Show the result of inserting the following sequence of keys into an initally empty AVL tree:...
Show the result of inserting the following sequence of keys into an initally empty AVL tree: 15, 10, 11, 16, 12, 30, 18, 20, 19, 17.
Homework Answers
Insert 15 : ------------Insert 10 : ------------
Insert 11 : ------------
Insert 16 : ------------
Insert 12 : ------------
Insert 30 : ------------
Insert 18 : ------------
Insert 20 : ------------
Insert 19 : ------------
Insert 17 : ------------
Insert 10 :
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Insert 11 :
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Insert 16 :
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Insert 12 :
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Insert 30 :
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Insert 18 :
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Insert 20 :
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Insert 19 :
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Insert 17 :
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Insert 15 : ------------Insert 10 : ------------
Insert 11 : ------------
Insert 16 : ------------
Insert 12 : ------------
Insert 30 : ------------
Insert 18 : ------------
Insert 20 : ------------
Insert 19 : ------------
Insert 17 : ------------
Insert 10 :
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Insert 11 :
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Insert 16 :
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Insert 12 :
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Insert 30 :
------------
Insert 18 :
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Insert 20 :
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Insert 19 :
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Insert 17 :
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Show the result of inserting the following sequence of keys into
an initally empty AVL tree:...
R-11.22 Consider the sequence of keys (5, 16, 22,45,2, 10, 18,30,50, 12,1. Draw the result of inserting entries with these keys (in the given order) into a. An initially empty (2,4) tree. b. An i...
R-11.22 Consider the sequence of keys (5, 16, 22,45,2, 10, 18,30,50, 12,1. Draw the result of inserting entries with these keys (in the given order) into a. An initially empty (2,4) tree. b. An initially empty red-black tree
R-11.22 Consider the sequence of keys (5, 16, 22,45,2, 10, 18,30,50, 12,1. Draw the result of inserting entries with these keys (in the given order) into a. An initially empty (2,4) tree. b. An initially empty red-black tree
Red-Black Tree: Show the sequence of red-black trees that result after successively inserting the keys into...
Red-Black Tree: Show the sequence of red-black trees that result after successively inserting the keys into an initially empty red-black tree in the order given: K = < 20, 5, 1, 12, 7 >. (Show at least one tree resulting from each insertion). State which case from the textbook (Introduction to Algorithms, 3rd Edition by Thomas H. Cormen et al) applies. Assume that the root is always colored black.)
• P1 (10 pts) Show the result of inserting 2, 9, 5, 8, 6, 4, 3,...
• P1 (10 pts) Show the result of inserting 2, 9, 5, 8, 6, 4, 3, 1 into an initially empty AVL tree (draw a resulting tree after inserting each number; you need to draw 8 AVL trees). • P2 (5 pts) What is the minimum number of nodes in an AVL tree of height 8? • P3 (5 pts) Show the result of deleting the element with key 9' from the following splay tree. • P4 (5 pts) Show...
Show the 2-3-4 tree after inserting the following keys: 12, 10, 15, 17, 19, 14, 16,...
Show the 2-3-4 tree after inserting the following keys: 12, 10, 15, 17, 19, 14, 16, 13, 22, 25, and 24. Show the tree after each insertion.
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
Trees and Heaps 1. Show that the maximum number of nodes in a binary tree of...
Trees and Heaps 1. Show that the maximum number of nodes in a binary tree of height h is 2h+1 − 1. 2. A full node is a node with two children. Prove that the number of full nodes plus one is equal to the number of leaves in a nonempty binary tree. 3. What is the minimum number of nodes in an AVL tree of height 15? 4. Show the result of inserting 14, 12, 18, 20, 27, 16,...
Show the result of inserting 3, 1, 4, 6, 9, 2, 5, 7 into an AVL...
Show the result of inserting 3, 1, 4, 6, 9, 2, 5, 7 into an AVL tree. Make sure to show each rotation. Note: There are no double rotations in this sequence.
Build a splay tree inserting keys: 2, 13, 17, 4, 7, 19, 5, 8, 22, 6,...
Build a splay tree inserting keys: 2, 13, 17, 4, 7, 19, 5, 8, 22, 6, 10. Show each step! a. Show the result of accessing keys 5, 8, 7 in order in the splay tree. Show the tree after each access. b. Show the result of deleting keys 10, 8, 7 in the splay tree. Start with the original tree and show the tree after each deletion.
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...
R-11.22 Consider the sequence of keys (5, 16, 22,45,2, 10, 18,30,50, 12,1. Draw the result of inserting entries with these keys (in the given order) into a. An initially empty (2,4) tree. b. An initially empty red-black tree
R-11.22 Consider the sequence of keys (5, 16, 22,45,2, 10, 18,30,50, 12,1. Draw the result of inserting entries with these keys (in the given order) into a. An initially empty (2,4) tree. b. An initially empty red-black tree
• P1 (10 pts) Show the result of inserting 2, 9, 5, 8, 6, 4, 3, 1 into an initially empty AVL tree (draw a resulting tree after inserting each number; you need to draw 8 AVL trees). • P2 (5 pts) What is the minimum number of nodes in an AVL tree of height 8? • P3 (5 pts) Show the result of deleting the element with key 9' from the following splay tree. • P4 (5 pts) Show...
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...
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