Following from Pillsy’s reference to matrix exponentiation, such that for the matrix M = [1 1] [1 0] then fib(n) = Mn1,2 Raising matrices to powers using repeated multiplication is not very efficient. Two approaches to matrix exponentiation are divide and conquer which yields Mn in O(ln n) steps, or eigenvalue decomposition which is constant … Read more
The ECMA specification does not specify a bounding complexity, however, you can derive one from the specification’s algorithms. push is O(1), however, in practice it will encounter an O(N) copy costs at engine defined boundaries as the slot array needs to be reallocated. These boundaries are typically logarithmic. pop is O(1) with a similar caveat … Read more
O(max(input)+n) The complexity just appears awkward to express because most sorting algorithms are data agnostic. Their time scales with the amount of data, not the data itself. FWIW, as pointed out here, this is not a reliable algorithm for sorting data.
EDIT: I had misunderstood the mechanism of a centrifuge and it appears that it does a comparison, a massively-parallel one at that. However there are physical processes that operate on a property of the entity being sorted rather than comparing two properties. This answer covers algorithms that are of that nature. A centrifuge applies a … Read more
In a tree where each node has exactly either 0 or 2 children, the number of nodes with 0 children is one more than the number of nodes with 2 children.{Explanation: number of nodes at height h is 2^h, which by the summation formula of a geometric series equals (sum of nodes from height 0 … Read more
Yes. Iterating over a list is O(n) and adding each element to the hash set is O(1), so the total operation is O(n).
The outer loop runs n times. For each iteration, the inner loops runs n / i times. The total number of runs is: n + n/2 + n/3 + … + n/n Asymptotically (ignoring integer arithmetic rounding), this simplifies as n * (1 + 1/2 + 1/3 + … + 1/n) This series loosely converges … Read more
Arrays Set, Check element at a particular index: O(1) Searching: O(n) if array is unsorted and O(log n) if array is sorted and something like a binary search is used, As pointed out by Aivean, there is no Delete operation available on Arrays. We can symbolically delete an element by setting it to some specific … Read more
I hope this is helpful to anybody having trouble understanding computational time complexity for Breadth First Search a.k.a BFS. Queue graphTraversal.add(firstVertex); // This while loop will run V times, where V is total number of vertices in graph. while(graphTraversal.isEmpty == false) currentVertex = graphTraversal.getVertex(); // This while loop will run Eaj times, where Eaj is … Read more
In CPython, the standard implementation of Python, there’s an implementation detail that makes this usually O(n), implemented in the code the bytecode evaluation loop calls for + or += with two string operands. If Python detects that the left argument has no other references, it calls realloc to attempt to avoid a copy by resizing … Read more