[Python] Creating a list of integer lists that have a fixed length and contain integers that...

I am trying to write some code that will generate all lists of a fixed length that have the property that the next integer in each list will either be same or an increment of the previous integer. All lists should start with 0.

I can write code that does this for size 4 BUT it uses 3 nested loops. If I want to continue down this path I will have to have n - 1 nested loops.

Just to be clear I will give some examples for length 5:

[0, 0, 0, 0, 0]
[0, 0, 1, 1, 1]
[0, 1, 2, 2, 2]
[0, 1, 2, 3 ,3]


The code will return all such lists of length 5. Instead of down voting, could you help me improve my question?

Here is my (really bad but working) code:

import math

def index_list(x):
IL = []
for i in [0,1]:
for j in [0,1,2]:
for k in [0,1,2,3]:
if i <= j and j <= k and abs(i-j) < 2 and abs(j-k) < 2:
IL.append([x, x + i, x + j, x + k])
return IL

print(index_list(0))


this produces:

[[0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 2], [0, 1, 1, 1], [0, 1, 1, 2], [0, 1, 2, 2], [0, 1, 2, 3]]


I have included a argument x as i wish to have the code to sometimes do the same thing but with a different starting index.

Continue reading...