C950 Data Structures and Algorithms II

Correct Answer

A. O(n)

Explanation

In the worst case, a sequential search must examine every element in the array to find the target (or determine it is not present). This results in a linear number of comparisons, giving it a time complexity of O(n). The search scales proportionally with the number of elements.

Why other options are wrong

B. O(n²)

This runtime suggests nested loops or operations where the number of steps grows quadratically. Sequential search involves a single loop through the array, not multiple nested iterations.

C. O(n/2)

Although on average a sequential search might find the element halfway through the array, Big-O notation ignores constant factors. Thus, O(n/2) simplifies to O(n) in asymptotic analysis and is not the correct way to express the worst case.

D. O(log n)

This applies to algorithms like binary search that divide the search space. Sequential search does not do this—it checks each element one by one—so logarithmic time is not applicable.

Correct Answer

B. To apply a function to the current node before traversing its children.

Explanation

In preorder traversal, the node is visited first before its children. The function call f(n) is used to perform some operation on the current node (such as processing or printing the value) before recursively visiting the left and right children. This is a fundamental characteristic of preorder traversal, where the "parent" node is handled first.

Why other options are wrong

A. To traverse the left child of the node before processing the current node.

This is incorrect because in preorder traversal, we process the current node first, then move to its left child, not the other way around.

C. To check if the current node is null before proceeding with the traversal.

This is a common check in recursive tree traversals to avoid null pointer errors, but it is not the primary purpose of the function call f(n) in preorder traversal. The purpose of f(n) is to perform an action on the current node.

D. To collect the values of the nodes in a list after visiting both children.

This is not part of the preorder traversal. Collecting values after visiting both children is characteristic of postorder traversal, not preorder.

Correct Answer

B. Destructors for ADT-based iterators have amortized constant runtime.

Explanation

In most cases, destructors for iterators do not involve significant overhead and have amortized constant time complexity. This is because they simply need to release any internal resources held by the iterator, which is typically done in constant time. The complexity is independent of the size of the container or the number of elements, so it is considered amortized constant.

Why other options are wrong

A. All iterator operations have amortized constant runtime, including destructors.

This is incorrect because iterator operations (such as dereferencing or incrementing) do not necessarily have amortized constant time. While destructors might have constant time, other operations like copying or moving iterators may depend on the underlying container's structure and can vary in runtime.

C. Copy operations for ADT-based iterators have Θ(n) runtime in the worst case.

This is incorrect because the copy operation for iterators typically has constant time complexity (Θ(1)), assuming the iterator itself is a simple object. However, copying the contents of the container to a new iterator might take Θ(n) time in some cases, but not the iterator copy itself.

D. All iterator operations, including copy operations, have Θ(n) runtime.

This is incorrect because iterator operations like incrementing and dereferencing typically take constant time (Θ(1)). The complexity of copying the iterator is also constant time (Θ(1)) unless dealing with the underlying container's complexity.

Correct Answer

B. A collection of data, a set of operations, and rules that define the behavior of those operations.

Explanation

An Abstract Data Type (ADT) defines a data structure purely in terms of what operations can be performed and what the expected behavior of those operations is. It does not specify how the operations are implemented. The key components include the data, the operations that can be performed on the data, and the rules governing these operations, such as their logical behavior and constraints.

Why other options are wrong

A. A collection of data, a set of operations, and a specific implementation language.

This is incorrect because an ADT is independent of implementation details, including programming languages. The concept focuses on what operations can be performed, not how or in what language.

C. A collection of data, a fixed number of operations, and constraints on data types.

This is wrong because ADTs are not necessarily limited to a fixed number of operations. They are defined by the operations relevant to the data abstraction, which may vary. Also, constraints on data types are part of implementation, not the abstract model.

D. A collection of data, a set of operations, and a graphical representation of the data structure.

This is incorrect because a graphical representation is not a required or defining feature of an ADT. ADTs are conceptual and do not rely on visualization for their definition or function.

Correct Answer

A. They return an iterator

Explanation

Generic algorithms in C++ typically use iterators to indicate the range of valid elements after modifying a container. For example, after calling a function like remove_if, the algorithm returns an iterator pointing to the new end of the container, indicating where the valid elements end. The invalid elements are left beyond this iterator, allowing users to know which elements have been removed or altered.

