I want to show that if I apply the Mergesort on a set $M$ with $n$ elements and divide $M$ in $2<b\le n$ parts instead of just $2$, that the I need $O(nlog_2 (b))$ time for the merging part.
So far I went and said I have $n = b^k$ elements. So I have k iterations of merging.
My first question, when I am merging, do I merge $b$ subsets together or just two?
So I went with $b$ subsets:
In the first merging part I have $b^k (b-1) $ comparisons.
In the next one I habe $b^{k-1} (b^2-1) $ comparisons.
So in general there are at most $\sum_{i=0}^k b^{k-i} (b^{i+1}-1) $ comparisons.
Now I set $k = log_b(n)$, but I cant get anywhere from there..
Is there another way to approach this Problem?
Regards,
Chiray
P.S.: I hope my English is good enough to understand this.