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Sec. 5.6 Huffman Coding Trees 1813060 1120 186E 0790 110107137U42D42L06532 33C0 19 240 1 M2Z17KFigure 5.26 A Huffman tree for the letters of Figure 5.24.Example 5.8 Figure 5.25 illustrates part of the Huffman tree constructionprocess for the eight letters of Figure 5.24. Ranking D and L arbitrarily byalphabetical order, the letters are ordered by frequency asLetter Z K M C U D L EFrequency 2 7 24 32 37 42 42 120Because the first two letters on the list are Z and K, they are selected tobe the first trees joined together. 6 They become the children of a root nodewith weight 9. Thus, a tree whose root has weight 9 is placed back on thelist, where it takes up the first position. The next step is to take values 9and 24 off the list (corresponding to the partial tree with two leaf nodesbuilt in the last step, and the partial tree storing the letter M, respectively)and join them together. The resulting root node has weight 33, and so thistree is placed back into the list. Its priority will be between the trees withvalues 32 (for letter C) and 37 (for letter U). This process continues until atree whose root has weight 306 is built. This tree is shown in Figure 5.26.Figure 5.27 shows an implementation for Huffman tree nodes. This implementationis similar to the VarBinNode implementation of Figure 5.10. There is anabstract base class, named HuffNode, and two subclasses, named LeafNode6 For clarity, the examples for building Huffman trees show a sorted list to keep the letters orderedby frequency. But a real implementation would use a heap to implement the priority queue forefficiency.