Double hashing

• Linear probing collision resolution leads to clusters in the table, because if two keys collide, the next position probed will be the same for both of them.
  
• The idea of double hashing: Make the offset to the next position probed depend on the key value, so it can be different for different keys
• Need to introduce a second hash function H 2 (K), which is used as the offset in the probe sequence (think of linear probing as double hashing with H 2 (K) == 1)
• For a hash table of size M, H 2 (K) should have values in the range 1 through M-1; if M is prime, one common choice is H2(K) = 1 + ( (K/M) mod (M-1) )
  
• The insert algorithm for double hashing is then:
  
  1. Set indx = H(K); offset = H 2 (K)
  2. If table location indx already contains the key, no need to insert it. Done!
  3. Else if table location indx is empty, insert key there. Done!
  4. Else collision. Set indx = (indx + offset) mod M.
  5. If indx == H(K), table is full! (Throw an exception, or enlarge table.) Else go to 2.
  
• With prime table size, double hashing works very well in practice