Give a search algorithm on an R-tree for efficiently finding the nearest neighbor to a given query point.

Suppose we consider the special case of IS, WIS where the input graph is a tree T (V, E) with an identified root r ≤ V (there are no other limitations on structure). This means that for every v € V(T), the subtree rooted at v is well-defined - we will refer to this subtree as Tv. = In this section, you are asked to develop a polynomial-time algorithm for solving WIS (and including IS, when weights are all 1). For every v € V, we define the following: Kv,o to be the total weight of the maximum-weight Independent set of subtree T, which does not include v itself. • Kv,1 to be the total weight of the maximum-weight Independent set of subtree T with v belonging to the independent set. D(i) Develop a pair of recurrences which express the value of к,0 (and similarly of ×,₁) in terms of the values of the child nodes of v. Include the "base case" whsn v is a leaf, and then describe how we can exploit the recurrences to design a polynomial-time algorithm to solve WIS for a tree. D(ii) In the…

How many children is each node allowed to have in a binary search tree?  Answer all that apply.  I know one of the answers is 2 but there is at least another one.     3     1     0     2

Let T be a rooted tree. The height of T is 5. Every node of T has at most 3 children. How many leaves can T have at the most?

Use the procedure TREE-SUCCESSOR and TREE-MINIMUM to write a function of x, x is a node in a binary search tree, to produce the output that INORDERTREE-WALK function would produce. Determine the upper bound running time complexity of F(x) and prove its correctness.