我有列表字典，如下：
D = {'x': [15, 20],
'y': [11, 12, 14, 16, 19],
'z': [7, 9, 17, 18]}
我想一次取3个键（我将使用itertools.permutations），然后计算我可以从每个列表中取出一个元素的所有方法，并对结果进行排序。
对于上面显示的三个键，我会得到2：
(15, 16, 17)
(15, 16, 18)
显然，我可以使用字典值的笛卡尔积，然后计算已排序的那些：
answer = 0
for v_x, v_y, v_z in product(D['x'], D['y'], D['z']):
if v_x < v_y < v_z:
answer += 1
但我可以做得更好吗？此解决方案不会针对键的数量和作为值的列表的长度进行缩放。我尝试了一些毫无结果的调查，但我怀疑我可能必须利用键如何映射到列表值。但是，我认为看看是否有一个解决方案我可以使用而不重新执行其余的程序是值得的。
ETA：这是一个更大的例子。
D = {'a': [15, 20],
'b': [8],
'c': [11, 12, 14, 16, 19],
'd': [7, 9, 17, 18],
'e': [3, 4, 5, 6, 10, 13],
'f': [2],
'g': [1]}
有14个有效答案：
(8, 9, 10) (8, 9, 13) (8, 11, 13) (8, 12, 13) (8, 11, 17) (8, 11, 18) (8, 12, 17) (8, 12, 18) (8, 14, 17) (8, 14, 18) (8, 16, 17) (8, 16, 18) (15, 16, 17) (15, 16, 18)
答案 0 :(得分：1)
您可以通过智能方式执行此操作 - 对于每个现有列表，将其中的每个数字映射到下一个大于它的数字列表中的计数。一旦你掌握了这些数量，明智的产品总结就可以得到你需要的数量。
以下是如何获得计数的示例：
D = {'x': [15, 20],
'y': [11, 12, 14, 16, 19],
'z': [7, 9, 17, 18]}
order = ['x', 'y', 'z']
pairs = zip(order[:-1], order[1:])
counts = dict()
for pair in pairs:
counts[pair[0]] = dict()
for num in D[pair[0]]:
counts[pair[0]][num] = len([el for el in D[pair[1]] if el >= num])
编辑以获得更清晰的问题：
您需要为此问题构建动态编程解决方案（我假设您有DP algorithms的背景;如果没有，请查看几个）。假设您的原始字典有n个键。然后，您需要三个长度为n的字典，例如M1，M2和M3。对于每个键和数字，M3[key][number]将存储number可以作为元组的第三个元素的方式的数量（这将是相同的1）。 M2[key][number]将是number可以作为元组的第二个元素的方式的数量（这必须从M3向后动态构建），M1[key][number]将是方式number可以成为元组的第一个元素。 M1必须由M2构建。您的最终解决方案将是M1中元素的总和。我将保留M1，M2和M3的更新规则和初始化。
例如，要填写M1[key][number]中的条目，假设downkeys是key之后的一组密钥。对于每个downkey，您会查看M2[downkey]的条目，并总结M2[downkey][num2] num2大于number的值。为所有downkey添加所有此类数字将为您提供M1[key][number]的条目。因此，这会为您提供有关更新M1和M2行的顺序的提示。
如果你认为这是一项很多工作 - 嗯，确实如此，但它仍然是多项式的，而不是像笛卡尔积一样的指数。即使是笛卡儿的产品方式 - 您必须首先找到3个n列表的所有可能组合，然后获取产品，然后过滤它们。这非常昂贵。动态编程解决方案重用每个步骤的信息，而不是每次重新计算它。
答案 1 :(得分：0)
在示例中，您已经预先对所有词典列表进行了排序，因此您可以在调用itertools.product之前自行进行一些排序，以减少枚举次数：
def count_sorted(x,y,z):
from itertools import ifilter, product, imap
_x = ifilter(lambda k: k<z[-1],x)
_y = ifilter(lambda k: x[0]<k<z[-1],y)
_z = ifilter(lambda k: k > x[0],z)
return sum(imap(lambda t: t[0]<t[1]<t[2], product(_x,_y,_z)))
D = {'a': [15, 20],
'b': [8],
'c': [11, 12, 14, 16, 19],
'd': [7, 9, 17, 18],
'e': [3, 4, 5, 6, 10, 13],
'f': [2],
'g': [1]}
for key1,key2,key3 in itertools.permutations(D.keys(),3):
print '[%s, %s, %s] has %i sorted combinations'%(key1,key2,key3,count_sorted(D[key1],D[key2],D[key3]))
结果：
[a, c, b] has 0 sorted combinations
[a, c, e] has 0 sorted combinations
[a, c, d] has 2 sorted combinations
[a, c, g] has 0 sorted combinations
[a, c, f] has 0 sorted combinations
[a, b, c] has 0 sorted combinations
[a, b, e] has 0 sorted combinations
[a, b, d] has 0 sorted combinations
[a, b, g] has 0 sorted combinations
[a, b, f] has 0 sorted combinations
[a, e, c] has 0 sorted combinations
[a, e, b] has 0 sorted combinations
[a, e, d] has 0 sorted combinations
[a, e, g] has 0 sorted combinations
[a, e, f] has 0 sorted combinations
[a, d, c] has 2 sorted combinations
[a, d, b] has 0 sorted combinations
[a, d, e] has 0 sorted combinations
[a, d, g] has 0 sorted combinations
[a, d, f] has 0 sorted combinations
[a, g, c] has 0 sorted combinations
[a, g, b] has 0 sorted combinations
[a, g, e] has 0 sorted combinations
[a, g, d] has 0 sorted combinations
[a, g, f] has 0 sorted combinations
[a, f, c] has 0 sorted combinations
[a, f, b] has 0 sorted combinations
[a, f, e] has 0 sorted combinations
[a, f, d] has 0 sorted combinations
[a, f, g] has 0 sorted combinations
[c, a, b] has 0 sorted combinations
[c, a, e] has 0 sorted combinations
[c, a, d] has 6 sorted combinations
