CareerCup

Consider a hash table with M slots. Suppose hash value is uniformly distributed between 1 to M, and it uses linked list to handle conflicts (if two keys hashed to the same slot). Suppose we put N keys into this M-slotted hash table, what is the probability that there will be a slot with i elements? i could vary from 0 to N.

How to find medium of 1 billion numbers across N distributed machines efficiently?

Suppose there is a new alphabet, eg. the original alphabet is (a b c d ...x,y,z), and the new one is (e k f a ....,o,p,q). Given file in which each line contains a single word and the words are sorted in the new alphabetic order.
e.g., a possible file according to the new alphabet is:

ek
kq
fo
fp
fq
aj

Use the file to reconstruct the new alphabet for as much as possible.