import numpy as np
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns

"""
Explanation: Numpy Exercise 2
Imports
End of explanation
"""


def np_fact(n):
    """Compute n! = n*(n-1)*...*1 using Numpy."""
    if n == 0:
        return 1
    else:
        a = np.arange(1,float(n)+1,1)
        return a.cumprod()[n-1]

assert np_fact(0)==1
assert np_fact(1)==1
assert np_fact(10)==3628800
assert [np_fact(i) for i in range(0,11)]==[1,1,2,6,24,120,720,5040,40320,362880,3628800]

"""
Explanation: Factorial
Write a function that computes the factorial of small numbers using np.arange and np.cumprod.
End of explanation
"""


def loop_fact(n):
    """Compute n! using a Python for loop."""
    if n == 0:
        return 1
    else:
        prod = 1
        for i in range(1, n+1):
            prod = prod * i
        return prod

assert loop_fact(0)==1
assert loop_fact(1)==1
assert loop_fact(10)==3628800
assert [loop_fact(i) for i in range(0,11)]==[1,1,2,6,24,120,720,5040,40320,362880,3628800]

"""
Explanation: Write a function that computes the factorial of small numbers using a Python loop.
End of explanation
"""


%timeit -n1 -r1 np_fact(50)
%timeit -n1 -r1 loop_fact(50)

"""
Explanation: Use the %timeit magic to time both versions of this function for an argument of 50. The syntax for %timeit is:
python
%timeit -n1 -r1 function_to_time()
End of explanation
"""


