CMPS 340  File Processing
Huffman's algorithm for assigning codewords to symbols


INPUT:  an alphabet A of "symbols" (of which some "source text" is composed),
  and a mapping f : A --> N  (N = set of all natural numbers), where,
  for a in A, f(a) is the "frequency" with which a occurs in the source text.

OUTPUT: a mapping g : A --> BS  (BS = set of all bit strings) associating 
  a (binary) codeword to each member of A.


BEGIN
   Q := empty priority queue of weighted binary trees (lower weight equals
                                                       higher priority     )
   DO FOR each a in A
      t :=  one-node tree with label a and weight f(a)
      Insert(t,Q)   --insert t into Q
   OD

   DO |A| - 1  TIMES
      t1 := Delete_Min(Q);     --extract from Q the two trees 
      t2 := Delete_Min(Q);     --having lowest weights
      construct t by creating an unlabeled root node and attaching to it as
         children the roots of t1 and t2.  Make the weight of t be the sum
         of the weights of t1 and t2
      Insert(t,Q)               --insert t into Q
   OD

   --at this point, Q contains a single tree, the leaves of which are
   --precisely the |A| nodes with which we began

   t := lone tree in Q
   perform depth first search in t so as to compute g(a) for each a in A.
   --(Label each edge of t by either 0 or 1, according to whether it goes
   --to a left child or a right child, respectively.  Then g(a) corresponds
   --to the sequence of labels on the edges along the path from the root of
   --t to the leaf node labeled a.)

END