[c, a, g] has 0 sorted combinations
[c, a, f] has 0 sorted combinations
[c, b, a] has 0 sorted combinations
[c, b, e] has 0 sorted combinations
[c, b, d] has 0 sorted combinations
[c, b, g] has 0 sorted combinations
[c, b, f] has 0 sorted combinations
[c, e, a] has 4 sorted combinations
[c, e, b] has 0 sorted combinations
[c, e, d] has 4 sorted combinations
[c, e, g] has 0 sorted combinations
[c, e, f] has 0 sorted combinations
[c, d, a] has 8 sorted combinations
[c, d, b] has 0 sorted combinations
[c, d, e] has 0 sorted combinations
[c, d, g] has 0 sorted combinations
[c, d, f] has 0 sorted combinations
[c, g, a] has 0 sorted combinations
[c, g, b] has 0 sorted combinations
[c, g, e] has 0 sorted combinations
[c, g, d] has 0 sorted combinations
[c, g, f] has 0 sorted combinations
[c, f, a] has 0 sorted combinations
[c, f, b] has 0 sorted combinations
[c, f, e] has 0 sorted combinations
[c, f, d] has 0 sorted combinations
[c, f, g] has 0 sorted combinations
[b, a, c] has 2 sorted combinations
[b, a, e] has 0 sorted combinations
[b, a, d] has 2 sorted combinations
[b, a, g] has 0 sorted combinations
[b, a, f] has 0 sorted combinations
[b, c, a] has 8 sorted combinations
[b, c, e] has 2 sorted combinations
[b, c, d] has 8 sorted combinations
[b, c, g] has 0 sorted combinations
[b, c, f] has 0 sorted combinations
[b, e, a] has 4 sorted combinations
[b, e, c] has 8 sorted combinations
[b, e, d] has 4 sorted combinations
[b, e, g] has 0 sorted combinations
[b, e, f] has 0 sorted combinations
[b, d, a] has 4 sorted combinations
[b, d, c] has 7 sorted combinations
[b, d, e] has 2 sorted combinations
[b, d, g] has 0 sorted combinations
[b, d, f] has 0 sorted combinations
[b, g, a] has 0 sorted combinations
[b, g, c] has 0 sorted combinations
[b, g, e] has 0 sorted combinations
[b, g, d] has 0 sorted combinations
[b, g, f] has 0 sorted combinations
[b, f, a] has 0 sorted combinations
[b, f, c] has 0 sorted combinations
[b, f, e] has 0 sorted combinations
[b, f, d] has 0 sorted combinations
[b, f, g] has 0 sorted combinations
[e, a, c] has 12 sorted combinations
[e, a, b] has 0 sorted combinations
[e, a, d] has 12 sorted combinations
[e, a, g] has 0 sorted combinations
[e, a, f] has 0 sorted combinations
[e, c, a] has 44 sorted combinations
[e, c, b] has 0 sorted combinations
[e, c, d] has 44 sorted combinations
[e, c, g] has 0 sorted combinations
[e, c, f] has 0 sorted combinations
[e, b, a] has 8 sorted combinations
[e, b, c] has 20 sorted combinations
[e, b, d] has 12 sorted combinations
[e, b, g] has 0 sorted combinations
[e, b, f] has 0 sorted combinations
[e, d, a] has 28 sorted combinations
[e, d, c] has 52 sorted combinations
[e, d, b] has 4 sorted combinations
[e, d, g] has 0 sorted combinations
[e, d, f] has 0 sorted combinations
[e, g, a] has 0 sorted combinations
[e, g, c] has 0 sorted combinations
[e, g, b] has 0 sorted combinations
[e, g, d] has 0 sorted combinations
[e, g, f] has 0 sorted combinations
[e, f, a] has 0 sorted combinations
[e, f, c] has 0 sorted combinations
[e, f, b] has 0 sorted combinations
[e, f, d] has 0 sorted combinations
[e, f, g] has 0 sorted combinations
[d, a, c] has 4 sorted combinations
[d, a, b] has 0 sorted combinations
[d, a, e] has 0 sorted combinations
[d, a, g] has 0 sorted combinations
[d, a, f] has 0 sorted combinations
[d, c, a] has 18 sorted combinations
[d, c, b] has 0 sorted combinations
[d, c, e] has 4 sorted combinations
[d, c, g] has 0 sorted combinations
[d, c, f] has 0 sorted combinations
[d, b, a] has 2 sorted combinations
