Homework 4
Due: Thursday, November 10
Turn in this assignment on paper in class.
- Question R-8.24 of textbook (p. 362): Draw an example of a heap whose keys are all the odd numbers from 1 to 59 (without repetition), such that inserting 32 into the heap will result in 32 bubbling up to a position as one of the children of the root. Draw the initial heap and the final heap. Then mark the path taken by 32 bubbling up in the final heap.
- Question C-8.14 of textbook (p. 364):
Given a min heap T and a key k, describe an algorithm that
prints out the entries of T that are less than or equal to
k (in any order). Your algorithm should run in time proportional
to the number of items printed out.
Describe your algorithm in English. Pseudo-code is optional and does not replace an English description. Briefly justify the running time of your algorithm.
- Suppose that we have a max heap stored as an array. You are
given an index i for an item to be removed from the heap.
Describe how this can be accomplished in O(log n) time.
Again, describe your algorithm in English. Pseudo-code is optional and does not replace an English description. Briefly justify the running time of your algorithm.
- We insert the numbers 1, 2, 3, 4, ..., 2k - 1 in
a Leftist Heap. Let's make that a min heap.
- Suppose that we insert the numbers in increasing order. What is the shape of the resulting Leftist Heap?
- Suppose that we insert the numbers in decreasing order (i.e., insert 2k - 1, 2k - 2, 2k - 3, ..., 3, 2, 1). What is the shape of the resulting Leftist Heap?