Dynamic programming best sum code in python - python-3.x

Question

I am trying to learn dynamic programming by followin an online video. The original video is using javascript and I am trying to use python to implement the same. However, I am not able to locate the error in my python implementation.
The question is as follows
write a fn. bestsum(targetsum, numbers) that takes in a targetsum and
an array of numbers as arguments.
The fn. should return an array containing the shortest combination of
numbers that add up to exactly the targetsum.
If there is a tie for the shortest combination, you may return any of
the shortest.
The javascript implementation is as follows.
const bestSum = (targetSum, numbers, memo={}) => {
if (targetSum in memo) return memo[targetSum];
if (targetSum === 0) return [];
if (targetSum < 0) return null;
let shortest_com = null;
for (let num of numbers) {
const remainder = targetSum - num;
const remainder_com = bestSum(remainder, numbers, memo);
if (remainder_com !== null) {
const combination = [...remainder_com, num];
if (shortest_com === null || combination.length < shortest_com.length) {
shortest_com = combination;
}
}
}
memo[targetSum] = shortest_com
return shortest_com;
};
console.log(bestSum(7, [5, 3, 4, 7]));
console.log(bestSum(8, [2, 3, 5]));
console.log(bestSum(8, [1, 4, 5]));
console.log(bestSum(100, [1, 2, 5, 25]));
Python code I implemented is
from typing import Any, Dict, List, Optional
def best_sum(target: int, numbers: List[int], memo:Dict[int, Any]={}) -> Optional[List[int]]:
if target in memo.keys():
return memo.get(target)
if target == 0:
return []
if target < 0:
return None
shortest_combination: Optional[List] = None
for num in numbers:
partial = best_sum(target=target - num, numbers=numbers, memo=memo)
if partial != None:
print(num)
partial.append(num)
if (shortest_combination == None) or (len(partial) < len(shortest_combination)):
shortest_combination = partial
memo[target] = shortest_combination
return shortest_combination
if __name__ == "__main__":
print(best_sum(target=100, numbers=[1, 2, 5, 25]))
For the test case: target=100, numbers=[1, 2, 5, 25].
Javascript implementation gives.
[ 25, 25, 25, 25 ]
But Python gives.
[25, 1, 1, 2, 1, 2, 1, 2, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25, 1, 2, 5, 25]

Answer 1

The problem is in this snippet:
if partial != None:
partial.append(num)
if (shortest_combination == None) or (len(partial) < len(shortest_combination)):
shortest_combination = partial
The Javascript appoach creates a copy of the list remainder_com with the element num appended. In your approach, you're appending to partial directly without creating a copy. Thus, in every iteration the same list will be used to modifications, which is not desired. Change it to
# Creates a copy of `partial` with `num` appended
combination = partial[:] + [num]
if (shortest_combination == None) or (len(combination) < len(shortest_combination)):
shortest_combination = combination
This outputs [25, 25, 25, 25] as expected.