Given a fixed tree and a tree we wish to rotate, this function goes through all of the k number of clusters (from 2 onward), and each time rotates the branch which was introduced in the new k'th cluster. This rotated tree is compared with the fixed tree, and if it has a better entanglement, it will be used for the following iterations.

This is a greedy forward selection algorithm for rotating the tree and looking for a better match.

This is useful for finding good trees for a tanglegram.

- dend1
a dendrogram object. The one we will rotate to best fit dend2_fixed.

- dend2_fixed
a dendrogram object. This one is kept fixed.

- L
the distance norm to use for measuring the distance between the two trees. It can be any positive number, often one will want to use 0, 1, 1.5, 2 (see 'details' in entanglement).

- direction
a character scalar, either "forward" (default) or "backward". Impacts the direction of clustering that are tried. Either from 2 and up (in case of "forward"), or from nleaves to down (in case of "backward")

If k_seq is not NULL, then it overrides "direction".

- k_seq
a sequence of k clusters to go through for improving dend1. If NULL (default), then we use the "direction" parameter.

- dend_heights_per_k
a numeric vector of values which indicate which height will produce which number of clusters (k)

- leaves_matching_method
a character scalar passed to entanglement. It can be either "order" or "labels" (default). If using "labels", then we use the labels for matching the leaves order value. And if "order" then we use the old leaves order value for matching the leaves order value.

Using "order" is faster, but "labels" is safer. "order" will assume that the original two trees had their labels and order values MATCHED.

Hence, it is best to make sure that the trees used here have the same labels and the SAME values matched to these values - and then use "order" (for fastest results).

If "order" is used, the function first calls match_order_by_labels in order to make sure that the two trees have their labels synced with their leaves order values.

- ...
not used

A dendlist with 1) dend1 after it was rotated to best fit dend2_fixed. 2) dend2_fixed.

```
if (FALSE) {
dend1 <- USArrests[1:10, ] %>%
dist() %>%
hclust() %>%
as.dendrogram()
set.seed(3525)
dend2 <- shuffle(dend1)
tanglegram(dend1, dend2)
entanglement(dend1, dend2, L = 2) # 0.4727
dend2_corrected <- untangle_step_rotate_1side(dend2, dend1)[[1]]
tanglegram(dend1, dend2_corrected) # FIXED.
entanglement(dend1, dend2_corrected, L = 2) # 0
}
```