Computer Science 221 Final Exam Reve

Solve this expression given in postfix form: 20 5 2 */ 10 + 12 3 16 20

12

What is the answer given the postfix notation 3 5 2 + * 2 1 - / 21 18 10 15 12

21

What is the maximum number of elements that can be contained in one node of a 2-4 tree? 3 2 1 4

3

The number of edges in a complete graph with 20 vertices, each with the same degree of 3 is: 15 40 30 60

30

In the DAG shortest path algorithm, you need a minimum priority queue to extract the shortest path. True False

False

Inserting an element into a sorted linked list MPQ is faster than inserting into an unsorted linked list MPQ. True False

False

The Bellman Ford algorithm does not work for graphs with negative-weight edges? True False

False

The SSSP (Single Source Shortest Path) problem is well defined for a graph with negative-weight cycles True False

False

There exists a positive weight cycle on the shortest path from the source to the destination. True False

False

What does it mean to have a strongly connected graph? For any two vertices, there exists a path from one vertex to the other. Each vertex has an in-degree. Each vertex has an out-degree. There are no self loops in the graph.

For any two vertices, there exists a path from one vertex to the other.

Convert this expression to postfix notation: (a*b)-(c+d/e) ab*cd+e/- II. ab*cde/+- III. ab-*cde/+ IV. ab-*cd+e/

II. ab*cde/+-

What is the runtime in terms of big-O notation for the insertion sort algorithm? I. O(n) II. O(log n) III. O(n^2) IV. O(n log n)

III. O(n^2)

Given a binary search tree (BST), what type of traversal would you apply to get the items of the tree in sorted order? Postorder Traversal Preorder Traversal Inorder Traversal

Inorder Traversal

You are running a catalog for library books. You know that the books in the collection are almost in sorted ascending order by title, except one book is in the wrong place. You want the collection to be completely sorted in ascending order. Choose the appropriate sorting method Insertion Sort Merge Sort Radix Sort Heap Sort Counting Sort

Insertion Sort

Which algorithm uses the disjoint-set data structure (with functions Make-Set, Union, and Find-Set) in order to build a minimum spanning tree (MST)? Kruskal's Algorithm Prim's Algorithm Djikstra's Algorithm Bellman-Ford Algorithm Topological Sort

Kruskal's Algorithm

In a binary tree, BFS will return an output equivalent to ___________ and DFS will return an output equivalent to __________. Preorder traversal, postorder traversal Level-order traversal, preorder traversal Level-order traversal, inorder traversal In-order traversal, postorder traversal

Level-order traversal, preorder traversal

Which Minimum Priority Queue implementation determines the minimum stored value in O(1), on average? MPQ based on Sorted List MPQ based on Unsorted List MPQ based on

MPQ based on Sorted List

Which shortest path algorithm will find the correct path when a graph has negative weights? Dijkstra's Algorithm DFS Bellman-Ford Algorithm BFS

Bellman-Ford Algorithm

List sorting algorithms from least to greatest (fastest to slowest) best-case time complexity. (Merge Sort, Bucket sort, Bubble Sort, Selection Sort). Bubble Sort -> Bubble Sort -> Selection Sort -> Merge Sort Bucket Sort -> Bubble Sort -> Merge Sort -> Selection Sort Selection Sort -> Bubble Sort -> Merge Sort -> Bucket Sort Merge Sort -> Bucket Sort -> Selection Sort -> Bubble Sort

Bucket Sort -> Bubble Sort -> Merge Sort -> Selection Sort

Select the most accurate statement from the following statements. i) Chaining method needs less memory than open hashing method. ii) Chaining method needs more memory than open hashing method. iii) Chaining method needs as much memory as the open hashing method.

Chaining method needs more memory than open hashing method.

