Question

In this problem you will memoize your recursive solution to ladder() so that it will work for large numbers, i.e. long ladders. Do this by adding a Python dictionary called knownResults as the second parameter to ladder. It will store all results that have been previously computed. Always check knownResults before making a recursive call, and store results from recursive calls into knownResults. Your new definition line will look something like.

def ladder(length, knownResults = {}):

The calls to ladder outside the function will still look like:

>>> ladder(10) 89

Use the following code

def ladder(rungs):
if rungs==1 or rungs==0: #Base Case 1
return 1
elif rungs==2: #Base Case 2
return 2
else:
return ladder(rungs-2)+ladder(rungs-1)

Answer 1

Code:

def ladder(length, knownResults = {}):
if length in knownResults:
return knownResults[length]
elif length==1 or length==0: #Base Case 1
return 1
elif length==2: #Base Case 2
return 2
else:
value = ladder(length-2)+ ladder(length-1)
knownResults[length]= value
return value
  

print(ladder(30))

print(ladder(300))

Output:                                                                                                                       

1346269                                                                                                                        

359579325206583560961765665172189099052367214309267232255589801