CS 3033 Data Structures Term 1 2019 2020 Enqueue and Dequeu

CS 3033 Data Structures Term 1 2019 2020

Enqueue and Dequeue are notations associated with which data structures

 

Answers with Explanation

1st and 2nd Question

Answer:

1. Queue 

2. True

Step by step explanation:

Explanation 1

• A queue is a data structure that represents a collection of elements in a linear sequence. Elements are added to one end of the queue and deleted from the other end of the queue as they pass through the queue. The Enqueue and Dequeue operations are used to add items to the queue and take things off the queue, respectively.

 
Explanation 2

• The "physical form" of an abstract data type is the "implementation" of a data type as a data structure. In other words, the data type is implemented in the form of a collection of data structures, which serve as the data type's fundamental building blocks. The data structures that are used to implement a data type can look different depending on the type of data.

Answers with Explanation

3rd Question

Answer:

The correct option is c:

Option 3

Step by step explanation:

• Option 3 is the most acceptable asymptotic analysis for this code segment O(nlogn). This is due to the fact that the outer loop operates in O(logn) time while the inner loop operates in O(n) time. Consequently, the total time complexity of this code segment is O (nlogn).
• Option 1, O(1), would not be a valid asymptotic analysis for this code fragment due to the non-constant time complexity. The temporal complexity depends on the magnitude of the input, n.
• Option 2 (O(2")) would not be an accurate asymptotic analysis for this code fragment due to the fact that the time complexity is not exponential. The temporal complexity depends on the magnitude of the input, n.
• Option 4, O(n²), would not be a correct asymptotic analysis for this code fragment due to the fact that the temporal complexity is not quadratic. The temporal complexity is proportional to the amount of the input, n, but is not quadratic.

 

Answers with Explanation

4th and 5th Question 

Answer:

Q.1

d. Choice 4

Q.2

true

Step by step explanation:

Q.1

• Assuming that perhaps the code fragment is meant to be functioning code, the asymptotic analysis that is most appropriate would be Choice 4, O. (n). This is due to the fact that the for loop is iterating throughout all n elements within the array, and the return statement is returning the value of the element that is now being iterated over (the last element in the array). As a result, the time complexity of the code fragment is linear, which is represented by the letter O. (n).
• If, on the other hand, the code snippet is not meant to be a functioning piece of code, then the asymptotic analysis choice that is most suited is choice 0 and choice 2. (2"). This is because the value of the array's final element is not being returned by the return statement, despite the fact that the for loop is iterating through all n items of the array during this process. Because of this, the time complexity of the code snippet is quadratic, which equals zero (2n).
• In either scenario, the asymptotic analysis for Choice 1 (O(n2)) would be flawed due to the fact that the temporal complexity of the code fragment does not exhibit quadratic behaviour. Because the temporal complexity of the code fragment is not cubic, the asymptotic analysis Choice 3, (n2), would likewise be erroneous.

Q.2

• When all of the items in a list have the value zero (or nothing), we say that the list is empty. This is due to the fact that none of the values in the list are representational of anything, and as a result, they can all be disregarded as irrelevant. When every value in a list is 0, the list might be interpreted as not containing any information and, as a result, can be interpreted as being empty.
• In the realm of computer science, despite the fact that this may look like a very unimportant issue, it is, in fact, quite significant. This is due to the fact that the majority of algorithms and data structures are developed under the assumption that lists would not be empty. If a list does not include any items, the algorithm or data structure might not function as expected.
• Therefore, it is essential to be aware of the fact that a list might be considered empty if all of its elements have a value of zero. This is one of the reasons why it is so vital to be aware of this information. Having this understanding can assist you in preventing problems and in designing algorithms and data structures that are more effective.

 

Answers with Explanation

6th and 7th Questions

Answer:

Answer 1

d. The growth rate demonstrated in the algorithm running time equation.

