CIS 2168 data structures quiz 2

Expanding and contracting arrays are operations. (a) O(n) (b) O(log2 n) (c) O(√n) (d) O(n2)

(a) O(n)

Which of the following is an example of a map? (a) (J, Jane), (B, Bill), (S, Sam), (B1, Bob), (B, Bill) (b) (J, Jane), (B, Bill), (S, Sam), (B1, Bob), (B2, Bill) (c) (J, Jane), (B, Bill), (S, Sam), (B1, Bob), (J, Jane) (d) (S, Sam), (B, Bill), (S, Sam), (B1, Bob), (B2, Bill)

(b) (J, Jane), (B, Bill), (S, Sam), (B1, Bob), (B2, Bill)

If you insert the letter M into the heap above (Exercise 1.11), which array entries change? (a) 3, 6, 7, 12, 13 (b) 3, 6, 13 (c) 1, 2, 4, 5, 8, 9, 10, 11, 13 (d) 6, 13 (e) 3, 6, 12, 13

(b) 3, 6, 13

Suppose that a client performs an intermixed sequence of (queue) enqueue anddequeue operations. The enqueue operations put the integers 0 through 9 in order onto the queue;the dequeue operations print out the return value. Which of the following sequence(s) could notoccur? (a) 0 1 2 3 4 5 6 7 8 9 (b) 4 6 8 7 5 3 2 9 0 1 (c) 2 5 6 7 4 8 9 3 1 0 (d) 4 3 2 1 0 5 6 7 8 9

(b) 4 6 8 7 5 3 2 9 0 1 (c) 2 5 6 7 4 8 9 3 1 0 (d) 4 3 2 1 0 5 6 7 8 9 queues always preserve order

Suppose that an intermixed sequence of (stack) push and pop operations are performed. The pushes push the integers 0 through 9 in order; the pops print out the return value. Which of the following sequence(s) could not occur? (a) 4 3 2 1 0 9 8 7 6 5 (b) 4 6 8 7 5 3 2 9 0 1 (c) 2 5 6 7 4 8 9 3 1 0 (d) 4 3 2 1 0 5 6 7 8 9 (e) 1 2 3 4 5 6 9 8 7 0 (f) 0 4 6 5 3 8 1 7 2 9 (g) 1 4 7 9 8 6 5 3 0 2 (h) 2 1 4 3 6 5 8 7 9 0

(b) 4 6 8 7 5 3 2 9 0 1 0 1 cannot occur (f) 0 4 6 5 3 8 1 7 2 9 1 7 cannot occur. (g) 1 4 7 9 8 6 5 3 0 2 0 2 cannot occur.

Complete the following algorithm which recursively inserts an item into a binary search tree. if the root is null Replace empty tree with a new tree with the item at the root and return true. else if the item is equal to root. data__________ else if the item is less than root.data Recursively insert the item in the left subtree. else Recursively insert the item in the right subtree. (a) The item is not in the tree; return false. (b) The item is already in the tree; return false. (c) The item is not in the tree; return true. (d) The item is already in the tree; return true.

(b) The item is already in the tree; return false.

Which one of the following hash functions on integers will distribute keys most uniformly over 10 buckets numbered 0 to 9 for x ranging from 0 to 2020? (a) x^2 mod 10 (b) x^3 mod 10 (c) (12·x^2) mod 1

(b) x^3 mod 10

If you delete the max from the original heap in Exercise 1.11, which entries change? (a) 1, 3, 6, 12 (b) 1, 3, 7, 12 (c) 1, 2, 4, 8, 12 (d) 1, 3, 12 (e) 1, 3, 6, 7, 12

(c) 1, 2, 4, 8, 12

Insertion into and removal from a heap is a operation. (a) O(n) (b) O(n2) (c) O(log2 n) (d) O(nlog2 n) (e) O(log10 n)

(c) O(log2 n)

Searching a binary search tree is a process. (a) O(n) (b) O(1) (c) O(logn) (d) O(n2)

(c) O(logn)

Which array corresponds to the following heap? Check the heap in ex 5.21 (a) [- X W V S P U Q R J D C H... ] (b) [- X S V P W Q U R C D J H... ] (c) [- X W J V U D H S P Q R C...]

(c) [- X W J V U D H S P Q R C...]

The following algorithm is a(n)___________ . if the tree is empty Return null (target is not found). else if the target matches the root node's data Return the data stored at the root node. else if the target is less than the root node's data Return the result of searching the left subtree of the root. else Return the result of searching the right subtree of the root.. (a) algorithm for removal from a heap (b) algorithm for insertion into a heap (c) algoithm for insertion into a a binary tree (d) recursive algorithm for searching a binary tree

(d) recursive algorithm for searching a binary tree

Suppose that initially a max-heap contains just a single node whose key is equalto 0. Then, for all i from 1 to n, you insert i into the max-heap. You do this by attaching a newkey to some leaf of the current tree. What is the height of the tree after you've attached the lastnode with key n? (a) Θ(n2) (b) Θ(n) (d) Θ(n log n)

(d) Θ(n log n)

Follow the heapify procedure to turn the array .a = [5, 3, 17, 10, 84, 19, 6, 22, 9] into a max-heap.

84, 5, 19, 22, 3, 17, 6, 10, 9

The keys 12, 18, 13, 2, 3, 23, 5 and 15 are inserted into an initially empty hash table of length 10 using open addressing with hash function h(k) = k mod 10 and linear probing. What is the resultant hash table?

C)

(True/False) Removal from a heap is always from the bottom.

False

(True/False) Using a hash table enables us to retrieve an item in O(n log n) time.

False Hash table retrival is O(1)

(True/False) Using Huffman codes to encode text files should give you files with more bits than you would get using other codes.

False Huffman codes uses fewer bits for the most common characters and more bits for the uncommon characters

The ________ is used to implement a priority queue.

Heap

The _____________ is the number of nodes in the longest path from the root node to a leaf node.

Height

The ___________ of a node is a measure of its distance from the root.

Level

Consider a document that has the following symbols and frequencies:(Check table in the the quiz) (a) Draw a Huffman Tree for these symbols. Break ties alphabetically. (b) Encode the string "Poets" into binary using this encoding.

Not sure

Suppose that the sequence P R I O * R * * I * T * Y * * * Q U E * * * U * E (where a letter means insert and an asterisk means remove-the-maximum) is applied to an initially empty priority queue. Give the sequence of values returned by remove-the-maximum operations.

R, R, P, O, T, Y, I, I, U, Q, E, U,

(True/False) Collections implementing the Set interface must contain unique elements.

True

(True/False) If node n is not the root of tree T, its level is 1 + the level of its parent.

True

(True/False) In Java's PriorityQueue, the poll method first saves the item at the top of the heap. (Check your answer by consulting the javadoc).

True

Add each of these elements into a min-heap. Show both the array and (draw) the tree. (a) 23, 17, 19, 21, 11, 7, 13, 10, 0, 7 (b) 1, 2, 3, 4, 5, 6, 7, 8, 9, 0

a) [0, 7, 11, 10, 7, 19, 13, 23, 17, 21] 0 7 11 10 7 19 13 23 17 21 b)[0, 1, 3, 4, 2, 6, 7, 8, 9, 5] 0 1 3 4 2 6 7 8 9 5