Time comlexity=?

Question

main()
{
    for(i=1;i<=n;i++)
    {
        for(i=1;i<=n*n;i++)
        {
            for(i=1;i<=n*n*n;i++)
            {
                x=y+z;
            }
            
        }
        
    }
    
}

Answer 1

0(n^3) because the internal loop runs n^3 times and now it does not satisfy the condition of 1st and 2nd loop so it comes out of the loop

Comments

how n⁶ please explain?

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in the inner for  loop when a condition is false then in the second for loop when we check $i\leq n^2$; so value of $i$ is taken from where the inner loop or second loop??

Answer 2

answer is n^3 since

for first loop i =1

second loop i=1

third will run i=n^3 now when it goes back to second it compares & fails since i has changed to n^3 so it will be transfer to first loop again fail coz i = n^3 so only one time loop will execute

so O(n^3)

Answer 3

First of all the variable  ' i ' is not initialised. If  ' i '  is declared outside all the for loops then the time complexity will be O(n³).  But instead if you are declaring  i each time inside a loop then time complexity will be O(n⁶).

So basically the complexity depends on the scope of the variable i.