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The initialization of the count array, and the second for loop which performs a prefix sum on the count array, each iterate at most k + 1 times and therefore take O(k) time. The other two for loops, and the initialization of the output array, each take O ( n ) time.
One example of the double counting method counts the number of ways in which a committee can be formed from people, allowing any number of the people (even zero of them) to be part of the committee. That is, one counts the number of subsets that an n {\displaystyle n} -element set may have.
As a collection algorithm, reference counting tracks, for each object, a count of the number of references to it held by other objects. If an object's reference count reaches zero, the object has become inaccessible, and can be destroyed. When an object is destroyed, any objects referenced by that object also have their reference counts decreased.
Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})
Graphical examination of count data may be aided by the use of data transformations chosen to have the property of stabilising the sample variance. In particular, the square root transformation might be used when data can be approximated by a Poisson distribution (although other transformation have modestly improved properties), while an inverse sine transformation is available when a binomial ...
Below are examples of all the properties of count nouns holding for the count noun chair, but not for the mass noun furniture. Occurrence in plural. There is a chair in the room. (correct) There are chairs in the room. (correct) There is chair in the room. (incorrect) There is a furniture in the room. (incorrect) There are furnitures in the ...