Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 12.2, Problem 6E
Program Plan Intro
To show that if right sub-tree of a node x in T is empty and x has a successor y then y is the lowest ancestor of x whose left child is also an ancestor of x.
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Consider a binary search tree (BST) whose elements are the name of animals.
Starting with an empty BST, show the effect of successively adding the following elements: cow, fox, bat, ant, lion, cat, goat, dog,and pig.
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Prove that any binary tree of height h (where the empty tree is height 0, and a tree witha single node is height 1) has between h and 2h − 1 nodes, inclusive. A binary tree is onein which every node has at most three edges (at most one to the ’parent’ and two to the’children.’)
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Chapter 12 Solutions
Introduction to Algorithms
Ch. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5E
Ch. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12 - Prob. 1PCh. 12 - Prob. 2PCh. 12 - Prob. 3PCh. 12 - Prob. 4P
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- Create a binary search tree as discussed in class, using the given numbers in the order they’re presented. State if the resulting tree is has the attributes of being FULL, BALANCED, or COMPLETE. 37, 20, 18, 56, 40, 42, 12, 5, 6, 77, 21, 54arrow_forwardLet T be an arbitrary splay tree storing n elements A1, A2, . An, where A1 ≤ A2 ≤ . . . ≤ An. We perform n search operations in T, and the ith search operation looks for element Ai. That is, we search for items A1, A2, . . . , An one by one. What will T look like after all these n operations are performed? For example, what will the shape of the tree be like? Which node stores A1, which node stores A2, etc.? Prove the answer you gave for formally. Your proof should work no matter what the shape of T was like before these operations.arrow_forward2. We are given a complete binary tree with height h and n nodes. The link between a node and its left child is labeled as 0 and the link between a node and its right child is labeled as 1. A path from the root to each external node at the last level can be labeled by an h-tuple (X1, X2, ..., xh) of 1s and Os that lie on its links. See the following example: 0 0 1 1 0 0 1 0 (0,0,0) (0,1,1)arrow_forward
- Show the result of inserting 30, 10, 40, 60, 90, 20, 50, 70 into an initially empty binary search tree. b) Is the above tree a full binary tree? Why? Why not? c)Draw the subtree with the root node as 60.arrow_forwardD) Draw a binary tree whose inorder traverse is T , W , B , P , Y , R , M , X , L , K , S , A and preorder traverse is R , T , P , W , B , Y , K , M , L , X , S , Aarrow_forwardFor the given complete binary tree (given in an array): 1 2 3 4 5 6 7 8 9 10 11 J B K A O T U X R Q D Convert it into a max heap and provide your answer by dragging and dropping the given alphabets on correct positions in array.arrow_forward
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- Given an empty Binary Search Tree (BST). After performing the following insertion operations, INSERT 78 23 11 44 22 45 98 2 16 what is the right child of 11 in the resulting BST?arrow_forwardWe say that a binary search tree T1 can be right-converted to binary search tree T2 if it is possible to obtain T2 from T1 via a series of right rotations. Please draw diagram and Give an example of two trees T1 and T2 such that T1 cannot be right-converted to T2. Explain your answer.arrow_forwardYour colleague proposed a different definition of a binary search tree: it is such binary tree with keys in the nodes that for each node the key of its left child (if exists) is bigger than its key, and the key of its right child (if exists) is less than its key. Is this a good definition for a binary search tree? A. Yes B. Noarrow_forward
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