Finding the GCD of a list of numbers (a.k.a. Reducing numbers in a list) (Python)

2010-07-06T18:52:55-07:00

Python recipe 577282 by Stephen Akiki (common, denominator, gcd, greatest, lisst, reduce).

http://akiscode.com/articles/gcd_of_a_list.shtml

This python code snippet allows you to find the GCD of a list of numbers, after this it is a simple matter of diving all the numbers in the list by the GCD to reduce it.

Why this works...

The GCD of a list of numbers [a, b, c] is GCD(GCD(a, b), c). The reduce function does exactly this and thus gives you the GCD of all the numbers in the list.

Functional selection sort (Python)

2009-09-29T13:34:35-07:00

Python recipe 576917 by pavel (algorithm, algorithms, functional, lambda, reduce, selection, sort, sorting). Revision 3.

This is a variant of selection sort without using for-statements. Do you like it? :-)

Sharing-aware tree transformations (Python)

2012-05-07T08:20:58-07:00

Python recipe 578117 by Sander Evers (fold, reduce, sharing, tree, yaml). Revision 2.

The function foldsh in this recipe is a general purpose tool for transforming tree-like recursive data structures while keeping track of shared subtrees.

# By default, a branch is encoded as a list of subtrees; each subtree can be a
# branch or a leaf (=anything non-iterable). Subtrees can be shared:
>>> subtree = [42,44]
>>> tree = [subtree,[subtree]]
# We can apply a function to all leaves:
>>> foldsh(tree, leaf= lambda x: x+1)
[[43, 45], [[43, 45]]]
# Or apply a function to the branches:
>>> foldsh(tree, branch= lambda t,c: list(reversed(c)))
[[[44, 42]], [44, 42]]
# The sharing is preserved:
>>> _[0][0] is _[1]
True
# Summing up the leaves without double counting of shared subtrees:
>>> foldsh(tree, branch= lambda t,c: sum(c), shared= lambda x: 0)
86

In particular, it is useful for transforming YAML documents. An example of this is given below.

Cycle-aware tree transformations (Python)

2012-06-20T08:09:13-07:00

Python recipe 578118 by Sander Evers (cyclic, fold, reduce, yaml).

A variation on Recipe 578117 that can deal with cycles. A cycle means that a tree has itself as a subtree somewhere. A fold over such a data structure has a chicken-and-egg-problem: it needs its own result in order to construct its own result. To solve this problem, we let branch construct a part of its result before going into recursion. After the recursion, branch gets a chance to complete its result using its children's results. Python's support for coroutines (using yield) provides a nice way to define such a two-stage branch function.

Traverse dotted attribute of an object using built-in function reduce (Python)

2013-01-05T05:49:27-08:00

Python recipe 578398 by Chaobin Tang (唐超斌) (attributes, bif, recursive, reduce).

Making good use of reduce() to traverse dotted attribute of an object.

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