# This is a phython3 script
import time, timeit

# Four functions/methods that compute the sum of the first natural numbers:

def sumRec(k):
    if(k==0):
        return 0
    return k+sumRec(k-1)

def sumIter(n):
    result = 0
    for k in range(0,n+1):
        result+=k
    return result

def sumPy(n):
    return sum(range(n+1))

def sumFormula(n):
    return n*(n+1)/2


# Comparing the execution time of the above:

print('Evaluate the functions 9999 times at 990:')
print('Evaluating the naive recursion  takes ',timeit.timeit('sumRec(990)', setup='from __main__ import sumRec', number=9999),' seconds.')
print('Evaluating the first iteration  takes ',timeit.timeit('sumIter(990)', setup='from __main__ import sumIter', number=9999),' seconds.')
print('Evaluating the second iteration takes ',timeit.timeit('sumPy(990)', setup='from __main__ import sumPy', number=9999),' seconds.')
print('Evaluating the closed formula   takes ',timeit.timeit('sumFormula(990)', setup='from __main__ import sumFormula', number=9999),' seconds.')