To improve the best case, all we have to do it to be able to
solve one instance of each size efficiently. We could modify
our algorithm to first test whether the input is the special
instance we know how to solve, and then output the canned
answer.
E.g. For sorting, we can check if the values are already ordered,
and if so output them.
Precompute answer for a special case. Check if the input is that special case and return immediately the result. Or you can store results of the most common inputs and return them (kinda caching)
Merge sort (or mergesort) is an algorithm. Algorithms do not have running times since running times are determined by the algorithm's performance/complexity, the programming language used to implement the algorithm and the hardware the implementation is executed upon. When we speak of algorithm running times we are actually referring to the algorithm's performance/complexity, which is typically notated using Big O notation. Mergesort has a worst, best and average case performance of O(n log n). The natural variant which exploits already-sorted runs has a best case performance of O(n). The worst case space complexity is O(n) auxiliary.
There is no worst case for merge sort. Each sort takes the same amount of steps, so the worst case is equal to the average case and best case. In each case it has a complexity of O( N * log(N) ).
All algorithms have a best, worst and average case. Algorithms that always perform in constant time have a best, worst and average of O(1).
Can't say without some detail about the algorithm in question.
By preparing test cases we can test an algorithm. The algorithm is tested with each test case.
Precompute answer for a special case. Check if the input is that special case and return immediately the result. Or you can store results of the most common inputs and return them (kinda caching)
Merge sort (or mergesort) is an algorithm. Algorithms do not have running times since running times are determined by the algorithm's performance/complexity, the programming language used to implement the algorithm and the hardware the implementation is executed upon. When we speak of algorithm running times we are actually referring to the algorithm's performance/complexity, which is typically notated using Big O notation. Mergesort has a worst, best and average case performance of O(n log n). The natural variant which exploits already-sorted runs has a best case performance of O(n). The worst case space complexity is O(n) auxiliary.
The difference between Big O notation and Big Omega notation is that Big O is used to describe the worst case running time for an algorithm. But, Big Omega notation, on the other hand, is used to describe the best case running time for a given algorithm.
These are terms given to the various scenarios which can be encountered by an algorithm. The best case scenario for an algorithm is the arrangement of data for which this algorithm performs best. Take a binary search for example. The best case scenario for this search is that the target value is at the very center of the data you're searching. So the best case time complexity for this would be O(1). The worst case scenario, on the other hand, describes the absolute worst set of input for a given algorithm. Let's look at a quicksort, which can perform terribly if you always choose the smallest or largest element of a sublist for the pivot value. This will cause quicksort to degenerate to O(n2). Discounting the best and worst cases, we usually want to look at the average performance of an algorithm. These are the cases for which the algorithm performs "normally."
Linear time. O(n).
The complexity of an algorithm is the function which gives the running time and/or space in terms of the input size.
By preparing test cases we can test an algorithm. The algorithm is tested with each test case.
There is no worst case for merge sort. Each sort takes the same amount of steps, so the worst case is equal to the average case and best case. In each case it has a complexity of O( N * log(N) ).
The linear search algorithm is a special case of the brute force search.
All algorithms have a best, worst and average case. Algorithms that always perform in constant time have a best, worst and average of O(1).
In case of canny detector, we may say that it is too complex to have its algorithm. It is more than minimax AI algorithm.
Asymptotic