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Aya Bouchiha
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)
Enter fullscreen mode Exit fullscreen mode

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)
Enter fullscreen mode Exit fullscreen mode

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)
Enter fullscreen mode Exit fullscreen mode

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)
Enter fullscreen mode Exit fullscreen mode

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)
Enter fullscreen mode Exit fullscreen mode

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

     15 (bf:-2)
      \
       16 (bf:-1)
        \
         19 (bf:0)
Enter fullscreen mode Exit fullscreen mode

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)
Enter fullscreen mode Exit fullscreen mode

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)
Enter fullscreen mode Exit fullscreen mode

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

     15 (bf:2)
    /
   13  (bf:1)
  /
11 (bf:0)
Enter fullscreen mode Exit fullscreen mode

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)
Enter fullscreen mode Exit fullscreen mode

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

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