Python 递归 - 求和堆栈

Question

I am trying to retrieve elements in a recursion that sum-up to a specific value (value of 9 in this case).

In the simplified example in the below image, where I have 3 branches (with the values 3, 4 and 5), and where the maximum possible sum is 9, I would expect the following output:

[3,3,3] (= 9)
[3,4]   (= 7)
[3,5]   (8)
[4,3]   (7)
[4,4]   (8)
[4,5]   (9)
[5,3]   (8)

My output in the code below, however, is quite different:

i =  [3, 3, 3]
i =  [3, 3, 3]
i =  [3, 3, 3]
i =  [3, 3]
i =  [3, 3]
i =  [3, 3]
i =  [3]
i =  [3, 4]
i =  [3, 4]
i =  [3, 4]
i =  [3]
i =  [3, 5]
i =  [3, 5]
i =  [3, 5]
i =  [3]

I know I can use itertools to get a similar output, but my actual code is more complex than this one and I cannot use iterools there. This is my current code:

import copy
maximum_sum = 9
branches = [3,5]
ar = []
big_ar = []

def recurse(summary, index):
    if summary + branches[index] <= maximum_sum:   
        summary += branches[index]
        ar.append(branches[index])

        for i in range(len(branches)):  
            recurse(summary, i)
            my_ar = copy.deepcopy(ar)
            big_ar.append(my_ar)
        del ar[-1]
    return (big_ar)

all_clusters = recurse(0, 0)
for i in all_clusters:
    print ('i = ', i)

Answer 1

maxsum = 9
branches = [3, 4, 5]

def recurse(maxsum):
    if maxsum < min_branch:
        yield []
    for b in branches:
        if maxsum >= b:
             for v in recurse(maxsum - b):
                   yield [*v, b]
        else:
            return

for i in recurse(9):
    print ('i = ', i)

Answer 2

Solution - this is what I was trying to achieve. Quick and dirty but it works:

import copy
maximum_sum = 9
branches = [3,4,5]
ar = []
sum_ar = []

def recurse(summary, index):
    if summary + branches[index] <= maximum_sum:   
        summary += branches[index]
        ar.append(branches[index])

        for i in range(len(branches)): 
            recurse(summary, i)

        if summary + branches[index] > maximum_sum:    
            my_ar = copy.deepcopy(ar)
            sum_ar.append(my_ar)
        del ar[-1]
    return (sum_ar)

for i in range(len(branches)):
    all_clusters = recurse(0, i)

for i in all_clusters:
print ('i = ', i)