Habibur Rahman (https://www.facebook.com/mmhabib89)
BUBT University Bangladesh
http://www.bubt.edu.bd/
If the array is unsorted, the complexity is O(n) for the worst case. Otherwise O(log n) using binary search.
Binary search is a log n type of search, because the number of operations required to find an element is proportional to the log base 2 of the number of elements. This is because binary search is a successive halving operation, where each step cuts the number of choices in half. This is a log base 2 sequence.
binary search
Merge sort is O(n log n) for both best case and average case scenarios.
Linear search takes linear time with a worst case of O(n) for n items, and an average of O(n/2). Binary search takes logarithmic time, with a worst and average case of O(n log n). Binary search is therefore faster on average.
If the array is unsorted, the complexity is O(n) for the worst case. Otherwise O(log n) using binary search.
Binary search is a log n type of search, because the number of operations required to find an element is proportional to the log base 2 of the number of elements. This is because binary search is a successive halving operation, where each step cuts the number of choices in half. This is a log base 2 sequence.
binary search
Merge sort is O(n log n) for both best case and average case scenarios.
Linear search takes linear time with a worst case of O(n) for n items, and an average of O(n/2). Binary search takes logarithmic time, with a worst and average case of O(n log n). Binary search is therefore faster on average.
The best case for a binary search is finding the target item on the first look into the data structure, so O(1). The worst case for a binary search is searching for an item which is not in the data. In this case, each time the algorithm did not find the target, it would eliminate half the list to search through, so O(log n).
In the worst case a binary search tree is linear and has a height equal to the number of nodes. so h=O(h).
In linear search, the searched key will be compared with each element of the array from the beginning and terminate comparing when the searched key is found or the array is reached. Here time complexity in worst case and average case is O (n). To find an element quickly we use divide and conquer method by using binary search algorithm. Here probed region is reduced from n to n/2. Time complexity is O (log2 n), but here the array should be sorted. But in interpolation search the probed region is reduced from n to n1/2. If the array elements are uniformly distributed the average case complexity is O (log2 (log2n)). Am also searching for hashing to compare & contrast with above.
the compexity of linear search in worst case is f(n) = n+1
The average case time complexity of an algorithm is the amount of time it takes to run on average, based on the input data. It is a measure of how efficient the algorithm is in terms of time.
For a list with n elements, the expected cost is the same as the worst-case cost, which is O(n). The average cost will be O(n/2). However, if the list is ordered by probability and geometrically distributed, the complexity becomes constant, O(1). Compare with a binary search which has a cost of O(log n).
The average case time complexity of the Bubble Sort algorithm is O(n2), where n is the number of elements in the array being sorted.