14
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
before starting, I want to remention that the BalanceFactor BalanceFactor = height(left sub-tree) - height(right sub-tree) should be -1, 0 or 1.
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)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)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)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!
14