 

Answer 2:

• b. Choice 2

Step by step explanation:

Explanation 1

• The goal of asymptotic algorithm analysis is to gain an understanding of the behavior of an algorithm as the input size increases to increasingly high values. In particular, it is concerned with the rate at which the amount of running time increases in proportion to the magnitude of the input.
• The execution time of an algorithm can be measured in a few different methods, the most common of which are the worst-case analysis and the average-case analysis. We are interested in the behavior of the algorithm in the worst-case scenario, which occurs when the inputs are very challenging (i.e., the inputs that result in the longest running time). In contrast, the focus of an average-case analysis is on the behavior of the algorithm taken as a whole, taking into account all of the possible inputs.
• Asymptotic notation is one method that can be used to measure the amount of time that an algorithm actually takes to run. This notation provides us with a means of simplifying the running time equation, which enables us to compare the growth rates of various algorithms in a manner that is more straightforward. The "Big-O notation, the Big-Theta notation, and the Big-Omega notation are the asymptotic notations" that are used the most frequently.
• When describing the longest possible execution time for an algorithm, the Big-O notation is typically employed. The Big-O notation can be intuitively understood as a method for calculating a "upper bound" on the amount of time it takes for an algorithm to complete its task. To put it another way, the execution time will never take longer than some function of the size of the input. For instance, if the running time of an algorithm is specified as O(n2), then we are aware that the running time will never exceed some constant multiplied by n2 and we may plan accordingly.
• When describing the exact amount of time it takes for an algorithm to run, the Big-Theta notation is utilized. That is to say, the amount of time it takes to complete the task will always be proportional to some function of the size of the input. For instance, if the running time of an algorithm is denoted by the notation (n2), then we know that the running time will always be equal to some constant multiplied by n2 regardless of the algorithm.
• When describing the fastest possible execution of an algorithm, the Big-Omega notation is the method of choice. The Big-Omega notation can be intuitively conceived of as a method for calculating the "lower bound" on the amount of time required for the execution of an algorithm. To put it another way, the execution time will never be less than some function of the magnitude of the data input. For instance, if the running time of an algorithm is denoted by the notation (n2), then we know that the running time will never be less than some constant multiplied by n2; this is a known fact.

Explanation 2

• 2. Big Omega
• The "lower bound for the growth of the Algorithms running time is represented by Big Omega." This means that the algorithm will always take at least a certain amount of time to run, regardless of the inputs. For example, if an algorithm has a Big Omega of n, then it will take at least n time to run, no matter what the inputs are.
• There are many reasons why an algorithm might have a lower bound. One reason is that the algorithm might be inherently complex, and there is no way to simplify it. Another reason is that the algorithm might be designed to work on a certain type of input, and any other type of input would take longer to process.
• Whatever the reason, if an algorithm has a lower bound, it is important to know what that bound is. This can help to determine how long the algorithm will take to run, and whether it is worth running at all.
• The other answers are not correct because they do not represent "the lower bound for the growth of the Algorithms running time." Big Oh represents the worst case scenario for the algorithm, while Big Theta represents the average case scenario. Exponential growth is not a bound at all, but rather a general description of how the algorithm might grow.

Answers with Explanation

11th and 12th Questions

Answer:

b. Union/Find
The Union/Find algorithm is used to determine if two objects are in the same set, and if so, to merge those sets. The algorithm works by keeping track of the sets to which each object belongs, and using that information to determine if two objects are in the same set. If two objects are in the same set, then they are merged into one set. This process is repeated until all objects are in the same set.

The Union/Find algorithm is a simple and efficient way to keep track of sets of objects. It is easy to implement, and it runs in time that is linear in the number of objects. The algorithm is also easy to understand and to use.

The Union/Find algorithm is a powerful tool for managing sets of objects. It can be used to find out if two objects are in the same set, and to merge sets of objects. The algorithm is simple to implement, and it runs in time that is linear in the number of objects.

 

d. 2-3 tree
A 2-3 tree is a type of tree data structure in which every internal node has either two or three child nodes. All leaves are at the same level in the tree.

2-3 trees are often used to store data in a sorted order, making it easy to search and retrieve data. Because all leaves are at the same level, data can be easily retrieved without having to traverse the entire tree.

