PROBLEM SET 4

Draw the 2-3-4 tree that results when the keys E A S Y Q U E S T I O N are inserted into an initially empty tree. Next, draw the red black tree that results when the same keys are again inserted into an empty tree.



Draw the randomized BST that results when the keys E A S Y Q U E S T I O N are inserted into an initially empty tree, assuming that the randomization results in the Q and the T being inserted at the top.



Draw the table that results when the keys 31 41 59 26 25 48 35 21 11 13 29 are inserted into an initially empty hash table of size 13 using linear probing with hash function h(x) = x mod 13. Answer the same question if if double hashing is used (h1(x) = x mod 13, h2(x)= x mod 8).



Extra Credit. Give upper and lower bounds on the height of a B-tree of order 100 with one billion keys.

Due: Wednesday, March 6.