python - Computing the "closure" of the attributes of an object given functions that change the attributes -

i have object obj , number of functions

    def func1(obj):     #...      def func2(obj):     #...      def func3(obj):     #... 

that each change values of attributes of obj.

i want input like

obj = myobject() obj.attr=22 

this should passed function closure() computes possible applictions of functions above, meaning func1(func2(obj)), func3(func1(func1(obj))) etc. stopping condition (e.g. no more 20 function compositions).

the output should list of possible outputs paths leading there. if, 104 , 93 1 possible final outputs if obj.attr=22, , there 2 ways arrive @ 104 , 1 arrive @ 93. then

print closure(obj) 

should like

[22, 64, 21, 104] #first path 104 through , func1(obj),func1(func1(obj)), func1(func1(func3(obj)))  [22, 73, 104] #second path 104 through , func3(obj),func3(func2(obj)),   [22, 11, 93] #the path arrive @ 94 

how implement this? suggested in comments, best done trees, although tried 2 days didn't make progress implementing (i'm new python/programming)!
example simple instead of func(obj) directly use func(22) example need work on more complicated, need use objects, minimal working example that.

the tree not full n-ary tree, since each function application contain test whether can applied current state (of attributes) of obj , in cases test fail leaving (the attributes of) obj unchanged.

here's simple example tries find whether number (goal) predecessor of (inital_state) when applying rule in collatz conjecture.

in example, obj state, , [func1, func2, ...] functions in example. version return path final output, minimizing number of function applications. instead of searching, can list states removing goal test , returning prev_states after loop finishes.

from collections import deque  def multiply_by_two(x):     return x * 2  def sub_one_div_three(x):     if (x - 1) % 3 == 0:         return (x - 1) // 3     else:         return none # invalid   functions = [multiply_by_two, sub_one_div_three]  # find path given function def bfs(initial_state, goal):     initial_path = []     states = deque([(initial_state, initial_path)])     # deque of 2-tuples: (state, list of functions there)     prev_states = {initial_state}                       # keep track of visited states avoid infinite loop      while states:         # print(list(map(lambda x: x[0], states)))      # print states, not paths. useful see what's going on         state, path = states.popleft()          func in functions:             new_state = func(state)              if new_state == goal:                       # goal test: if found state, we're done                 return new_state, path + [func]              if (new_state not none ,           # check state valid                 new_state not in prev_states):      # , state hasn't been visited                 states.append((new_state, path + [func]))             prev_states.add(new_state)              # make sure state won't added again     else:         raise exception("could not state")  print(functions) print(bfs(1, 5))  # prints (5, [<function multiply_by_two @ 0x000002e746727f28>, <function multiply_by_two @ 0x000002e746727f28>, <function multiply_by_two @ 0x000002e746727f28>, <function multiply_by_two @ 0x000002e746727f28>, <function sub_one_div_three @ 0x000002e7493c9400>]). can extract path here.