In [1]:
import numpy as np
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
Write a function that computes the factorial of small numbers using np.arange and np.cumprod.
In [25]:
def np_fact(n):
"""Compute n! = n*(n-1)*...*1 using Numpy."""
# YOUR CODE HERE
a = np.arange(1, n+1, 1) #Makes array from 1 to n+1
if n==0:
return 1 #If n is 1 or 0, returns value of 1.
elif n==1:
return 1
else:
return max(a.cumprod())#For all other n, takes max value of cumulative products
print np_fact(6)
In [26]:
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]
Write a function that computes the factorial of small numbers using a Python loop.
In [43]:
def loop_fact(n):
"""Compute n! using a Python for loop."""
# YOUR CODE HERE
f = n
if n == 0:
return 1 #Same as above.
elif n == 1:
return 1
while n > 1:
f *= (n-1) #For n > 1, takes continuous product of n to right before n = 0, otherwise it would all equal 0.
n -= 1
return f
print loop_fact(10)
In [44]:
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]
Use the %timeit magic to time both versions of this function for an argument of 50. The syntax for %timeit is:
%timeit -n1 -r1 function_to_time()
In [48]:
# YOUR CODE HERE
%timeit -n1 -r1 loop_fact(50)
%timeit -n1 -r1 np_fact(50)
In the cell below, summarize your timing tests. Which version is faster? Why do you think that version is faster?
YOUR ANSWER HERE: My loop_fact is faster, and I believe this is because the while function works inherently faster for small code than numpy does. np_fact is making a range of all values and then multiplyin them together, whil loop_fact is subtracts then multiplies without having to make an array.