2. Selection Sort

Sorting is a fundamental problem in computer science and has many practical applications. There are several algorithms for sorting, each with its own strengths and weaknesses. In this coursework, we will discuss some of the most commonly used algorithms for sorting problems and analyze their complexity.

1. Bubble Sort:

Bubble sort is a simple algorithm that repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order. The pass through the list is repeated until the list is sorted. The time complexity of bubble sort is O(n^2) in the worst case.

2. Selection Sort:

Selection sort is an algorithm that selects the smallest element from an unsorted list in each iteration and places that element at the beginning of the list. The time complexity of selection sort is O(n^2) in the worst case.

3. Insertion Sort:

Insertion sort is a simple sorting algorithm that builds the final sorted array one item at a time. The algorithm iterates through the list and compares each element with the elements before it. If the element is smaller, it is moved to its correct position in the sorted list. The time complexity of insertion sort is O(n^2) in the worst case.

4. Merge Sort:

Merge sort is a divide and conquer algorithm that divides the unsorted list into n sublists, each containing one element, and then repeatedly merges sublists to produce new sorted sublists until there is only one sublist remaining. The time complexity of merge sort is O(n log n) in the worst case.

5. Quick Sort:

Quick sort is a divide and conquer algorithm that selects a pivot element from the array and partitions the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. The sub-arrays are then sorted recursively. The time complexity of quick sort is O(n log n) in the average case and O(n^2) in the worst case.

6. Heap Sort:

Heap sort is a comparison-based sorting algorithm that uses a binary heap data structure. It divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element and moving that to the sorted region. The time complexity of heap sort is O(n log n) in the worst case.

In conclusion, each sorting algorithm has its own advantages and disadvantages, and the choice of algorithm depends on the specific requirements of the problem at hand. However, it is important to consider the time complexity of the algorithm when selecting a sorting algorithm, as it can have a significant impact on performance for large datasets.