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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Question
Chapter 13.1, Problem 7E
Program Plan Intro
To find the largest and the smallest possible ratio of red internal nodes to black internal nodes in a red black tree on n keys.
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For a full 5-ary tree, where n = the number of nodes, i = the number of internal nodes, and l = the number of leaves:
find i and l, if n = 996;
find n and l, if i = 333;
find n and i, if l = 569;
Every Red-Black Tree is an AVL tree (if we ignore colors)?
What is the maximum height of a 2-3 tree with n keys? Give the reasoning in terms of n.
Chapter 13 Solutions
Introduction to Algorithms
Ch. 13.1 - Prob. 1ECh. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.2 - Prob. 1ECh. 13.2 - Prob. 2ECh. 13.2 - Prob. 3E
Ch. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.4 - Prob. 1ECh. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Prob. 6ECh. 13.4 - Prob. 7ECh. 13 - Prob. 1PCh. 13 - Prob. 2PCh. 13 - Prob. 3PCh. 13 - Prob. 4P
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- A tree with ? nodes always has ___ edges. (A) ?−1 (B) ? (C) ?+1 (D) 2? Which is right answer and explain whyarrow_forwardAssume we have a full 4-ary tree, which contains 100 leaves. How many internal nodes are there, and how many nodes in total are there?arrow_forwardWhat is the optimal binary tree with weights 15,20,40,50arrow_forward
- Illustrate that the nodes of any AVL tree T can be colored “red” and “black” so that Tbecomes a red-black tree.arrow_forwardWhat maximum difference in heights between the leafs of a AVL tree is possible? * a) log(n) where n is the number of nodes b) n where n is the number of nodes c) 0 or 1 d) atmost 1arrow_forwardGive one example each for the following types of binary tree:(a) Unbalanced binary tree (b) Perfectly balanced binary tree (c) Complete binary tree (d) Full binary tree.arrow_forward
- Draw a AVL tree for given sequence of numbers: 2, 9, 7, 6, 5, 8, 11, 4, 3arrow_forwardConsider a binary tree with 11 levels and a root node at depth 0. What is the maximum number of nodes in the tree if it is full?arrow_forwardFor a Binary Tree with 1023 (= 2^10 - 1) items what is the minimum height? The maximum?arrow_forward
- Give an example set of 8 characters and their associated frequencies such that in the Huffman tree for this set, the binary tree is COMPLETE (not full)arrow_forwardis this true or false? In a red and a black tree all keys inside the right sub tree of a node has to be bigger than the key inside that node.arrow_forwardA tree is k-ary if every internal node has exactly ? children. Prove by Math. Induction that a k-ary tree with ? internal nodes has exactly ? + (? − 1)(? − 1) leavesarrow_forward
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