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public static void main(String[] args) { Concordance c = new Concordance(PATH+IN_FILE); c.write(PATH+OUT_FILE); } }

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8.1 A vector provides direct access to its elements by means of its integer index. A table provides direct access to its elements by means of a key field, which can be of any ordinal type: int, double, string, and so forth. A table is also called a map because, like a mathematical function, it maps each key value into a unique element. A table is also called an associative array because it acts like an array (see Answer 8.1) in which each key value is associated with its unique element. Like a mathematical function, it maps each key value into a unique element. A table is also called a dictionary because it is used the same way as an ordinary natural language dictionary: to look up elements, as one would look up words in a dictionary. A concordance is a list of words that appear in a text document along with the numbers of the lines on which the words appear. (See page 157.)

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To find the input to a linear shift-invariant filter that will produce a given output y ( n ) , we use the relationship Y(z) = H(z)X(z) to solve for X(z):

Computing the z-transform of y(n), we have Y (z) = - -----+ A 1-I 1 - 22--'

The output from the program in Example 8.9 demonstrates a critical feature of hash tables: Their contents are not ordered. To obtain an alphabetized printout of the concordance, we would have to sort it. THE TreeMap CLASS The TreeMap class extends the AbstractMap class and implements the SortedMap interface. It is called a tree map because its backing structure is a binary search tree instead of a hash table.

8.2 8.3

I -4 -

I (1

But it is still a map with key/value entries. As a binary search tree structure, it sacrifices its O(1) access time, but its keys are ordered. EXAMPLE 8.10 An Ordered Concordance

8.4 8.5

+ fz-'

- iz-l)(l - 2z-1)

By replacing HashMap with TreeMap at line 2 in the Concordance class of Example 8.9, we obtain an ordered concordance:

8.6 8.7 8.8 8.9

Therefore,

X(z) =

private Map<String,String> map = new HashMap<String,String>();

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A hash table is a table that uses a special function to compute the location of data values from their key values instead of storing the keys in the table. (See page 151.) Not much. The Java Hashtable class has generally been superseded by the Java HashMap class, which conforms a little better to the Java Collections Framework. If there are collisions, then the order of insertion is relevant. Quadratic probing generally results in fewer collisions because the probes jump over gaps in the index range. But unlike linear probing, quadratic probing can cause infinite loops even when the table is not full. A HashMap object is a hash table implemented with separate chaining and a default load threshold of 75 percent, so it provides nearly O(1) access time for insertions, deletions, and searches. A TreeMap object is a balanced binary search tree implemented as a red-black tree, so it provides nearly O(lgn) access time for insertions, deletions, and searches. So a HashMap is faster, but a TreeMap is ordered.

(1 (1

8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 What is the difference between a table and a vector Why is a table also called a map Why is a table also called an associative array Why is a table also called a dictionary What is a concordance What is a hash table What is the difference between the Java Hashtable class and the Java HashMap class The first two examples showed that the order of insertion into a hash table is irrelevant if there are no collisions. What if there are What are the advantages and disadvantages of quadratic probing compared to linear probing

+ iz-I)(1

8.1 Inserting 16 entries into the German-English dictionary:

- ;z-1)

CHAP. 8]

- $z-')(l - 2z-')(I + z-I)

public class Testing { public static void main(String[] args) { Map map = new HashMap(11); map.put("Ast","branch"); map.put("Eis","ice"); map.put("Hof","court, yard, farm"); map.put("Hut","hat"); map.put("Lob","praise"); map.put("Mal","mark, signal"); map.put("Mut","courage"); map.put("Ohr","ear"); map.put("Ost","east"); map.put("Rad","wheel"); map.put("Rat","advice, counsel"); map.put("Tag","day"); map.put("Tor","gate"); map.put("Uhr","clock"); map.put("Wal","whale"); map.put("Zug","procession, train"); System.out.println("map=" + map); System.out.println("map.keySet()=" + map.keySet()); System.out.println("map.size()=" + map.size()); } }

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