CUCKOO  Cuckoo Hashing
One of the most fundamental data structure problems is the dictionary problem: given a set D of words you want to be able to quickly determine if any given query string q is present in the dictionary D or not. Hashing is a wellknown solution for the problem. The idea is to create a function h : Σ ^{∗} → [0..n − 1] from all strings to the integer range 0,1,..,n − 1, i.e. you describe a fast deterministic program which takes a string as input and outputs an integer between 0 and n−1. Next you allocate an empty hash table T of size n and for each word w in D, you set T[h(w)] = w. Thus, given a query string q, you only need to calculate h(q) and see if T[h(q)] equals q, to determine if q is in the dictionary. Seems simple enough, but aren’t we forgetting something? Of course, what if two words in D map to the same location in the table? This phenomenon, called collision, happens fairly often (remember the Birthday paradox: in a class of 24 pupils there is more than 50% chance that two of them share birthday). On average you will only be able to put roughly √nsized dictionaries into the table without getting collisions, quite poor space usage!
A stronger variant is Cuckoo Hashing. The idea is to use two hash functions h_{1} and h_{2}. Thus each string maps to two positions in the table. A query string q is now handled as follows: you compute both h_{1}(q) and h_{2}(q), and if T[h_{1}(q)] = q, or T[h_{2}(q)] = q, you conclude that q is in D. The name “Cuckoo Hashing” stems from the process of creating the table. Initially you have an empty table. You iterate over the words d in D, and insert them one by one. If T[h_{1}(d)] is free, you set T[h_{1}(d)] = d. Otherwise if T[h_{2}(d)] is free, you set T[h_{2}(d)] = d. If both are occupied however, just like the cuckoo with other birds’ eggs, you evict the word r in T[h_{1}(d)] and set T[h_{1}(d)] = d. Next you put r back into the table in its alternative place (and if that entry was already occupied you evict that word and move it to its alternative place, and so on). Of course, we may end up in an infinite loop here, in which case we need to rebuild the table with other choices of hash functions. The good news is that this will not happen with great probability even if D contains up to n/2 words.
Input
On the first line of input is a single positive integer 1 ≤ t ≤ 50 specifying the number of test cases to follow. Each test case begins with two positive integers 1 ≤ m ≤ n ≤ 10000 on a line of itself, m telling the number of words in the dictionary and n the size of the hash table in the test case. Next follow m lines of which the i:th describes the i:th word d_{i} in the dictionary D by two nonnegative integers h_{1}(d_{i}) and h_{2}(d_{i}) less than n giving the two hash function values of the word d_{i}. The two values may be identical.
Output
For each test case there should be exactly one line of output either containing the string “successful hashing” if it is possible to insert all words in the given order into the table, or the string “rehash necessary” if it is impossible.
Example
Input: 2 3 3 0 1 1 2 2 0 5 6 2 3 3 1 1 2 5 1 2 5 Output: successful hashing rehash necessary
hide comments
offamitkumar:
20200509 11:45:10
must try problem :) 

:D:
20170826 17:49:36
I think description is a little unclear. If eviction sequence for h1(d) fails, you should try it for h2(d) as well. Last edit: 20190702 11:08:42 

mrinal_aich:
20160921 15:13:54
@1yr: If we are removing element h1, we are also inserting a new value hence only h2 of the removed element is the choice left. Last edit: 20160921 15:14:18 

birdie:
20150319 05:58:10
good 1! 

1yr:
20141216 20:44:36
IMP: first remove element from h1 then after the alternatives which can be h1 or h2 

Stephen Merriman:
20090404 05:20:39
Each key has two possible positions. You remove it from one, and put it in the other. 

SALVO:
20090328 18:25:09
what is "Alternative Place in the Table" in this problem ?

Added by:  Andres Galvis 
Date:  20090309 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  Nordic Collegiate Programming Contest 2007 