Design and Analysis of Algorithms 1. For each of the following lists, construct an AVL tree...
Design and Analysis of Algorithms
1. For each of the following lists, construct an AVL tree by inserting their elements successively, starting with the empty tree.
3, 2, 1, 4, 5, 6, 7
2. Construct a 2-3 tree for the list W, E, L, C, O, M, E, Y, O, U. Use the alphabetical order of the letters and insert them successively starting with the empty tree.
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Design and Analysis of Algorithms
1. For each of the following lists,
construct an AVL tree...
Not asking for code. For each of the following lists, construct both an AVL tree and...
Not asking for code.
For each of the following lists, construct both an AVL tree and a 2-3 tree by inserting their elements successively, starting with the empty tree. 1, 2, 3, 4, 5, 6 6, 3, 2, 1, 4, 5
a. Construct a 2-3 tree for the list C, O, M, P, U, T, I, N,...
a. Construct a 2-3 tree for the list C, O, M, P, U, T, I, N, G. Use the alphabetical order of the letters and insert them successively starting with the empty tree. b. Assuming that the probabilities of searching for each of the keys (i.e., the letters) are the same, find the largest number and the average number of key comparisons for successful searches in this tree.
1. Apply both the left-to-right and right-to-left binary exponentiation algorithms to compute a^ 25. 7. For...
1. Apply both the left-to-right and right-to-left binary exponentiation algorithms to compute a^ 25. 7. For each of the following lists, construct both an AVL tree and a 2-3 tree (use ascending and alphabetical order as applicable): ( a) 3 6 5 1 2 4 (b) A B C D E F (c) Z Y X W V W
True or false? (a) An insertion in an AVL tree with n nodes requires Θ (log(n))...
True or false? (a) An insertion in an AVL tree with n nodes requires Θ (log(n)) rotations. (b) A set of numbers are inserted into an empty BST in sorted order and inserted into an empty AVL tree in random order. Listing all elements in sorted order from the BST is O (n), while listing them in sorted order from the AVL tree is O (log(n)). (c) If items are inserted into an empty BST in sorted order, then the...
Will give thumb up for the correct answer. (20 points) Construct both the AVL and...
Will give thumb up for the correct answer.
(20 points) Construct both the AVL and 2-3 trees by inserting the elements 7, 2, 4, 9, 5, 1 into empty trees. Show the trees after every insertion. You also need to provide the balance factor for the nodes of the AVL tree.
6. Draw a diagram of the double RL-rotation in its general form. A partial solution is...
6. Draw a diagram of the double RL-rotation in its general form. A partial solution is given. Fill in the missing parts inside the box. (pt) For the following list of numbers, construct an AVI tree by inserting their elements successively, starting with the empty tree. 1.2.3.4.5.6. The insertions of the first 4 numbers are given. Draw diagrams to show the rest of the process. Note that you need to indicate the balance factor of each node, diagrams before and...
Draw an AVL tree (initially empty) at each step when inserting the following numbers in order:...
Draw an AVL tree (initially empty) at each step when inserting the following numbers in order: 1; 2; 5; 4; 6; 3; 10; 9; 7; 8 Now, draw the above AVL tree at each step when deleting the following numbers in order (assuming that the substitution on deleting a node is done by replacing it with the minimum in the right subtree): 4; 5; 6
Consider the AVL Tree built by inserting the following sequence of integers, one at a time:...
Consider the AVL Tree built by inserting the following sequence of integers, one at a time: 5, 2, 8, 7,9 Then we insert 11. After we insert 11, before we perform any necessary rotations, is the tree balanced? And if not, which is the root of the lowest imbalanced subtree? (a) None, since the tree is already balanced after inserting 11. (b) The node containing 5. (c) The node containing 8. (d) The node containing 11. (e) The node containing...
1. Let A = {a1, ..., an} and B = {b1, ..., bm} be two sets...
1. Let A = {a1, ..., an} and B = {b1, ..., bm} be two sets of numbers. Consider the problem of finding their intersection, i.e., the set C of all the numbers that are in both A and B. a. Design a presorting based algorithm for solving this problem and determine its efficiency class. 2. Estimate how many searches will be needed to justify time spent on presorting an array of 103 elements if sorting is done by mergesort...
Assume the following notation/operations on AVL trees. An empty AVL tree is denoted E. A non-empty AVL tree T has three...
Assume the following notation/operations on AVL trees. An empty AVL tree is denoted E. A non-empty AVL tree T has three attributes The key T.key is the root node's key. The left child T.left is Ts left subtree, which is an AVL tree (possibly E). The right child T.right is T's right subtree, which is an AVL tree (possibly E). (a) 5 marsl Write a function RANGECOUNT(T, lo, hi) to count the number of nodes in an AVL tree with...
Not asking for code.
For each of the following lists, construct both an AVL tree and a 2-3 tree by inserting their elements successively, starting with the empty tree. 1, 2, 3, 4, 5, 6 6, 3, 2, 1, 4, 5
a. Construct a 2-3 tree for the list C, O, M, P, U, T, I, N, G. Use the alphabetical order of the letters and insert them successively starting with the empty tree. b. Assuming that the probabilities of searching for each of the keys (i.e., the letters) are the same, find the largest number and the average number of key comparisons for successful searches in this tree.
True or false? (a) An insertion in an AVL tree with n nodes requires Θ (log(n)) rotations. (b) A set of numbers are inserted into an empty BST in sorted order and inserted into an empty AVL tree in random order. Listing all elements in sorted order from the BST is O (n), while listing them in sorted order from the AVL tree is O (log(n)). (c) If items are inserted into an empty BST in sorted order, then the...
Will give thumb up for the correct answer.
(20 points) Construct both the AVL and 2-3 trees by inserting the elements 7, 2, 4, 9, 5, 1 into empty trees. Show the trees after every insertion. You also need to provide the balance factor for the nodes of the AVL tree.
6. Draw a diagram of the double RL-rotation in its general form. A partial solution is given. Fill in the missing parts inside the box. (pt) For the following list of numbers, construct an AVI tree by inserting their elements successively, starting with the empty tree. 1.2.3.4.5.6. The insertions of the first 4 numbers are given. Draw diagrams to show the rest of the process. Note that you need to indicate the balance factor of each node, diagrams before and...
Consider the AVL Tree built by inserting the following sequence of integers, one at a time: 5, 2, 8, 7,9 Then we insert 11. After we insert 11, before we perform any necessary rotations, is the tree balanced? And if not, which is the root of the lowest imbalanced subtree? (a) None, since the tree is already balanced after inserting 11. (b) The node containing 5. (c) The node containing 8. (d) The node containing 11. (e) The node containing...
Assume the following notation/operations on AVL trees. An empty AVL tree is denoted E. A non-empty AVL tree T has three attributes The key T.key is the root node's key. The left child T.left is Ts left subtree, which is an AVL tree (possibly E). The right child T.right is T's right subtree, which is an AVL tree (possibly E). (a) 5 marsl Write a function RANGECOUNT(T, lo, hi) to count the number of nodes in an AVL tree with...
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