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COLLISION RESOLUTION ALGORITHMS The collision resolution algorithm used in the previous examples is called linear probing. When a new item hashes to a table component that is already in use, the algorithm specifies to increment the index until an empty component is found. This may require a wraparound back to the beginning of the hash table. EXAMPLE 8.6 Linear Probing
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This program extends the program in Example 8.4. It keeps track of which table components are used and the load factor after each hashing.
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public class Ex1406 public class TestLinearProbing { private static final int MASK = 0x7FFFFFFF; // 2^32-1 private static final int CAPACITY = 11; private static int size = 0; private static boolean[] used = new boolean[CAPACITY]; public static void main(String[] args) { printHash("Rad"); printHash("Uhr"); printHash("Ohr"); printHash("Tor"); printHash("Hut"); printHash("Tag"); printHash("Eis"); printHash("Ast"); printHash("Zug"); printHash("Hof"); printHash("Mal"); } private static void printHash(String word) { System.out.printf("hash(%s) = %d, load = %d%%%n", word, hash(word), 100*size/CAPACITY); } private static int hash(Object object) { ++size; int h = (object.hashCode() & MASK) % CAPACITY; while (used[h]) { System.out.printf("%d, ", h); h = (h+1)%CAPACITY; } used[h] = true; return h; } }
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hash(Rad) = 3, load = 9% hash(Uhr) = 4, load = 18% hash(Ohr) = 2, load = 27% hash(Tor) = 8, load = 36% hash(Hut) = 5, load = 45% 3, 4, 5, hash(Tag) = 6, load = 54%
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5, 6, hash(Eis) = 7, load = 63% 3, 4, 5, 6, 7, 8, hash(Ast) = 9, load = 72% 9, hash(Zug) = 10, load = 81% 3, 4, 5, 6, 7, 8, 9, 10, hash(Hof) = 0, load = 90% 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, hash(Mal) = 1, load = 100% The size field contains the number of items hashed into the table. The used[] array flags which components are occupied in the table. The printHash() method prints the hash table index and the
resulting load factor as a percent. When linear probing kicks in, each successive index number probe is printed. As seen in Example 8.4, the collision occurs with the insertion of "Tag" at line 14. This program shows that it had three collisions (at index numbers 3, 4, and 5) before finding a free hash location at index 6. After that insertion, the table is 54 percent full. Every item after that also collides. And of course, as the table fills up, the number of collisions becomes more frequent. The last item, "Mal", has 10 collisions. That means that thereafter, every time this item is accessed it will have to search every one of the 11 items before it is found; clearly an O(n) process. Notice the index wraparound on the insertion of "Mal": 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1.
Another collision resolution algorithm that usually performs better than linear probing is called quadratic probing. This algorithm jumps over items in its probing, with the result that the used components are more uniformly distributed with fewer large clusters. That improves performance because the resulting probe chains are shorter. EXAMPLE 8.7 Quadratic Probing
This program is the same as the program in Example 8.6 except for the modified hash() function shown here.
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public class TestQuadraticProbing { private static final int MASK = 0x7FFFFFFF; // 2^32-1 private static final int CAPACITY = 11; private static int size = 0; private static boolean[] used = new boolean[CAPACITY]; public static void main(String[] args) { printHash("Rad"); printHash("Uhr"); printHash("Ohr"); printHash("Tor"); printHash("Hut"); printHash("Tag"); printHash("Eis"); printHash("Ast"); printHash("Zug"); printHash("Hof"); printHash("Mal"); } private static void printHash(String word) { System.out.printf("hash(%s) = %d, load = %d%%%n", word, hash(word), 100*size/CAPACITY); } private static int hash(Object object) { ++size;
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