Python: Memoization can't be called in Function

Question

the memoization can't be initiated. if I make it memoglobal, then the subsequent print function will take stored memo during the first print. Please advise,

def howsumhelper(targetsum,numbers):
      memo = dict() #this memoization will not initiate. Why?
      return howsum(targetsum,numbers,[])


def howsum(targetsum,numbers,combo):
      print("Debug==",memo)
      if targetsum in memo: return memo[targetsum]
      if targetsum == 0:return combo
      if targetsum < 0: return None

      for number in numbers:
            remainder = targetsum - number
            if howsum(remainder,numbers,combo) != None:
                  combo.append(number)
                  memo[targetsum] = combo
                  return combo
      memo[targetsum] = None
      return None

print(howsumhelper(7,[3,4])) #output should be [3,4]
print(howsumhelper(8,[2,3])) #output should be [2,2,2,2]
print(howsumhelper(7,[2,4])) #output should be None

Answer 1

Suggest following changes

• Make memo a mutable default argument of howsum (to make it callable in function)
• You don't need howsumhelper

Reference--Efficient memorization in Python--using posted solution #2

Revised Code

def howsum(targetsum,numbers,combo=None,memo=None):
      # Initiaze default arguments
      if combo is None:
        combo = []
      if memo is None:
        memo = {}
        
      #print("Debug==",memo)
      if targetsum in memo: return memo[targetsum]
      if targetsum == 0:return combo
      if targetsum < 0: return None

      for number in numbers:
            remainder = targetsum - number
            if howsum(remainder,numbers,combo,memo) != None:
                  combo.append(number)
                  memo[targetsum] = combo
                  return combo
      memo[targetsum] = None
      return None

print(howsum(7,[3,4])) #output should be [3,4] #actually or [4, 3]
print(howsum(8,[2,3])) #output should be [2,2,2,2]
print(howsum(7,[2,4])) #output should be None

Output

[4, 3]
[2, 2, 2, 2]
None

Explanation

Function signature is : howsum(targetsum,numbers,combo=None,memo=None):

Arguments a value in function definition are called default arguments. So combo, and memo are have default arguments.

Python's default arguments are evaluated once when the function is defined, not each time the function is called.

Default values are used only when actual values are passed.

Thus:

howsum(7,[3,4]) # uses default values, so called with combo = None and memo = None
howsum(8,[2,3]) # uses default values, so called with combo = None and memo = None
howsum(7,[2,4]) # uses default values, so called with combo = None and memo = None

But:

howsum(remainder,numbers,combo,memo) # does not use defaults for combo and memo
                                     # since we are passing values for these arguments