Unformatted text preview: full binary tree (i.e., every internal node must have 2 children). (d) Let x and y be the two characters having the two lowest frequencies. Is it true that x and y are siblings (i.e., children of the same node) in every optimal preﬁx tree? Justify your answer brieﬂy. (e) Consider the optimal preﬁx tree T 1 built by Huﬀman’s algorithm, given n characters with frequencies f 1 ≤ f 2 ≤ ··· ≤ f n . A key idea underlying Huﬀman’s algorithm is that this tree T 1 is related to the optimal preﬁx tree T 2 for a certain set of n1 characters. Answer the following brieﬂy. (i) What are the frequencies of these n1 characters? (ii) And what is the relationship of tree T 1 to tree T 2 (i.e., how can you obtain tree T 1 from tree T 2 )? c ± 2006 Chung Kai Lun Peter. Comments are welcomed. Email: [email protected] 1...
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 Spring '10
 may
 English, Cryptography, Graph Theory, Ode, Binary heap

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