In my class my teacher calculated the time complexity for this algorithm, relative to the number of sum operations executed:
She represented the cost of the algorithm by the following sum:
$\sum\limits_{i=1}^n \sum\limits_{j=1}^i\sum\limits_{k=1}^j 3 = \frac{n^3}{2} + \frac{3n^2}{2} + n $
The step by step used to solve the sum bellow:
n = 10
count=0
for i in range (0, n):
for j in range (0, i):
for k in range (0, j):
count+=3
print count
Then, I wrote a algorithm in python to verify the solution, but it not produce the expected output, for example, for n = 10 we expected 660 operations, but it print 360.
Change the index to start with 1 like in the bellow didn't worked either, in fact it got more distance from the expected (252).
n = 10
count=0
for i in range (1, n):
for j in range (1, i):
for k in range (1, j):
count+=3
print count