Understanding How Many Times Nested Loops Will Run

Question

I am trying to understand how many times the statement \"x = x + 1\" is executed in the code below, as a function of \"n\":

for (i=1; i<=n; i++)
  for (j=1; j         


        

Answer 1

The 3rd inner loop is the same as the 2nd inner loop, but your n is a formula instead.

So, if your outer loop is n times...

and your 2nd loop is n(n+1)/2 times...

your 3rd loop is....

(n(n+1)/2)((n(n+1)/2)+1)/2

It's rather brute force and could definitely be simplified, but it's just algorithmic recursion.