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Assuming that I have 3 different dictionaries:

dict1 = {

  "A": "a"

}



dict2 = {

  "B": "b", 

  "C": "c",

  "D": "d", 

  "E": "e"

}



dict3 = {

  "F": "f", 

  "G": "g"

}

I want to compute the product of these dictionaries (excluding the product between dict2 and dict3) and combine both the keys and values where the keys are concatenated with _ and values with ' and '

The desired output would be a single dictionary:

{

  # dict1 x dict2 

  "A_B": "a and b", 

  "A_C": "a and c",

  "A_D": "a and d",

  "A_E": "a and e",



  # dict1 x dict3  

  "A_F": "a and f",

  "A_G": "a and g",



  # dict1 x dict2 x dict3 

  "A_B_F": "a and b and f",

  "A_B_G": "a and b and g",

  "A_C_F": "a and c and f",

  "A_C_G": "a and c and g",

  "A_D_F": "a and d and f",

  "A_D_G": "a and d and g",

  "A_E_F": "a and e and f",

  "A_E_G": "a and e and g"

} 

I had a look at the documentation for itertools but I was not able to understand how I can achieve the desired output.

The function that will do the job is itertools.product.
First, here is how you can print out the product dict1 x dict2 x dict3:

for t in product(dict1.items(), dict2.items(), dict3.items()): 

     k, v = zip(*t) 

     print("_".join(k), "-", " and ".join(v))   

Output:

A_B_F - a and b and f

A_B_G - a and b and g

A_C_F - a and c and f

A_C_G - a and c and g

A_D_F - a and d and f

A_D_G - a and d and g

A_E_F - a and e and f

A_E_G - a and e and g

Now, just populate a result dictionary:

result = {}

for t in product(dict1.items(), dict2.items(), dict3.items()): 

     k, v = zip(*t) 

     result["_".join(k)] = " and ".join(v)

You can now add to this dictionary the dict1 x dict2 and dict1 x dict3 products, that are even simpler to compute.

Based on @ShadowRanger's comment, here is a complete snippet:

import itertools

import pprint





dict1 = {

  "A": "a"

}



dict2 = {

  "B": "b",

  "C": "c",

  "D": "d",

  "E": "e"

}



dict3 = {

  "F": "f",

  "G": "g"

}





result = {}

for dicts in ((dict1, dict2), (dict1, dict3), (dict1, dict2, dict3)):

    for t in itertools.product(*(d.items() for d in dicts)):

        k, v = zip(*t)

        result["_".join(k)] = " and ".join(v)



pprint.pprint(result)

Output:

{'A_B': 'a and b',

 'A_B_F': 'a and b and f',

 'A_B_G': 'a and b and g',

 'A_C': 'a and c',

 'A_C_F': 'a and c and f',

 'A_C_G': 'a and c and g',

 'A_D': 'a and d',

 'A_D_F': 'a and d and f',

 'A_D_G': 'a and d and g',

 'A_E': 'a and e',

 'A_E_F': 'a and e and f',

 'A_E_G': 'a and e and g',

 'A_F': 'a and f',

 'A_G': 'a and g'}

To produce all pairings, you can use two recursive generator functions: one to find the overall combinations of dictionaries, and the other to pair the keys and values:

def pair_dicts(data, c):

   if not data:

     keys, values = zip(*c)

     yield ('_'.join(keys), ' and '.join(values))

   else:

     for i in data[0]:

        yield from pair_dicts(data[1:], c+[i])



def combos(d, c = ):

  if len(c) == len(d):

    yield c

  else:

    if len(c) > 1:

      yield c

    for i in d:

      if all(h != i for h in c):

         yield from combos(d, c+[i])



new_d = [[list(c.items()) for c in i] for i in combos([dict1, dict2, dict3])]

final_result = dict(i for b in new_d for i in pair_dicts(b, ))

Output:

