I need you to work on the project and all what you need to f…
I need you to work on the project and all what you need to follow is in the link below http://cs.boisestate.edu/~cs121/projects/p2/ also this is the grading rubric http://cs.boisestate.edu/~cs121/projects/p2/student-rubric.txt make sure clear work no complicated methods or concepts also no plagiarism Purchase the answer to view it
Answer
Analysis of Array Manipulation Algorithms
Introduction
Array manipulation algorithms are fundamental techniques used in computer science and computational mathematics to modify the elements of an array. These algorithms are essential for a wide range of applications, such as sorting, searching, and data transformation. In this project, we will explore and analyze three different array manipulation algorithms: bubble sort, merge sort, and selection sort.
Bubble Sort
Bubble sort is a simple comparison-based sorting algorithm that repeatedly steps through the array, compares adjacent elements, and swaps them if they are in the wrong order. This process is repeated until the array is sorted. The worst-case time complexity of bubble sort is O(n^2), as it requires nested iterations over the entire array. However, the best-case time complexity is O(n), which occurs when the array is already sorted.
Bubble sort has several advantages, such as its simplicity and ease of implementation. It also performs well for small-sized arrays or partially sorted arrays. However, it becomes less efficient when dealing with large-sized arrays or arrays with a large number of inversions. In such cases, other sorting algorithms, such as merge sort or quicksort, are more suitable.
Merge Sort
Merge sort is a divide-and-conquer sorting algorithm that recursively divides the array into smaller subarrays, sorts them individually, and then merges them back together. The key idea of merge sort is to divide the array in half until each subarray contains only one element. Then, it merges the subarrays in a sorted manner until the complete array is sorted.
The time complexity of merge sort is O(n log n) in both the average and worst cases. It guarantees consistent performance regardless of the input data, making it a reliable choice for sorting large-sized arrays. However, merge sort also requires additional memory space for creating temporary arrays during the merging process.
Selection Sort
Selection sort is another simple comparison-based sorting algorithm. It works by dividing the array into two parts: the sorted part and the unsorted part. It repeatedly selects the smallest (or largest) element from the unsorted part and swaps it with the first element of the unsorted part. This process is repeated until the entire array is sorted.
The worst-case and best-case time complexities of selection sort are both O(n^2), as it requires nested iterations for searching the minimum or maximum element. Selection sort has the advantage of having less memory overhead compared to merge sort, as it doesn’t require additional temporary arrays. However, it is not suitable for large-sized arrays or partially sorted arrays, as it performs the same number of comparisons even if the array is partially sorted.
Conclusion
In this project, we have explored and analyzed three different array manipulation algorithms: bubble sort, merge sort, and selection sort. Each algorithm has its advantages and disadvantages, making them suitable for different scenarios. By understanding the principles and time complexities of these algorithms, we can make informed decisions when choosing the most appropriate algorithm for a given situation.