Data Structures and Algorithm Analysis - Computer Science at ...

Sec. 5.8 Exercises 1915.23 What are the minimum and maximum number of elements in a heap ofheight h?5.24 Where in a max-heap might the smallest element reside?5.25 Show the max-heap that results from running buildHeap on the followingvalues stored in an array:10 5 12 3 2 1 8 7 9 45.26 (a) Show the heap that results from deleting the maximum value from themax-heap of Figure 5.20b.(b) Show the heap that results from deleting the element with value 5 fromthe max-heap of Figure 5.20b.5.27 Revise the heap definition of Figure 5.19 to implement a min-heap. Themember function removemax should be replaced by a new function calledremovemin.5.28 Build the Huffman coding tree and determine the codes for the following setof letters and weights:Letter A B C D E F G H I J K LFrequency 2 3 5 7 11 13 17 19 23 31 37 41What is the expected length in bits of a message containing n characters forthis frequency distribution?5.29 What will the Huffman coding tree look like for a set of sixteen characters allwith equal weight? What is the average code length for a letter in this case?How does this differ from the smallest possible fixed length code for sixteencharacters?5.30 A set of characters with varying weights is assigned Huffman codes. If oneof the characters is assigned code 001, then,(a) Describe all codes that cannot have been assigned.(b) Describe all codes that must have been assigned.5.31 Assume that a sample alphabet has the following weights:Letter Q Z F M T S O EFrequency 2 3 10 10 10 15 20 30(a) For this alphabet, what is the worst-case number of bits required by theHuffman code for a string of n letters? What string(s) have the worstcaseperformance?(b) For this alphabet, what is the best-case number of bits required by theHuffman code for a string of n letters? What string(s) have the bestcaseperformance?