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C8U ¨ ¨ Deﬁne Let us construct a full binary tree of depth (i.e. leaves are at depth whereas root is at depth ) and let us
mark leftward edges with and rightward edges with exactly as we did in the construction of Huffman
code trees. Then, exactly as with Huffman codes, to each node (except the to root) corresponds a certain
let us deﬁne
to be the set of all leaves that are descendants of the node that
code. For each
corresponds to the code
Then for
the sets
and
must be disjoint. In the opposite case,
would be a descendant
a common leaf would be a descendant of both and and therefore one of
of the other, contradicting the fact that is a preﬁx code. The total number of leaves is
so we...
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 Spring '12
 Blelloch
 Algorithms

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