strong>Question 1 What is the worst case running time for adding an item to an AVL tree? Group of answer choices (a) O(N log N) (b) O(log N) (c) O(1) (d) O(N) Question 2 What is the worst case running time for removing an arbitrary item from a singly linked list? Group of answer choices (a) O(N) (b) O(N log N) (c) O(1) (d) O(log N) Question 3 What is the worst case running time for adding an item to the rear of a doubly linked list? Group of answer choices (a) O(1) (b) O(N/2) (c) O(N) (d) O(log N) Question 4 What is the worst case running time for removing an item located exactly in the middle of a doubly linked list that is traversable from either end? Do not ignore coefficients. Group of answer choices (a) O(N/2) (b) O(log N) (c) O(N) (d) O(1)
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QUESTION 3: Construct an AVL tree by using the following data: 14, 17, 11, 7, 53, 4, 13, 12, 8, 60, 19, 16, 20. NOTE: Show insertions and balance factor for every node inserted. Write every new insertion in a different step. QUESTION 4: Show the Red-Black tree after successfully inserting the keys 42, 39, 33, 14, 20, 9. NOTE: Show insertions and specify color for every node inserted. Write every new insertion in a different step. QUESTION 5: i) Which traversal outputs the data in a sorted order in a BST? ii) What is the worst-case time complexity to delete an element from a BST? iii) What is a BST whose leaves are external nodes? iv) Write all the properties of Red-Black Trees. v) What are the advantages of Tree Data Structures? vi) What is the maximum difference in heights between the leaves of an AVL Tree that is possible? vii) Write the pseudocode for double rotation (Right, Left) in an AVL Tree. viii) Write the algorithm for deleting the element (all cases) in a BST. ix) Why do we prefer Red-Black Trees over AVL Trees? x) What is the worst-case time complexity to perform an operation in Red-Black Trees?
Madhur L.
4. (10%) Fill Big-O notations in the following table for the comparison of different Priority Queue implementations. Priority Queue Implementation Enqueue Dequeue Heap Binary Search Tree Balanced Skewed Unsorted List Sorted List 5. (10%) Select your answer from A, B, C, D, E, F, and G for each blank in the following statements. A. selectionSort B. bubbleSort C. shortBubble D. insertionSort E. mergeSort F. quickSort G. heapSort (1) ______'s Big-O complexity is O(N) for Best case. (2) ______ recognize(s) if the values are already sorted. (3) ______ is (are) inherently unstable. (4) ______'s Big-O complexity is always O(N^2) for Best case, Average case, and Worst case. (5) ______'s Big-O complexity is always O(log2N) for Best case, Average case, and Worst case.
Akash M.
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