Homework Answers
2.
Let the root of the tree is 'r', so the recursive algorithm to count the number of nodes of the tree rooted at 'r' we recursively count the number of nodes of the sub-trees rooted at the left and right child of thee root.
Count_Nodes(r)
1. count=0
2. if(r!=NULL)
3. { if(r 
left =NULL
and r right
=NULL)
4. return(1)
5. if(r left
!=NULL)
6. count= 1+Count_Nodes(r left)
7. if(r right
!=NULL)
8. count= count+Count_Nodes(r right)
9. }
10. return(count).
3.
In the above tree as all levels are complete, the function is called for each node is the worst-case condition of the algorithm.
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2. Write a recursive algorithm which computes the number of nodes in a general tree. 3....
(Pre-order and post-order traversal). Implement the textbook's algorithm (not the Java implementation) for pre-order and post-order...
(Pre-order and post-order traversal). Implement the textbook's
algorithm (not the Java implementation) for
pre-order and post-order traversal. To "process" or "visit" a node
means to print the data at that node.
Pre-order traversal output: 10 6 4 8 18 15 21
Post-order traversal output: 4 8 6 15 21 18 10
Additionally, create and traverse the following trees:
Algorithm preorder(p) perform the "visit" action for position p this happens before any recursion for each child c in children(p) do recursively...
Write a client method that returns a count of the number of nodes in a binary...
Write a client method that returns a count of the number of
nodes in a binary search tree that contain scores less than or
equal to a passed-in argument (parameter) value. The method header
is:
int countLowerScores (BinarySearchTree tree, int maxValue)
The BinarySearchTree contains these methods in the
picture.
public class BinarySearchTreecT> implements BSTInterfacecT> //reference to the root of this BST public BSTNode<T> root; public Comparator<T> comp: IIused for all comparisons public boolean found: / used by remove public BinarYSearchTree()...
You will be given several strings full of different keyboard characters, some of which are letters...
You will be given several strings full of different keyboard
characters, some of which are letters of the alphabet.
Write a java program that creates a binary tree that uses
only the alphabetical characters (a-z, A-Z) as the value within the
leaf nodes using recursion and preorder traversal. All
other values within the tree (either the root node or internal
nodes) will be null. You may create any methods you see fit, so
long as the final binary tree is...
2. A regular binary tree is a binary tree whose internal nodes all have two subtrees...
2. A regular binary tree is a binary tree whose internal nodes all have two subtrees (left and right). In other words, all their nodes have either zero subtrees (in which case they are leaves) or two subtrees (in which case they are internal nodes). Suppose that you have a boolean function that tells you, for each node of the tree, whether it is a leaf or not (call it: leaf(n), for node n). a) Write a recursive function that...
QUESTION 1 In a tree, a ____ is a node with successor nodes. root child descendent...
QUESTION 1 In a tree, a ____ is a node with successor nodes. root child descendent parent sibling QUESTION 2 In a tree, the ____ is a measure of the distance from a node to the root. count degree branch height level QUESTION 3 Which of the following is not a characteristic of a binary search tree? Each node has zero, one, or two successors. The preorder traversal processes the node first, then the left subtree, and then the right...
Recall from Assignment 2 the definition of a binary tree data structure: either an empty tree,...
Recall from Assignment 2 the definition of a binary tree data structure: either an empty tree, or a node with two children that are trees. Let T(n) denote the number of binary trees with n nodes. For example T(3) 5 because there are five binary trees with three nodes: (a) Using the recursive definition of a binary tree structure, or otherwise, derive a recurrence equation for T(n). (8 marks) A full binary tree is a non-empty binary tree where every...
1.Fix any tree T on 10 vertices. Draw the recursion tree of the algorithm Find-size-node when...
1.Fix any tree T on 10 vertices. Draw the recursion tree of the algorithm Find-size-node when run on the input T with a being the root of T. Can you use this to give a bound on the running time of T? 2. Consider the following problem. Check-BST • Input: A binary tree T • Output: 1 if T is a binary search tree, and 0 otherwise. Give an efficient algorithm for this problem. 3.Give a recursive algorithm for the...
In Java. How would this method look? LinkedBinaryTree.java import java.util.Iterator; public class LinkedBinaryTree implements BinaryTreeADT {...
In Java. How would this method look?
