CMPS 340  File Processing
Algorithms for extendible hashing (insertion and deletion)


procedure Insert ( REC )       --inserts REC into hash table

begin
  KEY    := KeyOf(REC);  
  ADDR   := the number whose binary representation is the first DIR_DEPTH
            bits of H(KEY), where H is our hash function.
  BUCKET := the bucket pointed to by DIRECTORY[ ADDR ]

  if a record R satisfying KeyOf(R) = KEY is already in BUCKET then

     Take appropriate action  (perhaps report "duplicate error")

  elsif BUCKET is not full then

     place REC into BUCKET

  else
     Split_Bucket(BUCKET);  --split BUCKET and redistribute its contents 
                            --appropriately between itself and the new bucket.
                            --If BUCKET's depth was equal to DIR_DEPTH, add 1
                            --to DIR_DEPTH and double the size of DIRECTORY.
     Insert( REC );         --recursively insert
  end if;
end Insert;


procedure Delete ( KEY )        --deletes from hash table the record R 
                                --satisfying KeyOf(R) = KEY 
begin
  ADDR   := the number whose binary representation is the first DIR_DEPTH
            bits of H(KEY), where H is our hash function.
  BUCKET := the bucket pointed to by DIRECTORY[ ADDR ]

  Let R be the record in BUCKET satisfying KeyOf(R) = KEY 

  if R does not exist then
     Report "nothing to delete" error
  else
     remove R from BUCKET

     while BUCKET has a "buddy bucket" BUDDY and the two are "collapsible" loop 
        
        --Note that two buckets are "buddies" iff their labels (a bucket's
        --label is the bit string which is the longest common prefix of the
        --hash values of all keys that "belong" in it) differ in only the last
        --bit.  Two buddies are collapsible if their contents can together fit
        --into a single bucket.  (Folk and Zoellick do not consider two buckets
        --to be buddies unless, in addition, their depths (lengths of their
        --labels) are equal to DIR_DEPTH, the depth of the directory.)

        Collapse(BUCKET, BUDDY ); --Combine contents of BUCKET and BUDDY into
                                  --BUCKET, freeing the space used by BUDDY and
                                  --changing directory cells pointing to BUDDY 
                                  --so as to point to BUCKET.  If appropriate, 
                                  --subtract 1 from DIR_DEPTH and halve the 
                                  --size of DIRECTORY.
     end loop;
  end if;
end Delete;