Sorting Algorithms Quiz

A sorting algorithm where the input array is sorted without needing extra memory proportional to the input size. It uses a fixed amount of additional memory, typically for temporary variables.

A type of sorting algorithm that requires additional memory that is proportional to the size of the input array. It uses a new array, often of equal size, to store the sorted elements.

Describes a memory allocation of constant size, independent of the input size. Typically refers to fixed numbers of local variables used in a sorting algorithm.

Describes a memory allocation that grows linearly with the size of the input array. For example, using a second, equally sized array for sorting.

A method of sorting algorithms that prioritize using in-place sorting as it often results in more efficient and memory-friendly solutions.

Sorting algorithms are often designed to work with arrays, both for input and output. This means data is organized in a linear sequence.

A sorting algorithm that repeatedly randomizes the elements of a list until they are in order. It is extremely inefficient and impractical for real-world use.

A sorting algorithm that randomly swaps two elements in a list until they are in order. It is even more inefficient than Bogosort and is not used in practice.

The number of pairs of elements in a list that are out of order. A list with zero inversions is sorted.

There is no single optimal sorting algorithm for all situations. The choice of the best algorithm depends on factors such as the size of the input, the type of data, and the required performance.

A list is considered sorted when all elements are in ascending order, meaning that each element is less than or equal to the element that follows it.

Operations performed by sorting algorithms are based on the type of action taken on data elements. These include insertion, swapping, selection, merging, and distribution.

Run-time of sorting algorithms can be categorized as O(n), O(n log(n)), or O(n^2). Complexity depends on the algorithm and data size.

Average-case and worst-case scenarios influence the performance of sorting algorithms. The efficiency of a sorting algorithm can vary based on the input data, influencing its run-time.

Traditional sorting algorithms like Insertion and Bubble sort have a run-time of O(n^2). They are simple but less efficient for large datasets.

Faster sorting algorithms, including Heap, Quick, and Merge sort, have a run-time of O(n log(n)). They are ideal for large datasets.

Linear-time sorting algorithms like Bucket and Radix sort have a run-time of O(n). They require assumptions about the data.

Any sorting algorithm must examine each element at least once. This means any sorting algorithm must be at least O(n) in complexity.

The general lower bound for sorting algorithms is O(n log(n)). This is the minimum time complexity achievable without assumptions about the data. It is related to the number of permutations of n objects (n!) and the height of comparison trees.

Sorting is a process where a list of objects is reorganized based on a specific order. It can be applied to numbers, strings, or any other data that can be linearly ordered. Think of it like organizing your books by alphabetical order: the result is a sequence where each element is less than or equal to the one following it.

While sorting can be applied to individual values like numbers, it's more common to sort records. Each record is a group of data, and we sort them based on a 'key' value. Think of a spreadsheet with columns for student ID, Name, and Grade. We could sort this data based on student ID to efficiently find specific student records.

The time efficiency of a sorting algorithm describes how long it takes to sort a list as the list's size grows larger. It's usually measured in terms of how many operations are required. For example, a sorting algorithm with a 'linear' time complexity would take twice as long to sort 100 items compared to 50 items.

An inversion is a pair of elements in a list that are out of order. Think about a mixed-up deck of cards. If the Ace of Hearts is above the King of Hearts, that's an inversion. The more inversions a list has, the more 'unsorted' it is.

Insertion sort is a simple sorting algorithm where you start with an empty sorted list and sequentially insert elements from the unsorted list in their correct position. Picture building a sorted deck of cards one by one. You look at the next card and place it in its correct position within the already sorted section.

The worst-case scenario for insertion sort happens when the list is sorted in reverse order. For example, if the list is (10, 9, 8, 7...). The algorithm must move all elements to find their correct position every time. This results in a relatively slow run-time, making it inefficient for very large datasets.

On average, insertion sort takes about 'n squared' steps to sort a list with 'n' elements. This means if we double the list's size, the sorting time increases by a factor of four. It's relatively efficient for smaller lists but can become slow for very large datasets.

A measure of how far out of order a list of numbers is. A list with many numbers that are in an order that is the opposite of the intended order has a high number of inversions.

In an unsorted list of numbers, the number of pairs (out of all pairs) that are in the incorrect order.

The number of inversions grows with the size of the list, as there are more pairs to compare.

The number of ways you can choose two items from a set. For example, if you have a set of 6 items, there are 15 ways you can choose 2 items.

The number of inversions in a list of n numbers is n * (n-1) / 2. The idea is similar to the binomial coefficient, as we are choosing two numbers out of n to see if they are in the incorrect order.

Insertion sort inserts each element into its correct position in the already sorted portion of the list, building up the sorted list one element at a time.

The process of rearranging the elements in a list so that they are in a specific order, usually ascending or descending.

A measure of how many times elements in a list need to be swapped to achieve a sorted order. It directly affects the efficiency of sorting algorithms. A list with fewer inversions can be sorted more efficiently.

The time it takes for an algorithm to complete, typically expressed in terms of how it grows with the input size. For example, insertion sort has an average runtime O(n^2), meaning the time increases quadratically with the size of the list.

The process of moving an element within a list while maintaining the order of the remaining elements. It is often used within sorting algorithms.

A type of sorting algorithm that uses a loop iterating through the list and examining or comparing elements to achieve sorting.

The case where the input list is already sorted, resulting in the algorithm requiring the least amount of work and time.

The case where the input list is in reverse sorted order, resulting in the algorithm requiring the most amount of work and time.

A sorting algorithm works by repeatedly comparing adjacent elements in a list and swapping them if needed until the list is sorted. An example of this type of sorting is bubble sort.

A type of sorting algorithm that does not rely on direct comparisons between elements, but rather uses the frequency of occurrences in the list to sort the elements. An example of this type of sorting is bucket sort.