Chapter 11, DATA COMPRESSION Video Solutions, Data Structures and Algorithms in C++

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Problem 1

For which probabilities $P\left(m_i\right)$ of $n$ symbols is the average length maximal? When is it minimal?

Adriano Chikande

Numerade Educator

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Find $L_{\text {ave }}$ for the letters $X, Y$, and $Z$ and their probabilities $.05, .05$, and .9 and compare it to $L_{\text {Huf }}$ computed for single letters and pairs of letters, as in Figure 11.6. Does $L_{\mathrm{Huf}}$ satisfactorily approximate $L_{\text {ave }}$ ? How can we remedy the problem?

Ashley Volpe

Numerade Educator

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Problem 3

Assess the complexity of all the implementations of the Huffman algorithm suggested in this chapter.

Nick Johnson

Numerade Educator

Problem 4

What are the lengths of the Huffman codewords of the least probable messages with respect to each other?

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Problem 5

In the adaptive Huffman algorithm, first the codeword for an encountered symbol is issued and then the conversion table is updated. Could the table be updated first and then the new codeword for this symbol be issued? Why or why not?

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Problem 6

The functions create Code words () and trans form Tree To Array of Lists () used in the case study seem to be vulnerable because the first thing they both do is access the pointer left of node $p$, which would be dangerous if p were null; therefore, the body of both functions should apparently be preceded by the condition if (p $!=0$ ). Explain why this is not necessary.

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Problem 7

What problem arises if, in run-length encoding, triples of the form $\langle c m, n, c h\rangle$ are used instead of triples of the form $\langle\mathrm{cm}, \mathrm{ch}, n\rangle$ ?

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