Profile the performance of the memoized version of the Fibonacci function defined in Project 6. The function should count the number of recursive calls. State its computational complexity using big-O notation, and justify your answer. The fib function header has been modified to include the counter as the second parameter. Define the Counter class, it should have three methods: __init__, increment, and __str__. When an instance of the Counter class is passed as a parameter, the count property of that instance should be incremented based on the number of recursive calls. The __str__ method should return the count property's value as a string.

C++ Programming: From Problem Analysis to Program Design
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ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter15: Recursion
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Profile the performance of the memoized version of the Fibonacci function defined in Project 6. The function should count the number of recursive calls. State its computational complexity using big-O notation, and justify your answer.

The fib function header has been modified to include the counter as the second parameter.

Define the Counter class, it should have three methods: __init__, increment, and __str__. When an instance of the Counter class is passed as a parameter, the count property of that instance should be incremented based on the number of recursive calls. The __str__ method should return the count property's value as a string.

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"""
File: fib.py
Project 11.7

Employs memoization to improve the efficiency of recursive Fibonacci.
Counts the calls and displays the results.
"""

class Counter(object):
    """Tracks a count."""
    # Define the Counter class here.

def fib(n, counter = None):
    """Fibonacci function with a table for memoization."""
    table = {}
    
    def memoizedFib(n):
        if n < 3:
            return 1
        else:
            # Attempt to get value for memoizedFib(n)
            # from the table
            # If unsuccessful, recurse and add results to
            # the table
            value = table.get(n, None)
            if value: return value
            else:
                value = memoizedFib(n - 1) + memoizedFib(n - 2)
                table[n] = value
                return value

    return memoizedFib(n)

def main():
    """Tests the function with some powers of 2."""
    problemSize = 2
    print("%4s%12s" % ("n", "fib(n)"))
    for count in range(5):
        print("%4d%12d" % (problemSize, fib(problemSize)))
        problemSize *= 2

if __name__ == "__main__":
    main()
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