[d, b, c] has 5 sorted combinations
[d, b, e] has 2 sorted combinations
[d, b, g] has 0 sorted combinations
[d, b, f] has 0 sorted combinations
[d, e, a] has 8 sorted combinations
[d, e, c] has 16 sorted combinations
[d, e, b] has 0 sorted combinations
[d, e, g] has 0 sorted combinations
[d, e, f] has 0 sorted combinations
[d, g, a] has 0 sorted combinations
[d, g, c] has 0 sorted combinations
[d, g, b] has 0 sorted combinations
[d, g, e] has 0 sorted combinations
[d, g, f] has 0 sorted combinations
[d, f, a] has 0 sorted combinations
[d, f, c] has 0 sorted combinations
[d, f, b] has 0 sorted combinations
[d, f, e] has 0 sorted combinations
[d, f, g] has 0 sorted combinations
[g, a, c] has 2 sorted combinations
[g, a, b] has 0 sorted combinations
[g, a, e] has 0 sorted combinations
[g, a, d] has 2 sorted combinations
[g, a, f] has 0 sorted combinations
[g, c, a] has 8 sorted combinations
[g, c, b] has 0 sorted combinations
[g, c, e] has 2 sorted combinations
[g, c, d] has 8 sorted combinations
[g, c, f] has 0 sorted combinations
[g, b, a] has 2 sorted combinations
[g, b, c] has 5 sorted combinations
[g, b, e] has 2 sorted combinations
[g, b, d] has 3 sorted combinations
[g, b, f] has 0 sorted combinations
[g, e, a] has 12 sorted combinations
[g, e, c] has 28 sorted combinations
[g, e, b] has 4 sorted combinations
[g, e, d] has 20 sorted combinations
[g, e, f] has 0 sorted combinations
[g, d, a] has 6 sorted combinations
[g, d, c] has 12 sorted combinations
[g, d, b] has 1 sorted combinations
[g, d, e] has 4 sorted combinations
[g, d, f] has 0 sorted combinations
[g, f, a] has 2 sorted combinations
[g, f, c] has 5 sorted combinations
[g, f, b] has 1 sorted combinations
[g, f, e] has 6 sorted combinations
[g, f, d] has 4 sorted combinations
[f, a, c] has 2 sorted combinations
[f, a, b] has 0 sorted combinations
[f, a, e] has 0 sorted combinations
[f, a, d] has 2 sorted combinations
[f, a, g] has 0 sorted combinations
[f, c, a] has 8 sorted combinations
[f, c, b] has 0 sorted combinations
[f, c, e] has 2 sorted combinations
[f, c, d] has 8 sorted combinations
[f, c, g] has 0 sorted combinations
[f, b, a] has 2 sorted combinations
[f, b, c] has 5 sorted combinations
[f, b, e] has 2 sorted combinations
[f, b, d] has 3 sorted combinations
[f, b, g] has 0 sorted combinations
[f, e, a] has 12 sorted combinations
[f, e, c] has 28 sorted combinations
[f, e, b] has 4 sorted combinations
[f, e, d] has 20 sorted combinations
[f, e, g] has 0 sorted combinations
[f, d, a] has 6 sorted combinations
[f, d, c] has 12 sorted combinations
[f, d, b] has 1 sorted combinations
[f, d, e] has 4 sorted combinations
[f, d, g] has 0 sorted combinations
[f, g, a] has 0 sorted combinations
[f, g, c] has 0 sorted combinations
[f, g, b] has 0 sorted combinations
[f, g, e] has 0 sorted combinations
[f, g, d] has 0 sorted combinations
答案 2 :(得分：0)
递归解决方案：
In [9]: f??
Definition: f(lists, triple)
Source:
def f(lists, triple):
out = set()
for i in range(len(lists)):
for x in lists[i]:
if len(triple) == 2 and triple[1] < x:
out.add(triple + (x,))
elif len(triple) == 0 or triple[0] < x:
for j in range(i+1, len(lists)):
out.update(f(lists[j:], triple + (x,)))
return out
输入：
In [10]: lists
Out[10]:
[[15, 20],
[8],
[11, 12, 14, 16, 19],
[7, 9, 17, 18],
[3, 4, 5, 6, 10, 13],
[2],
[1]]
输出：
In [11]: out = f(lists, ())
In [12]: len(out)
Out[12]: 14
In [13]: out
Out[13]:
set([(8, 9, 10),
(8, 12, 18),
(8, 11, 13),
(8, 16, 17),
(15, 16, 17),
(8, 12, 17),
(8, 14, 18),
(15, 16, 18),
(8, 11, 17),
(8, 9, 13),
(8, 14, 17),
(8, 11, 18),
(8, 12, 13),
(8, 16, 18)])