{'A_B': 'a and b', 'A_C': 'a and c', 'A_D': 'a and d', 'A_E': 'a and e', 'A_B_F': 'a and b and f', 'A_B_G': 'a and b and g', 'A_C_F': 'a and c and f', 'A_C_G': 'a and c and g', 'A_D_F': 'a and d and f', 'A_D_G': 'a and d and g', 'A_E_F': 'a and e and f', 'A_E_G': 'a and e and g', 'A_F': 'a and f', 'A_G': 'a and g', 'A_F_B': 'a and f and b', 'A_F_C': 'a and f and c', 'A_F_D': 'a and f and d', 'A_F_E': 'a and f and e', 'A_G_B': 'a and g and b', 'A_G_C': 'a and g and c', 'A_G_D': 'a and g and d', 'A_G_E': 'a and g and e', 'B_A': 'b and a', 'C_A': 'c and a', 'D_A': 'd and a', 'E_A': 'e and a', 'B_A_F': 'b and a and f', 'B_A_G': 'b and a and g', 'C_A_F': 'c and a and f', 'C_A_G': 'c and a and g', 'D_A_F': 'd and a and f', 'D_A_G': 'd and a and g', 'E_A_F': 'e and a and f', 'E_A_G': 'e and a and g', 'B_F': 'b and f', 'B_G': 'b and g', 'C_F': 'c and f', 'C_G': 'c and g', 'D_F': 'd and f', 'D_G': 'd and g', 'E_F': 'e and f', 'E_G': 'e and g', 'B_F_A': 'b and f and a', 'B_G_A': 'b and g and a', 'C_F_A': 'c and f and a', 'C_G_A': 'c and g and a', 'D_F_A': 'd and f and a', 'D_G_A': 'd and g and a', 'E_F_A': 'e and f and a', 'E_G_A': 'e and g and a', 'F_A': 'f and a', 'G_A': 'g and a', 'F_A_B': 'f and a and b', 'F_A_C': 'f and a and c', 'F_A_D': 'f and a and d', 'F_A_E': 'f and a and e', 'G_A_B': 'g and a and b', 'G_A_C': 'g and a and c', 'G_A_D': 'g and a and d', 'G_A_E': 'g and a and e', 'F_B': 'f and b', 'F_C': 'f and c', 'F_D': 'f and d', 'F_E': 'f and e', 'G_B': 'g and b', 'G_C': 'g and c', 'G_D': 'g and d', 'G_E': 'g and e', 'F_B_A': 'f and b and a', 'F_C_A': 'f and c and a', 'F_D_A': 'f and d and a', 'F_E_A': 'f and e and a', 'G_B_A': 'g and b and a', 'G_C_A': 'g and c and a', 'G_D_A': 'g and d and a', 'G_E_A': 'g and e and a'}

I created a (not so nice) function to do your task with arbitrary number of dictionaries.

(Explanation below)

import itertools as it



dict1 = {

  "A": "a"

}



dict2 = {

  "B": "b", 

  "C": "c",

  "D": "d", 

  "E": "e"

}



dict3 = {

  "F": "f", 

  "G": "g"

}







def custom_dict_product(dictionaries):

    return dict(zip(map("_".join, it.product(*map(dict.keys, dictionaries))), 

                    map(" and ".join, it.product(*map(dict.values, dictionaries)))))



result = custom_dict_product([dict1,dict2])

result.update(custom_dict_product([dict1,dict3]))

result.update(custom_dict_product([dict1,dict2,dict3]))

result

#{'A_B': 'a and b',

# 'A_B_F': 'a and b and f',

# 'A_B_G': 'a and b and g',

# 'A_C': 'a and c',

# 'A_C_F': 'a and c and f',

# 'A_C_G': 'a and c and g',

# 'A_D': 'a and d',

# 'A_D_F': 'a and d and f',

# 'A_D_G': 'a and d and g',

# 'A_E': 'a and e',

# 'A_E_F': 'a and e and f',

# 'A_E_G': 'a and e and g',

# 'A_F': 'a and f',

# 'A_G': 'a and g'}

The function takes the given dictionaries and gets their keys and values, which is done by map(dict.keys, dictionaries))and map(dict.values, dictionaries)). The results of the first call

list(it.product(*map(dict.keys, [dict1,dict2])))

# [('A', 'C'), ('A', 'E'), ('A', 'B'), ('A', 'D')]

The tuples insides this list are then forced to your desired structure with join(and again an map call to do this for every element):

"_".join(('A', 'C'))

# 'A_C'

list(map("_".join, it.product(*map(dict.keys, [dict1,dict2]))))

# ['A_C', 'A_E', 'A_B', 'A_D']

Finally the two resulting lists are transformed to tuples of (keys, values) with the call of zip and handed to the dictionary creation.

Here a dirty, but working, solution that makes use of itertools

from itertools import product, combinations





# create a list and sum dict to be used later

t = [dict1, dict2, dict3] 

k = {}

for d in t:

    k.update(d)





# iterate over "i" order of combinations ("dict1_X" or "dict1_X_Y") and 

# the cartesian product of keys for each combination



results = {}

for i in range(2, 4):

    a = [

        [

            results.update({"_".join(y): " and ".join([k[j] for j in y])})

            for y in product(*x)

        ]

        for x in combinations(t, i) 

        if dict1 in x

    ]



results

Output:

{'A_B': 'a and b',

 'A_B_F': 'a and b and f',

 'A_B_G': 'a and b and g',

 'A_C': 'a and c',

 'A_C_F': 'a and c and f',

 'A_C_G': 'a and c and g',

 'A_D': 'a and d',

 'A_D_F': 'a and d and f',

 'A_D_G': 'a and d and g',

 'A_E': 'a and e',

 'A_E_F': 'a and e and f',

 'A_E_G': 'a and e and g',

 'A_F': 'a and f',

 'A_G': 'a and g'}