返回树的分支作为Python中的列表

Question

I'm trying to write a recursive function in Python that returns branches of a tree as lists, given depth or max_sum of a branch. I'm really frustrated by this. Maybe there are easier implementations with classes or generators? Below is the detailed description of the function behaviour i want to achieve.

func(data, depth)
'''Accepts a list with numbers > 0 and depth, i.e. max elements per list; 
   returns each branch of a tree'''    

----------Examples--------------
Input:  func([2, 1], depth=2)
Output: [[2, 2], [2, 1], [1, 2], [1, 1]]

Input:  func([3, 2, 1], depth=2)
Output: [[3, 3], [3, 2], [3, 1]
         [2, 3], [2, 2], [2, 1]
         [1, 3], [1, 2], [1, 1]]

Input:  func([2, 1], depth=3)
Output: [[2, 2, 2], [2, 2, 1], [2, 1, 2], [2, 1, 1],
         [1, 2, 2], [1, 2, 1], [1, 1, 2], [1, 1, 1]]

Picture for the second example

Picture for the third example

Here's the code i wrote, which works only for the first example, it's horrible and i really feel ashamed of it :/ I tried dozens of approaches using classes and generators, but i'm not very familiar with those and the code only returned half of the options even for the first example.

tree = []
node_list = [2, 1]

def make_branch(depth=2, branch=None, d={0:2, 1:1}, switch=False, count=0):
    #print(count)

    if branch is None:
        branch = []

    for i in range(2):
        #print(i)
        if switch:
            branch.append(d[i+1]) 
            switch=False
        else:
            branch.append(d[i])

        if len(branch) >= depth:
            tree.append(branch)
            print(branch)
            return

        make_branch(count= count + 1, branch=branch)
        #print(-count)
        branch = branch[:-1]


for i in range(len(node_list)):
    if i % 2 == 0:
        make_branch()
    else:
        make_branch(switch=True)

print(tree)

Answer 1

I don't see why you want to relate this to traversing a tree. Your task basically is just generating all permutations (with replacement) - which is identical to the Cartesian product with a fixed set - of a given length over a set of numbers.

In Python you can do it as follows:

import itertools
for i in itertools.product([1,2], repeat=3):
  print i

This would eg output your third example. Just note that each output is a tuple and not a list - so you may want to convert them.

The simplest implementation would probably work like this:

def prod(lst, depth, buf=''):
    if depth == 0:
        print buf
        return
    for elem in lst:
        prod(lst, depth - 1, buf + str(elem))

prod([1,2], 3)
print 
prod([1,2,3], 2)

Output:

111
112
121
122
211
212
221
222

11
12
13
21
22
23
31
32
33