n = 10
denom = [1, 3, 4]
dpl = [[] for i in range(n+1)]
def f(n):
if dpl[n]:
return dpl[n]
if n <= 0:
return []
ans = list(range(n)) # this is the max size possible
for i in denom:
if n-i >= 0:
new = f(n-i) + [i] # append i to the end of the array
if len(new) <= len(ans):
ans = new
dpl[n] = ans
return ans
if __name__ == "__main__":
sol = f(n)
print(sol)
Overall I think it's a really cool extension idea and I would love to use it.