2-3 trees are also efficient when it comes to storage. Because all leaves are at the same level, there is no need to store extra data in the nodes, which means that 2-3 trees use less memory than other tree data structures.

2-3 trees are not well suited for data that is constantly being inserted and deleted. Because the tree needs to be rebalanced every time an insertion or deletion is made, 2-3 trees can become inefficient when there are a lot of insertions and deletions.
 

 

 

Step by step explanation:

b. Union/Find
The Union/Find algorithm is used to determine if two objects are in the same set, and if so, to merge those sets. The algorithm works by keeping track of the sets to which each object belongs, and using that information to determine if two objects are in the same set. If two objects are in the same set, then they are merged into one set. This process is repeated until all objects are in the same set.

The Union/Find algorithm is a simple and efficient way to keep track of sets of objects. It is easy to implement, and it runs in time that is linear in the number of objects. The algorithm is also easy to understand and to use.

The Union/Find algorithm is a powerful tool for managing sets of objects. It can be used to find out if two objects are in the same set, and to merge sets of objects. The algorithm is simple to implement, and it runs in time that is linear in the number of objects.

 

d. 2-3 tree
A 2-3 tree is a type of tree data structure in which every internal node has either two or three child nodes. All leaves are at the same level in the tree.

2-3 trees are often used to store data in a sorted order, making it easy to search and retrieve data. Because all leaves are at the same level, data can be easily retrieved without having to traverse the entire tree.

2-3 trees are also efficient when it comes to storage. Because all leaves are at the same level, there is no need to store extra data in the nodes, which means that 2-3 trees use less memory than other tree data structures.

2-3 trees are not well suited for data that is constantly being inserted and deleted. Because the tree needs to be rebalanced every time an insertion or deletion is made, 2-3 trees can become inefficient when there are a lot of insertions and deletions.

Answers with Explanation

13th, 14th and 15th Questions

Answer:

Question 1

c. A Dictionary search

Question 2

d. LFU

Question 3

Choice 3
3. Big Theta

Step by step explanation:

Explanation

Question 1

• The form of search known as a compound search is also known as a dictionary search. This sort of search begins with a binary search to reach relatively close to the desired record, and then transitions to a sequential search to locate the item. When looking up terms in a dictionary, people often use this kind of search since it may rapidly narrow down the search area and then discover the specific word that is being sought for.
• The following is how the method for searching the dictionary works:
  -First, a binary search is done to get a general idea of where the word might be.
  -Once the general area is found, a sequential search is done to find the specific word.
  -If the term in question can't be found, the search will be deemed unsuccessful and an error will be shown.
• The algorithm that is used to search the dictionary is particularly effective since it can rapidly discover the term that is sought for without having to search the dictionary in its entirety. In order for the binary search to function correctly, the dictionary must first be sorted. This is a prerequisite for the binary search.
• The dictionary search algorithm is a highly strong tool that can be used to a wide range of settings depending on the requirements of the task at hand. It is very helpful for looking up terms in a big dictionary since it can rapidly discover the word that is sought without having to scan the whole dictionary. This makes it a very valuable tool.
• The way to search the dictionary is often called a "compound search" because it combines a binary search with a sequential search.

