omega notation please see this website http://en.wikipedia.org/wiki/Merge_sort
Big O notation allows to specify the complexity of an algorithm in a simple formula, by dismissing lower-order variables and constant factors.For example, one might say that a sorting algorithm has O(n * lg(n)) complexity, where n is the number of items to sort.Big O notation is used in Computer Science to describe the performance or complexity of an algorithm. Big O specifically describes the worst-case scenario, and can be used to describe the execution time required or the space used (e.g. in memory or on disk) by an algorithm.
Complexity is a measure of how long an algorithm is expected to take and/or how much space is required to complete the task. It is not specific to C++ -- the language is immaterial -- it only applies to algorithms. Complexity is often expressed in big O notation, where O(1) is constant time (the best that can be expected of any algorithm).
Ether
Traversing a doubly linked list is generally faster than traversing a singly linked list, but the speedup depends on how you do the traversal:Traversing from first to last node: No difference.Random access: Doubly linked list is faster, the difference is a fixed factor. (Like twice as fast. Which makes it still very slow for random access compared to arrays.)Reverse order: Doubly linked list is just as fast traversing "backwards" as "forwards", while a singly linked list traversing in reverse order needs to traverse the entire list once for every element in the list - it is a LOT slower. (Time complexity O(n) for doubly linked list, O(n*n) for singly linked, if you are familiar with the notation.)If you are talking about the computer science "big O notation", doubly linked and singly liked lists are the same. This is because the Big O notation ignores fixed factors and only looks at how time increases with the length of the list, and in this respect the two are the same. (Except for the special case of traversing the list in reverse order. Even here a singly linked list could do it in O(n) time - same as a doubly linked list - by reversing the list (O(n)) before traversing it (O(n)) for a total time of 2*O(n), which by the rules of Big O is the same as O(n).)
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.
The Big O notation for finding the complexity of algorithms that involve both finding the character 'c' and 'k' in a given input is O(n), where n is the length of the input.
The Big O notation of the selection sort algorithm is O(n2), indicating that its time complexity is quadratic.
The time complexity of multiplication operations is O(n2) in terms of Big O notation.
The Big O notation of Quicksort algorithm is O(n log n) in terms of time complexity.
The time complexity of Quicksort algorithm is O(n log n) in terms of Big O notation.
The Big O notation of a while loop in terms of time complexity is O(n), where n represents the number of iterations the loop performs.
aka big O notation e.g. 2*x^2 = O(x^2)
Big O gives an upper bound whereas big theta gives both an upper bound and a lower bound.
In algorithm analysis, Big O notation is used to describe the upper bound of an algorithm's time complexity. Induction is a mathematical proof technique used to show that a statement holds true for all natural numbers. In algorithm analysis, induction can be used to prove the time complexity of an algorithm by showing that the algorithm's running time follows a certain pattern. The relationship between Big O notation and induction lies in using induction to prove the time complexity described by Big O notation for an algorithm.
omega notation please see this website http://en.wikipedia.org/wiki/Merge_sort
Big O notation allows to specify the complexity of an algorithm in a simple formula, by dismissing lower-order variables and constant factors.For example, one might say that a sorting algorithm has O(n * lg(n)) complexity, where n is the number of items to sort.Big O notation is used in Computer Science to describe the performance or complexity of an algorithm. Big O specifically describes the worst-case scenario, and can be used to describe the execution time required or the space used (e.g. in memory or on disk) by an algorithm.