Time Complexity with memoization(Doubt)

Python
1

I tried solving a basic problem with and without memoization technique,but the time complexity is almost same,so whats the exact difference,where the code with memoization is increasing the lines of code.

#memoization technique

#with
def memo(n):
    d = {}
    if n == 1:
        return 1
    elif n == 0:
        return 1

    else:
        d[n] = memo(n-1) + memo(n - 2)
        if n in d :
            return d[n]

print(memo(5)) 

#without
def memo(n):
    d = {}
    if n == 1:
        return 1
    elif n == 0:
        return 1

    else:
        return memo(n-1) + memo(n - 2)

print(memo(5))
2

Well yes, if you’re talking about Big O it’s exactly the same, worst case is there are no repeating values. But best case is that all the values are repeated, in which case it only ever does one calculation. Big O is just the upper bound. It is just one data point, it doesn’t mean the code won’t be much more efficient but that depends entirely on the data going in, and Big O doesn’t really care about that.