Question

1a) Draw the 2-3 tree that results when you insert the keys S E A R C H X M P L Y in that order into an initially empty tree.

1b) Construct the corresponding left leaning red-black tree from part a.

1c) Find a sequence of keys to insert into a BST and a left leaning red-black BST such that the height of the BST is less than the height of the left leaning red-black BST, or prove that no such sequence is possible.

Answer 1

a) Red/Black Tree

Step 1: Insert keys S & E        

Step 2: Insert key A                           

Step 3: Insert key R

Step 4: Insert key C                                                                

Step 5: Insert key H     

Step 6: Insert key X                                                                         

Step 7: Insert key M           

Step 8: Insert key P                                                                         

Step 9: Insert keys L                 

Step 10: Insert key Y            

Which is Required Red/Black Tree

b) Binary Search Tree

Step 1: Insert keys S & E        

Step 2: Insert key A                           

Step 3: Insert key R

Step 4: Insert key C                                                                

Step 5: Insert key H     

Step 6: Insert key X                                                                         

Step 7: Insert key M           

Step 8: Insert key P                                                                         

Step 9: Insert keys L                 

Step 10: Insert key Y       

Which is Required Binary Search Tree

In above BST and Red Black Trees the Height of Red black Tree is 3 and Height of BST is 5

Therefore Height of BST is not less than Height of Red black Tree