Why other options are wrong

B. They call the erase member function

This is incorrect because calling erase is an operation on the container that modifies its contents. While erase does remove elements, the purpose of generic algorithms is not to directly erase but to modify iterators or ranges. The algorithm typically returns iterators to show the new valid range.

C. They change the invalid elements to a different value

This is incorrect because generic algorithms do not modify elements in a way that invalid elements are marked with a different value. Instead, they indicate the range of valid elements through iterators, and the invalid elements are left at the end of the container.

D. They change a non-const argument to an index

This is incorrect because generic algorithms do not typically work by changing non-const arguments to indices. They operate on iterators, not direct indices, to work generically across various container types.

Correct Answer

A. Public components allow external access, while private components protect internal data.

Explanation

In an Abstract Data Type (ADT), public components are the methods and functions that are accessible to the outside world. They define the interface through which users interact with the data structure, enabling them to perform operations like insert, delete, push, pop, or traverse depending on the ADT. On the other hand, private components refer to the internal structure and implementation details that are hidden from the user. These private elements protect the integrity of the data and ensure that the ADT operates in a controlled and predictable manner, preventing external manipulation that could lead to inconsistencies or errors.

Why other options are wrong

B. Private components are only for internal use, while public components are used for data storage.

This is incorrect because private components are not used for data storage but for internal logic and management of the data. Public components provide access to the data but are not used for direct storage.

C. Public components are for data manipulation, while private components are for user interaction.

This is incorrect because public components are used for interaction with the ADT and manipulation of its data, while private components handle the internal workings of the ADT, not user interaction.

D. Both components serve the same purpose in an ADT.

This is incorrect because public and private components serve different roles. Public components provide an interface for external use, while private components handle the internal implementation details of the ADT.

Correct Answer

B. A Set is unordered and does not allow duplicates, unlike lists which are ordered.

Explanation

A Set is a data structure that stores unique elements and does not allow duplicates. Sets are typically unordered, meaning the elements are not stored in any specific sequence. Unlike lists or arrays, which maintain the order of insertion, a Set does not preserve this order. Sets are ideal when the uniqueness of elements is a primary concern, such as in situations where duplicates should be avoided.

Why other options are wrong

A. A Set allows duplicate elements, while lists do not.

This is incorrect because one of the defining features of a Set is that it does not allow duplicates. Lists, on the other hand, can contain duplicate elements.

C. A Set is a type of array that can only hold integers.

This is incorrect because a Set is a different type of data structure and is not an array. Additionally, Sets can hold any data type, not just integers.

D. A Set is a collection that maintains the order of elements.

This is incorrect because Sets are unordered collections, meaning they do not maintain the order in which elements are added.

Correct Answer

A. max_element

Explanation

The max_element algorithm in the C++ Standard Template Library (STL) is used to find the maximum element in a container. It returns an iterator to the element with the largest value within the given range.

Why other options are wrong

B. find

This is incorrect because find is used to search for a specific element in a container, not to find the maximum element. It returns an iterator to the first occurrence of the element or to the end of the container if the element is not found.

C. sort

This is incorrect because sort is used to sort the elements of a container in a specified order. It does not directly find the maximum element but may help in ordering elements in ascending or descending order.

D. replace

This is incorrect because replace is used to replace occurrences of a specific value in a container with another value. It is not related to finding the maximum element in a container.

Correct Answer

C. Deque

Explanation

A deque (double-ended queue) is a sequential container that allows efficient insertion and deletion of elements at both ends. It supports constant time (O(1)) operations for adding or removing elements at the front or back, while access to elements in the middle can still be performed but is not as efficient as with a vector. Since the question specifies that frequent middle access is not required, a deque is the most suitable option.

Why other options are wrong

A. Vector

Although a vector supports fast access to elements and efficient insertion at the back, it does not support efficient insertion or deletion at the front. Inserting or removing elements from the front of a vector requires shifting all other elements, which makes these operations O(n).

B. List

A list supports efficient insertion and deletion at both ends, but it does not offer constant time random access to elements. While it is efficient for adding/removing elements at both ends, it is less suitable when random access or modifying elements in the middle is not needed. In this case, a deque is more efficient than a list for operations at both ends.

D. Array

An array is a fixed-size container and does not support dynamic insertion or deletion of elements. It is not suitable for cases where elements need to be added or removed at both ends efficiently. Additionally, resizing an array involves copying all the elements to a new memory location, which is inefficient.