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Functions

Take a number and return its prime factors. Take a URL and return the text on the page. Take a code and output the hidden message. Functions make generalized tasks like these possible.

Level 1

Can you identify the function f(x,y) which takes two positive integers as its argument?

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def f(x,y):
    minimum = min(x,y)
    maximum = max(x,y)
    if minimum == 0:
        return maximum
    elif minimum == 1:
        return 1
    else:
        return f(minimum,maximum-minimum)

What would the following python code print out?

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current_year = 2015   
andy_birth = 1984   
andy_minus_adaline = 4   
adaline = andy - andy_minus_adaline   
andy = current_year - andy_birth   
print adaline

The Ackermann function is a computable function which grows very, very quickly as its inputs grow. For example, while \( A(1,2),\) \(A (2,2),\) and \(A(3,2) \) are equal to \(4,7,\) and \(29,\) respectively, \( A(4,2) \approx 2 \times 10^{19728} \).

The Ackermann function can be defined as follows: \[ A(m,n) = \begin{cases} n+1 & \mbox{if } m = 0 \\ A(m-1, 1) & \mbox{if } m > 0 \mbox{ and } n = 0 \\ A(m-1, A(m, n-1)) & \mbox{if } m > 0 \mbox{ and } n > 0. \end{cases} \]

What is the value of \( A(3,6)? \)

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