Question

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

Answer #1

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

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

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?

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)

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?

Java-
With Binary Tree we want to count the nodes after a certain
depth.
Add a recursive method countNodesAtDepth to
your Driver class, which takes two parameters: an Integer
node n and an integer d. This method should
return the number of nodes at depth d in the subtree
rooted at n.
Hint: if a node is at depth d in the subtree rooted at
n, what depth is it at in the subtree rooted at
n.left or n.right? What...

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