Hashing Algorithm

Not exactly clear what you are trying to do, or what your actual question is?

Are you searching, sorting, or hashing?

Is m (the number of buckets) greater than n (the number of elements)?  This is what you want for effective hashing.

But you also mentioned something about the "most filled bucket" which implies you are expecting some collisions.

Look-up performance for good hashing approaches O(1), although building the table is still O(n).

If all that matters is the location of the bucket with the most elements, you can keep track of that during the build phase so you won't have to search for it.

Assuming there are M buckets and N elements, with N greater than M. Ideally it should work for any M and N, but can assume M <=125. I am expecting collision, and finding out which bucket has the most elements. Is it possible to process each element in O(1) expected time and lookup for the most filled bucket (ie. Bucket C has the most elements, return C, the name of the bucket)  to also be in O(1) expected time.

My constraint is that it has to be done in some algorithm based on hashing and without any sort algorithm.

Currently I'm having trouble seeing how this can be done..

Thanks guys, I figured it out!