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In 2-3-4 trees, new elements are always inserted at the leaf nodes.

Give the Big-oh complexity for the following sorting algorithms. (2 pts each) a)  Quicksort (average case) b)  bottom-up Merge sort c)  Insertion sort on an almost sorted list d)  Heap sort (average case) e)  Shell sort (average case)

For the tree given in Question #1, give the results of using preorder traversal.

Show the order of elements in the array after each of the first two passes of the selection-sort algorithm applied to the array: int arr[10] = {12, 8, 22, 11, 7, 2, 4, 5, 9, 3}  Note: The array is to be sorted with the smallest element in position arr[0].  Pass 1: Pass 2:

Which of the following terms is a progressive, degenerative disorder that results in tremors, gait changes, and occassionally dementia?

For the tree given in Question #1, which node(s) is/are the leaves?

Show the result (on an element by element basis) of inserting the following integers into an initially empty heap.  Use the property that the root is to be the largest element.  Make sure that you clearly draw all 8 heaps using sequential representation for each heap.  Be complete in your representation giving the index values.                   5      9     13     3     7    15    26    10 

Quicksort performs with complexity Big Oh (n log n) when the list being sorted is in reverse-sorted order.

Consider the heap shown below.  It will be used for Questions #14-16. Give the sequential representation of this heap (uses an array). Be sure to correctly indicate the index positions for each element. 

Show the resulting 7 Red/Black trees that occur when inserting the following keys: T   W   V   Y   M   E   B   For each tree, CLEARLY denote which links are “red”.  Also, clearly denote where splits, single rotations and double rotations occur.  Follow the conventions discussed and demonstrated in class.