janymuong / sorting_algorithms

Implementation of sorting algorithms, asymptotic analysis, and BIG - O notation

C- Sorting algorithms & Big O

data structures, algorithms
covers: implementation of sorting algorithms, asymptotic analysis, and BIG - O notation

Sorting Algorithms

Sorting algorithms are a type of algorithm that takes an array of elements and sorts them based on some defined order e.g. ascending or descending, or some form of a lexicographical operation.

sample algorithms, for context:
bubble sort, selection sort, insertion sort, quick sort, merge sort, radix sort
focuses on the first 4

Asymptotic Analysis

Asymptotic analysis is a way of gauging the performance of algorithms as the size of the input increases and not paying attention to the machine specific implementation. Asymptotic analysis is used to compare the performance of different algorithms and to choose the best algorithm for a given problem.

The most common way to express the asymptotic running time of an algorithm is using Big-O notation. Big-O notation is a way of classifying the asymptotic running time of an algorithm based on its growth rate.

Examples of Big-O notations:

• O(1): this means that the algorithm's running time is constant, regardless of the size of the input.
• O(n): (time complexity of linear growth), and it increases with the size of the input.
• O(n^2): this means that the algorithm's running time is quadratic, and it increases quadratically with the size of the input.
• O(2^n): the time complexity of exponential growth, and it increases exponentially with the size of the input
• O(n!): the time complexity of factorial growth
• O(log(n)): is the time complexity of logarithmic growth
• O(nlog(n)): the time complexity of nlog(n) growth, which is possible if we are using a balanced binary search tree and working with some array that is sorted.

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