Question 1

The removeMin operation for both the linked and array implementations is O(log n).

Accepted Answer

A) True 
 B)False  True

Question 2

The removeMin operation for both implementations replaces the element at the root with the element in the last leaf of the heap. Why is this the proper replacement?

Accepted Answer

To maintain the completeness of the tree, the only valid replacement for the element at the root is the element at the last leaf. Then the heap must be reordered as necessary to maintain the ordering property.

Question 3

In an array implementation of a binary tree, the root of the tree is in position 0, and for each node n, n's left child is in position ______ and n's right child is in position ______.

Accepted Answer

2n+1, 2(n+1

Question 4

Does a heap ever have to be rebalanced?

Accepted Answer

No. By definition, a complete

Question 5

Because of the requirement that we be able to traverse up the tree after an insertion, it is necessary for the nodes in a heap to store a pointer to their ______.

Accepted Answer

The answer of Because of the requirement that we be...

Question 6

The __________ method adds a given Comparable element to the appropriate location in the heap, maintaining both the completeness property and the ordering property of the heap.

Accepted Answer

A)  add 
B)  addNext 
C)  addElement 
D)  none of the above 
A)  add 
B)  addNext 
C)  addElement 
D)  none of the above

Question 7

Typically, in heap implementations, we keep track of the position of the last node or, more precisely, the last leaf in the tree.

Accepted Answer

A)  root 
B)  internal node 
C)  leaf 
D)  tree 
A)  root 
B)  internal node 
C)  leaf 
D)  tree

Question 8

Because of the requirement that we be able to traverse up the tree after an insertion, it is necessary for the nodes in a heap to store a pointer to their parent.

Accepted Answer

A) True 
 B)False

Question 9

A minheap is a complete binary tree in which each node is less than or equal to both the left child and the right child.

Accepted Answer

A)  Minheap 
B)  Maxheap 
C)  Heap 
D)  Binary search tree 
A)  Minheap 
B)  Maxheap 
C)  Heap 
D)  Binary search tree

Question 10

A minheap is a complete ______ tree in which each node is less than or equal to both the left child and the right child.

Accepted Answer

The answer of A minheap is a complete ______ tree...

Question 11

In an array implementation of a binary tree, the root of the tree is in position 0, and for each node n, n's left child is in position ________ and n's right child is in position ________.

Accepted Answer

A)  2n + 1 
B)  2n + 2 
C)  2(n + 1) 
D)  A and B 
E)  A and C
F) B and C 
A)  2n + 1 
B)  2n + 2 
C)  2(n + 1) 
D)  A and B 
E)  A and C
F) B and C

Question 12

Though not a queue at all, a minheap provides an efficient implementation of a priority queue.

Accepted Answer

A) True 
 B)False

Question 13

To maintain the completeness of the tree, there is only one valid element to replace the root, and that is the element stored in the first leaf in the tree.

Accepted Answer

A) True 
 B)False

Question 14

Since a heap is a binary search tree, there is only one correct location for the insertion of a new node, and that is either the next open position from the left at level h or the first position on the left at level h+1 if level h is full.

Accepted Answer

A) True 
 B)False

Question 15

What is the difference between a heap (a minheap) and a binary search tree?

Accepted Answer

A binary search tree has the ordering pr

Question 16

The heapSort method consists of adding each of the elements of the list to a ______ and then removing them one at a time. If the heap is a minheap, this results in ______ order. However, if the heap is a maxheap, this results in ______ order.

Accepted Answer

heap, asce

Question 17

Both children of the root of a minheap are _________.

Accepted Answer

A)  Minheaps 
B)  Maxheaps 
C)  Heaps 
D)  Binary search trees 
A)  Minheaps 
B)  Maxheaps 
C)  Heaps 
D)  Binary search trees

Question 18

To maintain the completeness of the tree, there is only one valid element to replace the ________, and that is the element stored in the last leaf in the tree.

Accepted Answer

A)  root 
B)  internal node 
C)  leaf 
D)  tree 
A)  root 
B)  internal node 
C)  leaf 
D)  tree

Question 19

The removeMin operation for both the linked and array implementations is O(______)

Accepted Answer

The answer of The removeMin operation for both the linked...

Question 20

A minheap is a complete binary tree in which each node is less than or equal to both the left child and the right child.

Accepted Answer

A) True 
 B)False

The removeMin operation for both the linked and array implementations is O(log n).

The removeMin operation for both implementations replaces the element at the root with the element in the last leaf of the heap. Why is this the proper replacement?

In an array implementation of a binary tree, the root of the tree is in position 0, and for each node n, n's left child is in position and n's right child is in position .

Does a heap ever have to be rebalanced?

