Introduction to Algorithms
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 14.2, Problem 4E
Program Plan Intro

To describe the implementation of RB-ENUMERATE procedure in Θ(m+lgn) time where m is the number of keys that are output and n is the number of interval nodes in the tree.

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Tl and T2 are two very large binary trees, with Tl much bigger than T2. Create an algorithm to determine if T2 is a subtree of Tl.A tree T2 is a subtree of Tl if there exists a node n in Tl such that the subtree of n is identical to T2. That is, if you cut off the tree at node n, the two trees would be identical.
You are given a tree of N nodes rooted at node 1 and each node has a value where value of i'th node is A₁. You're given Q queries, in each query two integers x, k given. Find if possible such that all nodes in the subtree of node a (including x) has values greater than or equal to k by performing swapping of two nodes any number of times. You can swap two nodes u and v such that u belongs to subtree of x (including x) and v does not. If possible then find minimum number of swapping of nodes required otherwise print -1. Note: Since the queries are independent, the initial tree is retained after each query. Input format • The first line contains T denoting the number of test cases. The description of each test case is as follows. o The first line contains an integer N denoting the number of nodes in tree. o Next line contains space-separated integers denoting value of each node. o Each of the following N- 1 lines contain two integers u and v denoting edge between nodes u and V. o The…
In java and in O(logn) time Write a method that balances an existing BST, call it balance(). A BST is balanced if the height of its left and right sub-trees are different by at most one. Recursively applied. If the tree is balanced, then searching for keys will take act like binary search and require only logn comparisons. No performance requirements on your balancing algorithm. (Come up with a way yourself - don't skip to 3.3. That section is really complicated and meant for the harder case where you need to do it in log time.)
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