ECS32B California Davis Stable Merge Sort and Heap Representations Problem Paper All the work should be done in the file hwX.py, so the structure of the co

ECS32B California Davis Stable Merge Sort and Heap Representations Problem Paper All the work should be done in the file hwX.py, so the structure of the code should be exactly same as hwX.py

Please see both of the attchments

the instruction and homework is attached

you will work in hwX.py(in the zip),

and after you finished,

run hwX_test.py all statement should be saying “ok” Makeup Assignment:
Problem 1? (30 points) stable merge sort
Consider the following unsorted list of integers containing duplicates where the relative position
of each duplicated integer in the unsorted list is noted as a subscript. For example, 1?1? is at a
smaller index than 1?2?. The subscript is ignored when comparing two values since it would not
actually be present in the underlying Python representation of this list.
8?1
4?1
1?1
4?2
8?2
1?2
A sorting algorithm is ?stable? if the relative position of duplicate items is preserved. Stable
sorting can be a useful property in many instances. The list below represents a stable sort of he
list above.
1?1
1?2
4?1
4?2
8?1
8?2
Another example would be sorting a list by first name and then by last using a stable sorting
algorithm. This would order everybody with the same last name by their first name.
You will modify the merge sort procedure from lecture 20 to demonstrate that merge sort can be
stable. Hint: consider how ties should be broken during the merge phase.
To demonstrate that the modified merge sort procedure modify it so it sorts a list of tuples by
their second position. The tuples contain the first and last names of some random individuals.
Problem 2? (15 points) unstable selection sort
You will show that selection sort is unstable by sorting the same list of tuples in part 1 by their
second position. Note that the first names of people with the same last name are no longer in
sorted order.
Problem 3: ?(30 points) Heap Representations
Part 1:
Convert the following maxheap from a tree representation to a Python list representation.
Part 2:
Show the new state of the maxheap in a Python list representation after inserting the value 63
into the maxheap and restoring the heap order property.
Part 3:
Show the state of the maxheap in a Python list representation after removing the value 89 from
the ?original? maxheap and restoring the heap order property.
Problem 4 ?(25 points) Tree traversal
Consider the following tree containing integer values at each node. Traverse the tree in the
order specified. When visiting each node, the operation you will perform is to append the integer
to the end of a Python list. In your homework file specify the list of integers that results from
each traversal approach.
Part a. inorder
Part b. preorder
Part c. postorder
Part d. levelorder (see lecture 23)

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