Because of the requirement that we be able to traverse up the tree after an insertion, it is necessary for the nodes in a heap to store a pointer to their ______.

The __________ method adds a given Comparable element to the appropriate location in the heap, maintaining both the completeness property and the ordering property of the heap.

Typically, in heap implementations, we keep track of the position of the last node or, more precisely, the last leaf in the tree.

Because of the requirement that we be able to traverse up the tree after an insertion, it is necessary for the nodes in a heap to store a pointer to their parent.

A minheap is a complete binary tree in which each node is less than or equal to both the left child and the right child.

A minheap is a complete ______ tree in which each node is less than or equal to both the left child and the right child.

In an array implementation of a binary tree, the root of the tree is in position 0, and for each node n, n's left child is in position and n's right child is in position .

Though not a queue at all, a minheap provides an efficient implementation of a priority queue.

To maintain the completeness of the tree, there is only one valid element to replace the root, and that is the element stored in the first leaf in the tree.

Since a heap is a binary search tree, there is only one correct location for the insertion of a new node, and that is either the next open position from the left at level h or the first position on the left at level h+1 if level h is full.

What is the difference between a heap (a minheap) and a binary search tree?

The heapSort method consists of adding each of the elements of the list to a and then removing them one at a time. If the heap is a minheap, this results in order. However, if the heap is a maxheap, this results in __ order.

Both children of the root of a minheap are _________.

To maintain the completeness of the tree, there is only one valid element to replace the ________, and that is the element stored in the last leaf in the tree.

The removeMin operation for both the linked and array implementations is O(______)

A minheap is a complete binary tree in which each node is less than or equal to both the left child and the right child.

Introduction

Analysis of Algorithms

Introduction to Collections - Stacks

Linked Structures - Stacks

Queues

Lists

Iterators

Recursion

Searching and Sorting

Trees

Heaps and Priority Queues

Sets and Maps

Multi-Way Search Trees

Graphs

UML

Object-Oriented Design

Filters

Exam 11: Binary Search Trees

The removeMin operation for both the linked and array implementations is O(log n).

The removeMin operation for both implementations replaces the element at the root with the element in the last leaf of the heap. Why is this the proper replacement?

In an array implementation of a binary tree, the root of the tree is in position 0, and for each node n, n's left child is in position ______ and n's right child is in position ______.

Does a heap ever have to be rebalanced?

Because of the requirement that we be able to traverse up the tree after an insertion, it is necessary for the nodes in a heap to store a pointer to their ______.

The __________ method adds a given Comparable element to the appropriate location in the heap, maintaining both the completeness property and the ordering property of the heap.

Typically, in heap implementations, we keep track of the position of the last node or, more precisely, the last leaf in the tree.

Because of the requirement that we be able to traverse up the tree after an insertion, it is necessary for the nodes in a heap to store a pointer to their parent.

A minheap is a complete binary tree in which each node is less than or equal to both the left child and the right child.

A minheap is a complete ______ tree in which each node is less than or equal to both the left child and the right child.

In an array implementation of a binary tree, the root of the tree is in position 0, and for each node n, n's left child is in position ________ and n's right child is in position ________.

Though not a queue at all, a minheap provides an efficient implementation of a priority queue.

To maintain the completeness of the tree, there is only one valid element to replace the root, and that is the element stored in the first leaf in the tree.

Since a heap is a binary search tree, there is only one correct location for the insertion of a new node, and that is either the next open position from the left at level h or the first position on the left at level h+1 if level h is full.

What is the difference between a heap (a minheap) and a binary search tree?

The heapSort method consists of adding each of the elements of the list to a ______ and then removing them one at a time. If the heap is a minheap, this results in ______ order. However, if the heap is a maxheap, this results in ______ order.

Both children of the root of a minheap are _________.

To maintain the completeness of the tree, there is only one valid element to replace the ________, and that is the element stored in the last leaf in the tree.

The removeMin operation for both the linked and array implementations is O(______)

A minheap is a complete binary tree in which each node is less than or equal to both the left child and the right child.

Introduction

Analysis of Algorithms

Introduction to Collections - Stacks

Linked Structures - Stacks

Queues

Lists

Iterators

Recursion

Searching and Sorting

Trees

Heaps and Priority Queues

Sets and Maps

Multi-Way Search Trees

Graphs

UML

Object-Oriented Design

Filters

In an array implementation of a binary tree, the root of the tree is in position 0, and for each node n, n's left child is in position and n's right child is in position .

In an array implementation of a binary tree, the root of the tree is in position 0, and for each node n, n's left child is in position and n's right child is in position .

The heapSort method consists of adding each of the elements of the list to a and then removing them one at a time. If the heap is a minheap, this results in order. However, if the heap is a maxheap, this results in __ order.