Dynamic Huffman Coding

نویسنده

  • Donald E. Knuth
چکیده

Given nonnegative weights (wr, . . . , w,,), the well-known algorithm of Huffman [2] can be used to construct a binary tree with n external nodes and n 1 internal nodes, where the external nodes are labeled with the weights (wr, . . . , w,) in some order. Huffman’s tree has the minimum value of WJ, + * * . + w,,l, over all such binary trees, where lj is the level at which wj occurs in the tree. Binary trees with n external nodes are in one-to-one correspondence with sets of n strings on (0, 1) that form a “minimal prefix code.” A prefix code is a set of strings in which no string is a proper prefix of another; and a minimal prefix code is a prefix code such that, if (Y is a proper prefix of some string in the set, then (~0 is either in the set or a proper prefix of some string in the set, and so is ~yl. The correspondence between trees and codes is simply to represent the path from the root to each external node as a string of O’s and l’s, where 0 corresponds to a left branch and 1 to a right branch. An external node at level I corresponds in this way to a string of

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عنوان ژورنال:
  • J. Algorithms

دوره 6  شماره 

صفحات  -

تاریخ انتشار 1985