Question 2

• The following heuristics for the buffer pool are specified in the text: FIFO, LIFO, and LRU. LFU is not mentioned as one of the strategies set up for the buffer pool in the text.
• The LFU policy is a cache replacement strategy that replaces the things that are utilized the least often first. This policy is often used when getting access to a certain item costs a lot of money and it's important to limit the number of times that item is used.
  The heuristics stated in the text are more vital for the buffer pool since they dictate how pages are replaced in the pool. This makes the heuristics the most important part of the buffer pool. Because it does not take into consideration the frequency with which pages are viewed, the LFU policy would not be as successful in this scenario as it otherwise might have been.
• Because it replaces the pages that haven't been accessed in the shortest amount of time first, the LRU policy is the most efficient of the three heuristics stated in the text. Because of this approach, it is more probable that buffered pages will continue to include content from pages that are browsed more often.
• Because it replaces the pages that have been used the least recently first, the Least Recently Used (LIFO) strategy is the least effective of the three heuristics outlined in the text. Because of this approach, there is a possibility that certain sites that are seen much less often may be removed and replaced with newer content.
• The FIFO policy is more effective than the LIFO policy, while the LRU policy is more effective than FIFO. The pages are replaced according to the sequence in which they were added to the buffer pool when this policy is applied. Because of this, there is a possibility that pages that are viewed more often will be updated more frequently than those that are seen less frequently.
• In most cases, the LRU policy is the ideal option for the buffer pool since it ensures that the pages that are used the most often are more likely to stay in the pool once the policy is applied.

Question 3

• The two functions are considered to have the same growth rate when the big-Oh notation and the big-Omega notation coincide. This is denoted by the use of the big-Theta notation. To put it another way, the functions f(n) and g(n) are big-Oh counterparts to one another.
• This is beneficial because it enables us to compare the rates of expansion of two functions with greater precision. For example, if we know that f(n) is the big-Theta of g(n), we can conclude that f(n) expands at the same rate as g.This is because big-Theta is a measure of exponential growth (n). This is useful information to have when trying to figure out how fast a function will grow as the value of n goes up.
• In addition, the big-Theta notation might be helpful for doing algorithm analysis. If we know that the execution time of an algorithm is f(n), then we can use the big-Theta notation to state that the algorithm will execute in the amount of time that is equivalent to O(f(n)). This is helpful because it gives us a more exact way to compare how well two algorithms work.
• The big-Theta notation is a method that may be used in general to provide a more exact description of the growth rate of a function. It is useful in comparing the growth rates of two different functions as well as in measuring the effectiveness of different methods.
  

Answers with Explanation

16th and 17th Questions

Answer:

1. Circular linked list
2. Option 1. (n²)

Step by step explanation:

1

• A circular linked list is a special kind of linked list in which every node is linked to every other node.to the next node in the list and the last node is connected to the first node. This type of list is often used for applications that need to loop through data or where data is constantly being added and removed from the list.
• One advantage of a circular linked list is that it can be easily traversed. For example, if we wanted to print out all the data in the list, we could simply start at the first node and follow the links until we reach the first node again.
• Another advantage of a circular linked list is that it can be easily modified. For example, if we wanted to add a new node to the list, we could simply insert it between any two existing nodes.
• There are a few disadvantages to using a circular linked list. One is that it can be difficult to keep track of the first and last nodes in the list. Another is that it can be easy to accidentally create a loop in the list, which would cause the list to become infinite.
• Overall, a circular linked list is a good choice for applications that need to loop through data or where data is constantly being added and removed from the list.
• One sort of linked list is known as a single linked list, and it differs from other linked lists in that each node in the list is only connected to the node that comes after it. The very last node in the list is completely disconnected from the rest of the nodes in the list.
• Linear doubly linked list: A linear doubly linked list is a sort of linked list in which each node in the list is connected to both the following node in the list and the node in the list that came before it. Both the first and the last nodes on the list do not have any connections to the other nodes on the list. Both of these nodes are isolated from the rest of the graph.

2. EXPLANATION

• This piece of code has a temporal complexity of O(n2) when executed. This occurs because every time the outer for loop executes, the inner for loop also executes n times. As a result, n2 iterations will be finished. Option 1 is the best asymptotic analysis to carry out because it correctly determines the temporal complexity of the code segment.

Option 2. (n)

• This piece of code has an O time complexity rating (n).The reason for this is that each time the outer for loop iterates, the inner for loop also iterates n times. As a result, n2 iterations will be finished.
• Because it provides an erroneous estimate of the temporal complexity of the code fragment, Option 2 is not the most appropriate choice for an asymptotic analysis. In reality, the time complexity of the code fragment is O(n2).

