Generating permutations

Next we consider the problem of generating all permutations of a set of $n$ elements. For example, the permutations of $\{0,1,2\}$ are $(0,1,2)$, $(0,2,1)$, $(1,0,2)$, $(1,2,0)$, $(2,0,1)$ and $(2,1,0)$.

Like subsets, permutations can be generated using recursion. The following function .search() goes through the permutations of the set $\{0,1,\ldots,n-1\}$. The function builds a vector permutation that contains the permutation, and the search begins when the function is called with parameters:

#![allow(unused)]
fn main() {
fn search(permutation: &mut Vec<usize>, n: usize, chosen: &mut Vec<bool>){
    if permutation.len() == n{
        // process permutation
        println!("{permutation:?}");
    } else {
        for i in 0..n{
            if chosen[i] {continue}
            chosen[i] = true;
            permutation.push(i);
            search(permutation, n, chosen);
            chosen[i] = false;
            permutation.pop();
        }
    }
}
let mut permutation = Vec::new();
let n = 4;
let mut chosen = vec![false;n];
println!("Permutation of {n}:");
search(&mut permutation, n, &mut chosen);
}