I have a very straightforward combination problem. I have two arrays (a and b). Array a indicates all the values one of the three slots in array b can take on. Each slot in array b can have a value between 1 and 5. An example of which would be [1, 4, 5]. I would like to generate an array (c) with all possible combinations. I like to extend the basic example larger arrays.
Input:
a = [1, 2, 3, 4, 5]
b = [1, 2, 3]
Output:
c = [[1, 1, 1], [1, 1, 2],[1, 1, 3], [1, 1, 4], [1, 1, 5],
[1, 2, 1], [1, 2, 2],[1, 2, 3], [1, 2, 4], [1, 2, 5],
[1, 3, 1], [1, 3, 2],[1, 3, 3], [1, 3, 4], [1, 3, 5],
[1, 4, 1], [1, 4, 2],[1, 4, 3], [1, 4, 4], [1, 4, 5],
[1, 5, 1], [1, 5, 2],[1, 5, 3], [1, 5, 4], [1, 5, 5],
[2, 1, 1], [2, 1, 2],[2, 1, 3], [2, 1, 4], [2, 1, 5],
[2, 2, 1], [2, 2, 2],[2, 2, 3], [2, 2, 4], [2, 2, 5],
[2, 3, 1], [2, 3, 2],[2, 3, 3], [2, 3, 4], [2, 3, 5],
[2, 4, 1], [2, 4, 2],[2, 4, 3], [2, 4, 4], [2, 4, 5],
[2, 5, 1], [2, 5, 2],[2, 5, 3], [2, 5, 4], [2, 5, 5],
[3, 1, 1], [3, 1, 2],[3, 1, 3], [3, 1, 4], [3, 1, 5],
[3, 2, 1], [3, 2, 2],[3, 2, 3], [3, 2, 4], [3, 2, 5],
[3, 3, 1], [3, 3, 2],[3, 3, 3], [3, 3, 4], [3, 3, 5],
[3, 4, 1], [3, 4, 2],[3, 4, 3], [3, 4, 4], [3, 4, 5],
[3, 5, 1], [3, 5, 2],[3, 5, 3], [3, 5, 4], [3, 5, 5],
[4, 1, 1], [4, 1, 2],[4, 1, 3], [4, 1, 4], [4, 1, 5],
[4, 2, 1], [4, 2, 2],[4, 2, 3], [4, 2, 4], [4, 2, 5],
[4, 3, 1], [4, 3, 2],[4, 3, 3], [4, 3, 4], [4, 3, 5],
[4, 4, 1], [4, 4, 2],[4, 4, 3], [4, 4, 4], [4, 4, 5],
[5, 5, 1], [5, 5, 2],[5, 5, 3], [5, 5, 4], [5, 5, 5],
[5, 1, 1], [5, 1, 2],[5, 1, 3], [5, 1, 4], [5, 1, 5],
[5, 2, 1], [5, 2, 2],[5, 2, 3], [5, 2, 4], [5, 2, 5],
[5, 3, 1], [5, 3, 2],[5, 3, 3], [5, 3, 4], [5, 3, 5],
[5, 4, 1], [5, 4, 2],[5, 4, 3], [5, 4, 4], [5, 4, 5],
[5, 5, 1], [5, 5, 2],[5, 5, 3], [5, 5, 4], [5, 5, 5]]
Solution for the problem above:
d = []
for i in range(len(a)):
for j in range(len(a)):
for k in range(len(a)):
e = []
e.append(i+1)
e.append(j+1)
e.append(k+1)
d.append(e)
I am looking for a more generic way. One which can accommodate larger arrays (see below) without the need to use a nested for loop structure. I searched for a comparable example, but was unable to find one on stackoverflow.
Input:
a = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
b = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
You are looking for itertools.product().
a = [1, 2, 3, 4, 5]
b = 3 # Actually, you just need the length of the array, values do not matter
c = itertools.product(a, repeat=b)
Note that this returns an iterator, you may need to cast it using list() but be aware this can take forever and highly consume memory if the sizes grow.