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HASH TABLES
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EXAMPLE 8.3 Hash Codes of Some String Objects
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This program prints the intrinsic hash codes of the String objects stored in the previous programs:
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public class TestHashCodes { public static void main(String[] args) { printHashCode("Rad"); printHashCode("Uhr"); printHashCode("Ohr"); printHashCode("Tor"); printHashCode("Hut"); printHashCode("Tag"); } private static void printHashCode(String word) { System.out.printf("%s: %s%n", word, word.hashCode()); } }
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The output is:
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Rad: Uhr: Ohr: Tor: Hut: Tag: 81909 85023 79257 84279 72935 83834
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The fact that all six codes are relatively close 5-digits integers reflects the fact that these String objects all have length 3.
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HASH TABLES 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. The special function is called the hash function for the table. Since the lookup time is independent of the size of the table, hash tables have very fast access time. Java defined a Hashtable class in its java.util package. But it has essentially been upgraded to the HashMap class. That is, a HashMap table can do everything that a Hashtable object can do. Moreover, the HashMap class is more consistent with rest of the Java Collections Framework. A general hash table looks like the one pictured in Figure 8.2: an array of Objects indexed by their hash values. This requires that the range of the hash function match the range of index values in the array. This is Figure 8.2 Hash table almost always managed by simply using the remainder operator modulo the size of the array: EXAMPLE 8.4 Mapping Keys into a Hash Table of Size 11
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This program prints hash code values for String objects to be stored in a hash table of size 11:
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public class TestHashing { private static final int MASK = 0x7FFFFFFF; // private static final int CAPACITY = 11;
= 2^32-1
HASH TABLES
[CHAP. 8
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
public static void main(String[] args) { printHash("Rad"); printHash("Uhr"); printHash("Ohr"); printHash("Tor"); printHash("Hut"); printHash("Tag"); } private static void printHash(String word) { System.out.println("hash(" + word + ") = " + hash(word)); } private static int hash(Object object) { return (object.hashCode() & MASK) % CAPACITY; } }
The output is:
hash(Rad) hash(Uhr) hash(Ohr) hash(Tor) hash(Hut) hash(Tag) = = = = = = 3 4 2 8 5 3
The hash function values are computed at line 19, where CAPACITY is 11 and MASK is 2147483647, expressed in hexadecimal as 0x7FFFFFFF. The operation n & MASK simply removes the sign from whatever integer n has. This is the right thing to do in Java before using the remainder operator to compute an array index because (unlike C++) Java may give a negative result to m % CAPACITY if m is negative. So the resulting value returned by the hash() function in this example is guaranteed to be in the range of 0 to 10. The first five strings hash into index values 3, 4, 2, 8, and 5, so they would be stored in those locations in the hash table. But the sixth string ("Tag") also hashes to 3, causing a collision with "Rad", which would already be stored in component 3. The most common algorithm to apply when such collisions occur is to simply put the new item in the next available component. That would be component 6 in this example, since "Uhr" would already be in component 4 and "Hut" would already be in component 5. This collision resolution algorithm is called linear probing.
The HashMap class uses a hash function just like the one in Example 8.4 to implement its accessor methods: containsKey(), get(), put(), remove(), and entrySet(). Its sets the hash table size at 101 initially. With that knowledge, we can see why the six strings in the previous examples were stored in the order indicated. EXAMPLE 8.5 Mapping Keys into a Hash Table of Size 101
This program is identical to the one in Example 8.4 except that the hash table CAPACITY is 101 instead of 11:
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public class TestHashing { private static final int MASK = 0x7FFFFFFF; // private static final int CAPACITY = 101; public static void main(String[] args) { printHash("Rad"); printHash("Uhr"); printHash("Ohr");
= 2^32-1
CHAP. 8]
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