Average-case time complexity refers to the amount of time it takes to execute an algorithm assuming input that has average properties. In other words, average-case time complexity is defined in terms of the statistical distribution of the input data.
For example, consider the problem of sorting a large array of numbers. The average-case time complexity of an algorithm to sort an array is usually O(n log n). This means that the time it takes to sort an array of n elements is proportional to n log n on average. However, this assumes that the input data is randomly ordered, as it would be if the data was generated from a uniformly distributed probability distribution.
If the input array is already sorted or contains many duplicates, this could result in a worst-case time complexity that is higher than O(n log n). Conversely, if the input array contains a lot of randomness, the actual running time of the algorithm may be lower than O(n log n) on average. Therefore, average-case time complexity is a more realistic measure of an algorithm’s performance than worst-case time complexity.
Average-case time complexity refers to the amount of time it takes for an algorithm to complete on average, given a set of inputs.
It is based on the probability distribution of the input data, rather than the specific input values.
Average-case time complexity is usually measured using the expected value of the number of basic operations performed by an algorithm on a set of inputs.
It is useful for estimating how well an algorithm will perform in real-world scenarios, where the input data is not known in advance.
Average-case time complexity can vary widely depending on the characteristics of the input data, such as its size, shape, and structure.
In general, algorithms with lower average-case time complexity are considered better performers than those with higher complexity.
However, it is important to note that average-case time complexity does not guarantee optimal performance in all cases, and algorithms with higher complexity can sometimes outperform those with lower complexity in certain circumstances.
What is the average-case time complexity of quicksort algorithm if the input is a random array of n elements?
Answer: The average-case time complexity of quicksort algorithm is O(nlogn).
What is the average-case time complexity of linear search algorithm if the target element is randomly distributed in the input array of n elements?
Answer: The average-case time complexity of linear search algorithm is O(n/2).
What is the average-case time complexity of bubble sort algorithm if the input is a partially sorted array of n elements?
Answer: The average-case time complexity of bubble sort algorithm is O(n^2).
What is the average-case time complexity of binary search algorithm if the target element is randomly distributed in the sorted input array of n elements?
Answer: The average-case time complexity of binary search algorithm is O(logn).
What is the average-case time complexity of insertion sort algorithm if the input is a randomly ordered array of n elements?
Answer: The average-case time complexity of insertion sort algorithm is O(n^2).