2	4

This will be the output of this first iterator.

Now let's look at the second iterator over the range (1..=n) where $n = 5$ and we increment by 2 in each iteration:

1	3	5

When we now combine the outputs we get:

2	4	1	3	5

We have a beautiful permutation!

In Rust we can use the chain() method to chain together two iterators. When the first iterator iterated over each element, then the second iterator will start iterating.

Code

In Rust 🦀 code:

fn main() {
    let inp = std::io::read_to_string(std::io::stdin())
        .unwrap()
        .trim()
        .parse::<u64>()
        .unwrap();

    if inp == 2 || inp == 3 { println!("NO SOLUTION"); }
    else {
        (2..=inp)
            .step_by(2)
            .chain((1..=inp).step_by(2))
            .for_each(|e| print!("{e} "));
        println!("");
    }
}