如何迭代笛卡尔积，使顶级项首先组合？ [英] How to iterate the cartesian product so top items combine first?

问题描述

我需要获得可迭代的笛卡尔积，比如 itertools.product 给我，但出于优化原因，我希望那些具有最低索引总和的对/组合首先出现。

I need to get the cartesian product of iterables, like itertools.product gives me, but for optimization reasons I want those pairs/combinations with the lowest sum of indices to appear first.

因此，例如，如果我有两个列表， a = [1,2,3,4,5] 和 b = ['a'，'b'，'c'，'d'，'e'] ， itertools .product 给了我：

So, for example, if I have two lists, a = [1, 2, 3, 4, 5] and b = ['a', 'b', 'c', 'd', 'e'], itertools.product gives me:

>>> list(itertools.product(a, b))
[(1, 'a'), (1, 'b'), (1, 'c'), (1, 'd'), (1, 'e'), (2, 'a'), (2, 'b'), (2, 'c'), (2, 'd'), (2, 'e'), (3, 'a'), (3, 'b'), (3, 'c'), (3, 'd'), (3, 'e'), (4, 'a'), (4, 'b'), (4, 'c'), (4, 'd'), (4, 'e'), (5, 'a'), (5, 'b'), (5, 'c'), (5, 'd'), (5, 'e')]

相反，我想要在（1，'c'）之前看（2，'a'）。确切的顺序，例如， （1，'b'）和（2，'a'），并不重要。

Instead, I would want to see (2, 'a') before (1, 'c'). The exact order, between e.g. (1, 'b') and (2, 'a'), is unimportant.

目前，我正在根据指数范围的乘积对列表进行排序：

Currently, I am sorting a list based on the product of the index ranges:

>>> sorted(list(itertools.product(range(len(a)), range(len(b)))), lambda a, b: sum(a) - sum(b))
[(0, 0), (0, 1), (1, 0), (0, 2), (1, 1), (2, 0), (0, 3), (1, 2), (2, 1), (3, 0), (0, 4), (1, 3), (2, 2), (3, 1), (4, 0), (1, 4), (2, 3), (3, 2), (4, 1), (2, 4), (3, 3), (4, 2), (3, 4), (4, 3), (4, 4)]

然后用它来索引列表。但是，长列表会占用太多内存。我需要某种具有与 itertools.product 相同的调用约定的生成器，但是我无法弄清楚迭代的方式以便我得到排序和所有可能的对一次。

Then using that to index the lists. However, this takes too much memory with long lists. I need some kind of generator with the same calling convention as itertools.product, but I cannot figure out the way to iterate so that I get both the ordering and all the possible pairs exactly once.

推荐答案

def cartprod(x,y):
    nx = len(x)
    ny = len(y)
    for i in range(nx+ny):
        for j in range(max(0,i-ny+1), min(i+1,nx)):
            yield (x[j],y[i-j])

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