Question

Maximum how many nodes can there be in a complete Binary Tree
with level *h*? (java programing)

Answer #1

1. a) Suppose that a binary tree of height h has n nodes. Show
that h ≥ log2 (n+2) - 1.
b) Using the formula in part (a) find the minimum height if a
binary tree with 1000 nodes.
c) What is the maximum possible height of a binary tree with
1000 nodes?

How
many levels will there be in a complete binary tree is it has n
number of nodes?
looking for formula

Write a routine to list out the nodes of a binary tree in
level-order. List the root, then nodes at depth 1, followed by
nodes at depth 2, and so on. You must do this in linear time. Prove
your time bound (Java)

How can I prove that any node of a binary search tree of n nodes
can be made the root in at most n − 1 rotations?

Suppose a binary tree stores integers. Write efficient methods
(and give their Big-Oh running times) that take a reference to a
binary tree root T and compute
a. the number of nodes with two children that contain the same
value
**JAVA**

A binary tree isfullif every non-leaf node has exactly two
children. For context, recallthat we saw in lecture that a binary
tree of heighthcan have at most 2h+1−1 nodes, and thatit achieves
this maximum if it iscomplete, meaning that it is full and all
leaves are at the samedistance from the root. Findμ(h),
theminimumnumber of nodes that a full tree of heighthcan have, and
prove your answer using ordinary induction onh. Note that tree of
height of 0 isa single...

Prove that a full non-empty binary tree must have an odd number
of nodes via induction

Problem 3
Given a BST with N nodes, how many tree shapes are there with
height N-1? Explain your reasoning.
Problem 4
Given a BST with N nodes, how many tree shapes are there with
height N-2? Explain your reasoning .
Problem 5
Consider an empty 2-3 tree. Draw the tree after each of the
following operations is executed:
insert 0, insert 9, insert 2, insert 6, insert 7, insert 3,
insert 8, delete 2, delete 6

what is the common between binary search tree and B tree? Can
all the binary search tree be considered a special case of some
vaild B tree why or why not?

Let T be a complete binary tree such that node v stores
the entry (p(v), 0), where p(v) is the level number of v. Is tree T
a heap? Why or why not?
I know that a complete binary tree is a heap, but shouldn't we
also take into consideration the values that it is storing into the
tree: (p(v), 0)? The heap tree could be either a min-heap or
max-heap. If we order the the value based of p(v)...

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