Chapter 5: Q13E (page 162)
A long string consists of the four characters ; they appear with frequency and respectively. What is the Huffman encoding of these four characters?
Short Answer
Huffman encoding of the characters is respectively.
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Chapter 5: Q13E (page 162)
A long string consists of the four characters ; they appear with frequency and respectively. What is the Huffman encoding of these four characters?
Huffman encoding of the characters is respectively.
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Question: Suppose the symbols a,b,c,d,e occur with frequencies respectively.
(a) What is the Huffman encoding of the alphabet?
(b) If this encoding is applied to a file consisting of characters with the given frequencies, what is the length of the encoded file in bits?
Prove the following two properties of the Huffman encoding scheme.
(a) If some character occurs with frequency more than , then there is guaranteed to be a codeword of length 1 .
(b) If all characters occur with frequency less than , then there is guaranteed to be no codeword of length 1 .
Give a linear-time algorithm that takes as input a tree and determines whether it has a perfect matching: a set of edges that touches each node exactly once.
A feedback edge set of an undirected graph G(V,E) is a subset of edgesthat intersects every cycle of the graph. Thus, removing the edges will render the graph acyclic.
Give an efficient algorithm for the following problem:
Input: Undirected graph G(V,E) with positive edge weights .
Output: A feedback edge set minimum total weight .
Let be an undirected graph. Prove that if all its edge weights are distinct, then it has a unique minimum spanning tree
Consider the following graph.
(a) What is the cost of its minimum spanning tree?
(b) How many minimum spanning trees does it have?
(c) Suppose Kruskal’s algorithm is run on this graph. In what order are the edges added to the MST? For each edge in this sequence, give a cut that justifies its addition.

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