Which of the following sort algorithms is NOT comparison based? Insertion Sort Counting Sort Bubble Sort Selection Sort

Counting Sort

Which of the following Big O represents the time complexity of building a graph using the adjacent list? O (n) O (|n + m|) O (nm) O (nlog2n)

O (|n + m|)

What is the efficiency of the Depth-First Search on an adjacency list with V vertices and E edges? O(V+E) O(V^2) O(E^2) O(Vlog(E))

O(V+E)

The traversal of a single path on a balanced binary tree from root to leaf is bounded by _____? O(n) O(logn) O(nlogn) O(n^2)

O(logn)

What is the cost of a single insert operation in a Minimum Priority queue implemented using Binary heap? O(n) O(nlogn) O(1) O(logn)

O(logn)

What is the efficiency of BFS and DFS for adjacency list representation? For n is number of edges, and m is number of vertices. O(m^2) O(n+m) O(n^2) O(n-m)

O(n+m)

Using the Master Method, solve the following recurrence relation: T(n) = 4T(n/2) + O(n) O(n) O(nlogn) O(n^2) log_(2) {4} = 2 > 1. T(n) = O(n^(log_(2) {4})) = O(n^2) O(logn)

O(n^2)

What is the efficiency of BFS and DFS for matrix representation? For n is number of edges, and m is number of vertices. O(m^2) O(logn) O(mlogn) O(n^2)

O(n^2)

What is the best case Big-O of merge sort? O(log(n)) O(nlog(n)) O(n) O(1)

O(nlog(n))

What is the Big O for building a heap? O(n) O(logn) O(n^2) O(nlog2(n))

O(nlog2(n))

What is the time complexity for the worst case performance of merge sort? O(nlogn) O(logn) O(n) O(n!)

O(nlogn)

What is the efficiency of the Depth-First Search algorithm with a graph represented as an adjacency list? O(|V| * log(|V|)) O(|V| + |E|) O(|V|^2) O((|V| + |E|) * log(|V|))

O(|V| + |E|)

What is the time complexity of DFS on a graph assuming implementation using adjacency list? O(|V|^2) O(|E|^2) O(|V|+|E|) O(|V| log |E|)

O(|V|+|E|)

What is the efficiency of the Breadth-First Search algorithm with a graph represented as an adjacency matrix? O(|V| * log(|V|)) O(|V| + |E|) O(|V|^2) O((|V| + |E|) * log(|V|))

O(|V|^2)

A stable sorting algorithm: Preserves the order of the first and last elements Ensures the median element = average element Preserves the order of elements with the same key in the sorted output Differentiates between elements of the same key and creates new distinct elements

Preserves the order of elements with the same key in the sorted output

The Breadth-First Search algorithm is commonly implemented with what data structure? Queue Stack BS Tree List

Queue

When traversing a tree using breadth first search (BFS), visited nodes are typically stored in a/an ____? Queue Stack Binary Heap Array

Queue

Which sorting algorithm corresponds to a minimum priority queue implemented based on an unsorted array? Selection sort Insertion sort Heap sort Bubble sort

Selection sort

Which of the following conditions is NOT required for a minimum spanning tree (MST)? Undirected Graph Sum of the edge weights must be negative Tree is Acyclic (no cycles) Tree connects to all vertices in the graph

Sum of the edge weights must be negative

Which recurrence relation represents the worst case for the Quick Sort Algorithm? T(n) = 2T(n / 2) + O(n) T(n) = T(n + 1) + O(n) T(n) = T(n - 1) + O(n) T(n) = T(n - 1) + O(1)

T(n) = T(n - 1) + O(n)

Which of the following is not a difference between the quicksort and mergesort? The ratio of the sizes of the auxiliary subarrays Their worst case time complexities Their best case time complexities The stability of the algorithms

Their best case time complexities

Huffman's algorithm is a technique used for data compression. i) True ii) False

True

Is the selection sort an in-place comparison-based algorithm? True False

True

The efficiency for heapsort is O(nlog2n) for all cases. True False

True

The insertion operation takes up the majority of time in a priority queue based on a sorted array. True False

True

Find the postfix form of the algebraic expression a / b * c / (d + e) ab / c * de + / abc / * de + / a / b c * de + / ab / c * d + e /

ab / c * de + /

Using the queue implementation based on a singly linked list, the enqueue operation___ and the dequeue operation___ inserts at the beginning of the linked list;removes at the beginning of the linked list. inserts at the end of the linked list; removes at the beginning of the linked list. inserts at the end of the linked list;removes at the end of the linked list inserts at the beginning of the linked list; removes at the beginning of the linked list

inserts at the beginning of the linked list; removes at the beginning of the linked list

Which is the correct explanation for the way the stack abstract data type accepts inputs and outputs? first in, last out last in, first out first in, first out last in, last out

last in, first out

What is the space complexity of an adjacency matrix graph G with n vertices and m edges? n^2 m^2 n+m nlog(m)

n^2