/// <https://en.wikipedia.org/wiki/Steinhaus%E2%80%93Johnson%E2%80%93Trotter_algorithm>
pub fn steinhaus_johnson_trotter_permute<T: Clone>(array: &[T]) -> Vec<Vec<T>> {
    let len = array.len();
    let mut array = array.to_owned();
    let mut inversion_vector = vec![0; len];
    let mut i = 1;
    let mut res = Vec::with_capacity((1..=len).product());
    res.push(array.clone());
    while i < len {
        if inversion_vector[i] < i {
            if i % 2 == 0 {
                array.swap(0, i);
            } else {
                array.swap(inversion_vector[i], i);
            }
            res.push(array.to_vec());
            inversion_vector[i] += 1;
            i = 1;
        } else {
            inversion_vector[i] = 0;
            i += 1;
        }
    }
    res
}

#[cfg(test)]
mod tests {
    use quickcheck_macros::quickcheck;

    use crate::general::permutations::steinhaus_johnson_trotter::steinhaus_johnson_trotter_permute;
    use crate::general::permutations::tests::{
        assert_permutations, assert_valid_permutation, NotTooBigVec,
    };

    #[test]
    fn test_3_different_values() {
        let original = vec![1, 2, 3];
        let res = steinhaus_johnson_trotter_permute(&original);
        assert_eq!(res.len(), 6); // 3!
        for permut in res {
            assert_valid_permutation(&original, &permut)
        }
    }

    #[test]
    fn test_3_times_the_same_value() {
        let original = vec![1, 1, 1];
        let res = steinhaus_johnson_trotter_permute(&original);
        assert_eq!(res.len(), 6); // 3!
        for permut in res {
            assert_valid_permutation(&original, &permut)
        }
    }

    #[quickcheck]
    fn test_some_elements(NotTooBigVec { inner: original }: NotTooBigVec) {
        let permutations = steinhaus_johnson_trotter_permute(&original);
        assert_permutations(&original, &permutations)
    }
}