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Tham khảo tài liệu 'feaculty of computer science and engineering department of computer scienc tutorial 4 questions', công nghệ thông tin, kỹ thuật lập trình phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Faculty of Computer Science and Engineering Department of Computer Science DATA STRUCTURES ALGORITHMS Tutorial 4 Questions AVL Tree and Heap Part 1. AVL Tree Required Questions Question 1. For each of the following key sequences determining the AVL tree obtained when the keys are inserted one-by-one in the order given into an initially empty tree a 1 2 3 4 5 6 7. b 4 2 1 3 6 5 7. c 1 6 7 2 4 3 5. d 45 9 2 17 84 92 71 18 30 62 55 20 27 Question 2. For each of the AVL trees obtained in Question 1 determine the tree obtained when the root is withdrawn. Question 3. Write a global function in pseudo code to generate an AVL tree from an input list by insert elements in the list into an initial empty AVL. Refer to Question 1 for an example. algorithm generateAVLfromList val list List This algorithm generate a AVL from the input list Pre Post the AVL is built by inserting elements in the list into an initial empty tree one-by-one from the beginning of the list. Return the AVL end generateAVLfromList Question 4. Devise an algorithm to test whether a given binary search tree is AVL balanced. algorithm testAVL val tree BSTTree Pre Post. Return true if tree is an AVL otherwise return false end testAVL Advanced Questions Question 5. Devise an algorithm to merge the contents of two binary search trees into one. What is the running time of your algorithm 1 3 Faculty of Computer Science and Engineering Department of Computer Science Question 6. Suggest a data structure that supports the following operation and given time complexities Operation Complexity Init Init the DS with n real numbers unordered O nlogn Insert x Insert x to the DS O logn findMin Return the value of the minimal element O logn findMax Return the value of the maximal element O logn findMed Return the value of the median element O 1 DelMin Remove the minimal element O logn DelMax Remove the maximal element O logn DelMed Remove the median element O logn Part 2. Heap Required Questions Question 7. Show the heap .