Option 3. O(log n)

• This snippet of code does not have an O time complexity (log n). This is because the outer for loop iterates n times, and the inner for loop iterates n times for each time the outer loop iterates. This causes the situation described above. This results in a grand total of n2 iterations being carried out successfully.
• Because it provides an erroneous estimate of the temporal complexity of the code fragment, Option 3 is not the most suited choice for an asymptotic analysis. In reality, the time complexity of the code fragment is O(n2).

Option 4. O(2")

• This snippet of code does not have an O time complexity (2"). The reason for this is that each time the outer for loop iterates, the inner for loop also iterates n times.
  

Answers with Explanation

18th Questions

Answer:

• c. Choice 3

Step by step explanation:

• The binary search algorithm is a classic example of an algorithm that has a worst-case asymptotic runtime complexity of O(logn). This means that, as the input size grows larger, the number of operations required to execute the algorithm will grow at most logarithmically.
• There are a few reasons why this is the case. First, the binary search algorithm only needs to consider a small subset of the input data set at each step. It does this by discarding half of the remaining data set at each iteration. Second, the algorithm is able to make use of an efficient data structure, such as an array, which allows for quick access to the data elements.
• Overall, the binary search algorithm is a very efficient algorithm for searching through large data sets. It is also a good example of an algorithm that has a worst-case runtime complexity of O(logn).
  

Answers with Explanation

19th and 20th Questions

Answer:

d. Selection sort

A straightforward algorithm for sorting, and selection sort splits the array into two parts: a subarray that contains components that have been sorted, and another subarray that contains elements that still need to be sorted. At the outset, there is no data in the sorted subarray. We perform (n - 1) repetitions of the array's iteration. During each iteration, we search the unsorted subarray for the element that has the least value and append that value to the end of the sorted subarray.

 

Option 1. O(n) 

This snippet of code will print out the array's contents, one element at a time, in sequential order. Because of this, the asymptotic analysis will be linear, also written as O. (n).

Step by step explanation:

d. Selection sort

The selection sort takes the element with the smallest value and sets it in the location with the least value. This algorithm splits the array into two parts: the sorted subarray, which is on the left, and the unsorted subarray, which is on the right. It finds the element in the unsorted subarray with the least value and inserts it in the first position in that subarray (ascending order). It does this by constantly picking the piece that is one size smaller.

The selection sort is distinct from other algorithms for sorting in that it performs the fewest number of swaps possible—in the worst case scenario, n fewer than one—than any other sorting method.

 

Option 1. O(n) 

This piece of code will print out the contents of the array in sequential order, one entry at a time. Because of this, the asymptotic analysis will be linear, also written as O. (n).

Calculating the amount of time required to complete any operation using mathematical units of computation is an example of asymptotic analysis. In asymptotic analysis, the performance of an algorithm is evaluated based on the number of its inputs (we do not measure the actual amount of time it takes to run the algorithm). It is also possible to calculate how the amount of time (or space) required by an algorithm varies with the quantity of the input.

Answers with Explanation

21th and 22nd Questions

Answer:

Question 1

b. Bubble sort

 

Question 2

b. Choice 1

Step by step explanation:

Rationale:

Question 1

Bubble sort is a simple sorting algorithm that utilizes nested loops where the inner loop moves through the array from bottom to top, comparing adjacent pairs and swapping them if they are out of order.

 

Question 2

The asymptotic notation Big Oh(O) represents the upper bound of an algorithm (or just Oh). For example, if U(n) is the running time of an algorithm A, then g(n) is its Upper Bound if there are two constants K and T such that U(n) = K*g(n) for n > T.

Answers with Explanation

23rd and 24th Questions

Answer:

Answer 1- 

Max-heap structure 

Because Where the value of the root node is greater than or equal to either of its children. So u can see in tree the root node is 100 and their child have smaller value. Option b is correct 

 

Answer 2-

S.pop();

S.pop();
S.pop();

In a stack pop(); would access the 3rd element from the top of the stack S.

The pop() function is used to remove or 'pop' an element from the top of the stack(newest or the topmost element in the stack).

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