####### Lecture 13 #######

####### Recursion #######

# 1. Break a problem into smaller parts
# 2. Evaluate these sub-parts
# 3. Put everything back together

# Recursion is usually written as a function
# calling itself

# Recursion generally DOES NOT involved for
# or while loops


fibCount = 0

def fibMemo(n):
    return fibonacci(n, {})

# From http://www.greenteapress.com/thinkpython/thinkCSpy/html/chap04.html
def fibonacci(n, memoDict):
    """Calculates the nth fibonacci number"""
    # Counting the number of calls
    global fibCount
    fibCount += 1
    # Memoized solution
    if n in memoDict:
        return memoDict[n]
    # Base cases
    if n == 0 or n == 1:
        return 1
    # Recursive case
    else:
        result = fibonacci(n-1, memoDict)  + fibonacci(n-2, memoDict)
        # Add the result to the dictionary
        memoDict[n] = result
        return result

print fibMemo(3), fibCount
print fibMemo(36), fibCount - 5 # I know fibCount is 5 for fib(3)
















def reverseString(string):
    """returns string in reverse"""
    # Base case
    if string == '':
        return ''
##    if len(string) == 1:
##        return string
    # Recursive case
    else:
        return string[-1] + reverseString(string[:-1])

#print reverseString('hello')