## DEV Community

Aya Bouchiha

Posted on • Updated on

# Rotation in AVL tree

Hi, on this amazing day we're going to discuss rotation in the AVL tree! if you're not familiar with AVL trees check this post.

#day_19

## Type of Rotation

before starting, I want to remention that the BalanceFactor `BalanceFactor = height(left sub-tree) - height(right sub-tree)` should be -1, 0 or 1.

### Right rotation

We use this rotation when the tree is a left unbalanced tree like this example below:

``````     15 (bf:2)
/
11 (bf:1)      left unbalanced tree
/
9 (bf:0)
``````

in this case, the tree needs a right rotation (RR), so the unbalanced node(15) becomes a right child of its left child (11)

``````           11  (bf:0)
/    \
(bf:0)  9     15 (bf:-0)
``````

### Left rotation

We use this rotation when the tree is a right unbalanced tree like this example below:

`````` 15 (bf:-2)
\
17 (bf:-1)   right unbalanced tree
\
19 (bf:0)
``````

in this case, the tree needs a left rotation (LL), so the unbalanced node(15) becomes a left child of its right child (17)

``````           17  (bf:0)
/    \
(bf:0)  15     19 (bf:0)
``````

### Right-Left rotation

The Right Left Rotation is a combination of right rotation followed by a left rotation. Let's see this example:

``````15 (bf:-2)
\
19 (bf:1)
/
16 (bf:0)
``````

firstly, we'll perform a right rotation so this tree we'll be like this:

``````     15 (bf:-2)
\
16 (bf:-1)
\
19 (bf:0)
``````

then we'll perform a left rotation because the tree becomes a right unbalanced tree. That's why (15) will become the left child of its right child (16)

``````         16 (bf:0)
/  \
(bf:0)15    19 (bf:0)
``````

### Left-Right rotation

The Left-Right Rotation is a combination of left rotation followed by a right rotation. Let's see this example:

``````    15  (bf:2)
/
11 (bf:-1)
\
13 (bf:0)
``````

firstly, we'll perform a left rotation of the tree we'll be like this:

``````     15 (bf:2)
/
13  (bf:1)
/
11 (bf:0)
``````

then we'll perform a right rotation because the tree becomes a left unbalanced tree. That's why (15) will become the right child of its left child (13)

``````          13 (bf:0)
/  \
(bf:0) 11    15 (bf:0)
``````

Tomorrow, I'll cover the implementation of insertion using python!
Thank you for your time and happy coding!