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The inverse of the Ackermann function appears in some time complexity results. For instance, the disjoint-set data structure takes amortized time per operation proportional to the inverse Ackermann function, [24] and cannot be made faster within the cell-probe model of computational complexity. [25]
For a sequence of m addition, union, or find operations on a disjoint-set forest with n nodes, the total time required is O(mα(n)), where α(n) is the extremely slow-growing inverse Ackermann function. Although disjoint-set forests do not guarantee this time per operation, each operation rebalances the structure (via tree compression) so that ...
The final iteration through all edges performs two find operations and possibly one union operation per edge. These operations take amortized time O(α(V)) time per operation, giving worst-case total time O(E α(V)) for this loop, where α is the extremely slowly growing inverse Ackermann function. This part of the time bound is much smaller ...
What is Maslow’s hierarchy of needs? We explain the commonly circulated concept with some examples of how it translates in the real world.
Here's an example of a modified Ackermann function which simplifies the explicit formulas for each level in the hierarchy. This function is defined for positive integers m,n both starting at 1 instead of 0:
the inverse grows much slower: . For all values of n relevant to counting the running times of algorithms implemented in practice (i.e., n ≤ 2 65536 , which is far more than the estimated number of atoms in the known universe), the iterated logarithm with base 2 has a value no more than 5.
A class hierarchy in an object-oriented language can be thought of as a tree, with different types of object inheriting from their parents. If different classes need to be combined, such as in a comparison (like A < B ) then the number of possible combinations which may occur explodes.
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