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A generator expression may be used in Python versions >= 2.4 which gives lazy evaluation over its input, and can be used with generators to iterate over 'infinite' input such as the count generator function which returns successive integers:
The sieve starts with a list of the integers from 1 to n. From this list, all numbers of the form i + j + 2ij are removed, where i and j are positive integers such that 1 ≤ i ≤ j and i + j + 2ij ≤ n. The remaining numbers are doubled and incremented by one, giving a list of the odd prime numbers (that is, all primes except 2) below 2n + 2.
Introduced in Python 2.2 as an optional feature and finalized in version 2.3, generators are Python's mechanism for lazy evaluation of a function that would otherwise return a space-prohibitive or computationally intensive list. This is an example to lazily generate the prime numbers:
[1] [2] It follows 4,294,967,294 and precedes 4,294,967,296. It has a factorization of 3 ⋅ 5 ⋅ 17 ⋅ 257 ⋅ 65537 {\displaystyle 3\cdot 5\cdot 17\cdot 257\cdot 65537} . In computing, 4,294,967,295 is the highest unsigned (that is, not negative) 32-bit integer, which makes it the highest possible number a 32-bit system can store in memory.
The other two for loops, and the initialization of the output array, each take O(n) time. Therefore, the time for the whole algorithm is the sum of the times for these steps, O(n + k). [1] [2] Because it uses arrays of length k + 1 and n, the total space usage of the algorithm is also O(n + k). [1]
By default, a Pandas index is a series of integers ascending from 0, similar to the indices of Python arrays. However, indices can use any NumPy data type, including floating point, timestamps, or strings. [4]: 112 Pandas' syntax for mapping index values to relevant data is the same syntax Python uses to map dictionary keys to values.
A graph exemplifying merge sort. Two red arrows starting from the same node indicate a split, while two green arrows ending at the same node correspond to an execution of the merge algorithm. The merge algorithm plays a critical role in the merge sort algorithm, a comparison-based sorting algorithm. Conceptually, the merge sort algorithm ...
In Raku, a sister language to Perl, for must be used to traverse elements of a list (foreach is not allowed). The expression which denotes the collection to loop over is evaluated in list-context, but not flattened by default, and each item of the resulting list is, in turn, aliased to the loop variable(s). List literal example: