How to calculate the time cost of a nested loop

Question

Is there a math formula that I can put in my Windows calculator to calculate the time cost of my nested loop?

From what I read, I saw things like O(n) but I don't know how to put that in a calculator.

I have a 300 levels nested loop, each loop level will go from 0 to 1000

So it is like:

for i as integer =0 to 1000
{
 //300 more nested loops, each goes from 0 to 1000
}

I am assuming that 1 complete loop will take 1 second (i.e. the 300 levels from the top most loop to the inner most loop will take 1 second).

How can I find out how many seconds it will take to complete the whole loop operation?

Thank you

Answer 1

If you have M nested loops each with N steps, the total number of times the inner-most code will run is N^M. Consequently, if this code takes t seconds to execute, the total running time will be no less than N^Mt.

In your case, N = 1001 and M = 301. Thus

N^M = 1351006135283321356815039655729366684349803831988739053240801914465955329955010318785683390381893021480038259097571556568393033624125663039020474816807139123124687688667110651554536455554983313531622053666601142890485454586020409971220427023079449603217442510854172465669657551198374621035716253537483681789962979899381794117593366167602159102878741666110186140811771157661856975727227011774938173689257851684515033630838203428990519981303994460521486651131205651440789014004132287034501678194895276766533222238644463714676717122486815519675003623218747516074833762258750872602504763945523812443905022112877989765178585281722001229086777672022301235387486256207147702409003911671750616133700186863997717468027217550738860605995255072363983914048955786591110292838269781981812167453230775137941595147968127169264749956845265384891251656562329411331097495063637387550896404766837508698223985774995150301001.

If, in addition, we assume that the inner-most code is really fast, like t = 1 µs, the total running time will be no less than N^Mt = 1.35... × 10⁸⁹⁷ s.

When the universe comes to its end, your code will be at almost exactly 0.0000000000000000000000000000 % completion, assuming the hardware hasn't faulted by then and the human civilization hasn't come to an end (thus making it difficult for you to find the electrical power you need to run your hardware).