Question

Determine whether each of the following statements is true or false. If false, explain why. a) Elements in a Collection must be sorted in ascending order before a binarySearch may be performed. b) Method first gets the first element in a TreeSet. c) \(A\) List created with Arrays method asList is resizable. d) Class Arrays provides static method sort for sorting array elements.

Short answer

a) True; b) True; c) False; d) True.

Step-by-step solution

Evaluate Statement a

For statement (a), consider the requirements for performing a binary search. A binary search requires the elements in the collection to be sorted in ascending (or any consistent) order to function correctly, as it works by comparing the middle element and dividing the search interval in half. Therefore, statement (a) is true.

Evaluate Statement b

For statement (b), consider how a TreeSet data structure works. A TreeSet in Java is implemented as a NavigableSet backed by a TreeMap, and it maintains elements in sorted order. Method `first()` returns the first (lowest) element in this sorted order. Therefore, statement (b) is true.

Evaluate Statement c

For statement (c), assess the characteristics of a list created with `Arrays.asList()`. This method returns a fixed-size list backed by the original array, meaning that while you can modify the elements in the list, you cannot change its size. Therefore, statement (c) is false because the List is not resizable.

Evaluate Statement d

For statement (d), consider the static methods provided by the `Arrays` class in Java. The `Arrays` class includes a static method `sort()`, which can be used to sort the elements of an array in place. Therefore, statement (d) is true.

Key concepts

Binary Search

Binary search is a highly efficient algorithm used to find a specific element within a sorted collection, often employed in programming for its speed compared to linear searching methods. The mechanism of binary search involves:

• Checking the middle element of the sorted collection.
• If the target value is equal to the middle element, the search concludes successfully.
• If the value is less than the middle one, the search narrows down to the left half; if greater, it focuses on the right half.

This process of halving continues until the target value is found or the range is fully explored. It is crucial to ensure that the list is sorted in a consistent order (ascending is typical) prior to performing a binary search, as its efficient halving technique relies on this order. Without sorting, the algorithm can fail to return the correct result.

TreeSet

A TreeSet in Java is a part of the Java Collections Framework that implements a NavigableSet based on a TreeMap. This means it stores its elements in a sorted order. Some of the main features and methods of TreeSet are:

• Unique Elements: TreeSet does not allow duplicate elements.
• Sorted Order: The elements are kept in ascending order, based on either the natural ordering of the elements or according to a provided comparator.
• Efficiency: Operations like add, remove, and search have a time complexity of O(log n).

The method `first()` in TreeSet is used to retrieve the smallest, or first, element according to the defined order. This makes TreeSet especially useful in scenarios where order matters, and elements need to be accessed in a sorted manner.

Arrays.asList()

The `Arrays.asList()` method in Java is utilized to convert an array into a list. While handy, this method has a particular limitation to be aware of: it creates a list of fixed size. Here's how it works and what to remember:

• Fixed Size: The list is essentially a view of the original array, meaning that you cannot add or remove elements from it.
• Element Modification: Although the size is fixed, you can modify the elements within the list, which will be reflected in the original array.
• Mismatch Expectations: Trying to perform resizing operations, like `add` or `remove`, results in an `UnsupportedOperationException`.

Understanding this behavior is critical when working with lists in Java, especially when flexibility in size is a requirement for the task at hand.

Java Arrays Sorting

Sorting arrays in Java is made simple through the use of the `sort()` method provided in the Arrays class. This static method allows for in-place sorting of arrays. Important aspects of this function include:

• In-place Sorting: The original array is modified, with elements rearranged into ascending order.
• Efficiency: It uses a modified version of the QuickSort algorithm for primitives and a stable, adaptive merge sort for objects, leading to efficient time complexity.
• Overloaded Methods: There are multiple versions of the sort method to handle different data types, both primitive and object types.

By utilizing the `sort()` method, Java developers can quickly and reliably arrange data in arrays, preparing it for further processing, like running a binary search.