**pr. 9-1**you can use the algorithms discussed in the book as subroutines

(hint: if you need to you can use randomized algorithms)

**6.1-3****6.1-4****6.1-5****6.2-6****6.4-3****6.4-4**- Make a min-heap from elements a, b, c, d, e, f, g, h, i
(given as a list in that order). Use alphabetic order: a<b.
**make sure to use the efficient algorithm for this!* Show intermediate steps!**

- Insert (in the
given order and according to the
algorithms on the web)
the following elements
into leftist min-heap H

_{1}: e, b, j, k, dand into leftist min-heap H

_{2}: i, a, c, f -
RemoveMin
from H
_{1}above - Merge the heaps H
_{1}and H_{2}after first question above (i.e.*before*RemoveMin of the previous question). -
Make a leftist
heap from elements a, b, c, d, e, f, g, h, i (given as a list in
that order)
**make sure to use the efficient algorithm for this!**

In all the above, show intermediate steps, marking the rank of each node.

**8.3-4****8.4-2****8-4**

**10.1-6**

(that is write two simple procedures to implement Enqueue and Dequeue, using the Push and Pop)**10.1-7****10.2-5****10.2-6****10.2-7****10-1****10-2**

**Extra credit problems:**

*6.1-7***6.2-5****8.1-2****8.1-3****8.1-4***(hint - in addition to the hint in the book: use the same technique as in that section to obtain lower the bound)*

This problem is highly recommended, though not assigned - it can really tell you whether you have mastered the lower bounds proof for sorting!**8.2-4****8.3-2****8.3-3***8-1**8-2***10.1-2**