LinkedBinaryTree.java
import java.util.Iterator;
public class LinkedBinaryTree implements BinaryTreeADT {
private BinaryTreeNode root;
/**
* Creates an empty binary tree.
*/
public LinkedBinaryTree() {
root = null;
}
/**
* Creates a binary tree from an existing root.
*/
public LinkedBinaryTree(BinaryTreeNode root) {
this.root = root;
}
/**
* Creates a binary tree with the specified element...
The INORDER traversal output of a binary tree is U,N,I,V,E,R,S,I,T,Y and the POSTORDER traversal output of the same tree is N,U,V,R,E,T,I,S,I,Y
a. The INORDER traversal output of a binary tree is U,N,I,V,E,R,S,I,T,Y and the POSTORDER traversal output of the same tree is N,U,V,R,E,T,I,S,I,Y. Construct the tree and determine the output of the PREORDER traversal output. b. One main difference between a binary search tree (BST) and an AVL (Adelson-Velski and Landis) tree is that an AVL tree has a balance condition, that is, for every node in the AVL tree, the height of the left and right subtrees differ by at most 1....
Question B1 You are given the following Java classes: public class Queue { private static class...
Question B1 You are given the following Java classes: public class Queue { private static class Node { Object object; Node next; Node () { object = null; next = null; } Node (Object object, Node next) { this.object = object; this.next = next; private Node header; private int size = 0; // size shows the no of elements in queue public Object dequeue () { if (size == 0 ) { return null; else { Object remove_object = header.object;...
(Pre-order and post-order traversal). Implement the textbook's
algorithm (not the Java implementation) for
pre-order and post-order traversal. To "process" or "visit" a node
means to print the data at that node.
Pre-order traversal output: 10 6 4 8 18 15 21
Post-order traversal output: 4 8 6 15 21 18 10
Additionally, create and traverse the following trees:
Algorithm preorder(p) perform the "visit" action for position p this happens before any recursion for each child c in children(p) do recursively...
Write a client method that returns a count of the number of
nodes in a binary search tree that contain scores less than or
equal to a passed-in argument (parameter) value. The method header
is:
int countLowerScores (BinarySearchTree tree, int maxValue)
The BinarySearchTree contains these methods in the
picture.
public class BinarySearchTreecT> implements BSTInterfacecT> //reference to the root of this BST public BSTNode<T> root; public Comparator<T> comp: IIused for all comparisons public boolean found: / used by remove public BinarYSearchTree()...
You will be given several strings full of different keyboard
characters, some of which are letters of the alphabet.
Write a java program that creates a binary tree that uses
only the alphabetical characters (a-z, A-Z) as the value within the
leaf nodes using recursion and preorder traversal. All
other values within the tree (either the root node or internal
nodes) will be null. You may create any methods you see fit, so
long as the final binary tree is...
2. A regular binary tree is a binary tree whose internal nodes all have two subtrees (left and right). In other words, all their nodes have either zero subtrees (in which case they are leaves) or two subtrees (in which case they are internal nodes). Suppose that you have a boolean function that tells you, for each node of the tree, whether it is a leaf or not (call it: leaf(n), for node n). a) Write a recursive function that...
Recall from Assignment 2 the definition of a binary tree data structure: either an empty tree, or a node with two children that are trees. Let T(n) denote the number of binary trees with n nodes. For example T(3) 5 because there are five binary trees with three nodes: (a) Using the recursive definition of a binary tree structure, or otherwise, derive a recurrence equation for T(n). (8 marks) A full binary tree is a non-empty binary tree where every...
In Java. How would this method look?
LinkedBinaryTree.java
import java.util.Iterator;
public class LinkedBinaryTree implements BinaryTreeADT {
private BinaryTreeNode root;
/**
* Creates an empty binary tree.
*/
public LinkedBinaryTree() {
root = null;
}
/**
* Creates a binary tree from an existing root.
*/
public LinkedBinaryTree(BinaryTreeNode root) {
this.root = root;
}
/**
* Creates a binary tree with the specified element...
Question B1 You are given the following Java classes: public class Queue { private static class Node { Object object; Node next; Node () { object = null; next = null; } Node (Object object, Node next) { this.object = object; this.next = next; private Node header; private int size = 0; // size shows the no of elements in queue public Object dequeue () { if (size == 0 ) { return null; else { Object remove_object = header.object;...
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