Assignment 1A Solution

# The total number of leaves is so we have f 10 8 20v f

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Unformatted text preview:  ¨£ C8U ¨ ¨ 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 left-ward edges with and right-ward 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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