University:
University of California, San Diego
Course:
CSE 100/101 | Data Structures and Algorithms
Academic year:

2023
Views:

133

Pages:

2
Author:

anon

Amortized Analysis and Dynamic Arrays: Understanding the Constant Factor An significant data structure in computer science, dynamic arrays offer a handy way to store data sets that can change in size as needed. Dynamic arrays are most frequently implemented by doubling the size of the array each time it fills up. This article will investigate the significance of utilizing a constant factor in the growth of dynamic arrays and how it affects the amortized cost of operations as alternatives to this method. In dynamic arrays, what does a constant factor mean? A fixed value that is utilized to calculate the array's growth rate is referred to as a constant factor in dynamic arrays. In dynamic arrays, the most prevalent constant factor is 2, which causes the array size to double each time it reaches capacity. But you could also use an other constant factor, like 2.5 or 3. The constant factor that is employed must be constant and must not change over time. The significance of a constant factor in dynamic arrays Because it affects the amortized cost of operations, the application of a constant factor in dynamic arrays is crucial. The amortized cost of operations changes from O to O(n) if a constant quantity rather than a constant factor is utilized to grow the dynamic array each time (1). This is due to the fact that there isn't enough time to build up enough work to perform the required movement as the array gets bigger and bigger. Amortized Cost of Operations: An Overview Instead of the worst-case cost of a single operation, the amortized cost of operations in dynamic arrays refers to the average cost of a series of operations. The aggregate technique, the banker's method, and the physicist's method are the three methods for analyzing the amortized cost of operations in dynamic arrays. The cost of each operation is calculated, added, and divided by the total number of operations in the aggregate technique. This method offers a calculation of the amortized cost via brute force. The amortized cost of operations are represented by tokens in the banker's technique with the understanding that they are conceptually saved within the data structure. The amortized cost of operations is determined using the physicist's method, which defines a potential function and analyzes the change in that potential. This approach offers a mechanism to examine the dynamic array's runtime rather than altering the code. To maintain an O(1) amortized cost of operations, it is crucial to employ a constant factor in dynamic arrays. This can be done by analyzing the amortized cost using the aggregate approach, the banker's method, or the physicist's method. For those developing effective algorithms and working with dynamic arrays, understanding these ideas is crucial.