given array A of size $n$ which is made of $logn + 1$ sub arrays which are sorted, I need to sort ASAP.
example of array : $A[500,501,3,8,100,1,2,9]$ as you can see, sub arrays are :$[1:2][3:5][6:]$
my solution was: merge all logn + 1 arrays together, simultaneously.
so like I compare : $1:3:500$ >> append 1 to sorted array $2:3:500$ >> append 2 and so on until all is done.
i thought the complexity of my solution is expected to be $O(n)$ because each sub array on average has $\frac{n}{logn+1}$ values and there are $logn+1$ subarrays ..
chatgpt says its $O(nloglogn)$ ..
can you please explain the complexity analysis? does my solution even work?