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Illustrate that the nodes of any AVL tree T can be
colored "red" and "black" so that T becomes a
red-black tree.
```plaintext
AVL Tree Red-Black Tree
(20:3) (20:b)
/ \ --> / \
(15:2) (30:2) (15:b) (30:b)
/ \ \ / \ \
(10:1) (17:1) (35:1) (10:r) (17:r) (35:r)
* perform pre order traversal
* assign colour of Red/Black node based on height of each AVL node
Step 1:
(20:b)
Step 2:
(20:b)
/
(15:b)
Step 3:
(20:b)
/
(15:b)
/
(10:r)
Step 4:
(20:b)
/
(15:b)
/ \
(10:r) (17:r)
Step 5:
(20:b)
/ \
(15:b) (30:b)
/ \
(10:r) (17:r)
Step 6:
(20:b)
/ \
(15:b) (30:b)
/ \ \
(10:r) (17:r) (35:r)
```
Illustrate that via AVL single rotation, any binary search tree T1 can be
transformed into another search tree T2 (with the same items).
Left rotation:
```plaintext
(10) (20)
\ / \
(20) -> (10) (30)
\
(30)
```
Right rotation:
```plaintext
(30) (20)
/ / \
(20) --> (10) (30)
/
(10)
```
Left-Right rotation:
```plaintext
(30) (20)
/ / \
(10) -> (10) (30)
\
(20)
```
Right-Left rotation:
```plaintext
(10) (20)
\ / \
(30) --> (10) (30)
/
(20)
```
Give an algorithm to perform this transformation using O(N log N) rotation on average.
See `./avl_tree.c`.
|
