functoolsreduce

functools.reduce is a function in the Python standard library that applies a binary function cumulatively to the items of an iterable, from left to right, to produce a single value. It is defined in the functools module; in Python 2 it was a built-in function, but in Python 3 it resides in functools and is imported with from functools import reduce.

Signature and behavior: reduce(function, iterable [, initializer]). The function is called with two arguments: the accumulated value and the next item. If an initializer is provided, it is placed before the first item and the reduction starts with that value. If no initializer is given, the first item of the iterable serves as the initial value. If the iterable is empty and no initializer is provided, reduce raises TypeError: reduce() of empty sequence with no initial value. If an initializer is provided and the iterable is empty, the initializer is returned.

Examples: reduce(lambda a, b: a + b, [1, 2, 3, 4]) returns 10. reduce(lambda a, b: a * b, [1, 2, 3, 4], 1) returns 24. Using an operator: from operator import add; reduce(add, [1, 2, 3, 4]) also yields 10.

Notes: reduce implements a left fold, applying the function from the first element (or the initializer) toward the end. It accepts any callable that takes two arguments. For simple numeric sums, sum is often preferred. Other patterns include using reduce with complex merging logic or combining elements into a single structure.