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Figure 7.2 The end reference in the Ring class
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accessed by the iterator s next() method. It will be null initially and immediately after each call to the iterator s remove() method. The preLast field points to the node that points to the last node. It is used by the remove() method. The iterator s hasNext() method returns true at line 51, unless the list is empty. In a circular list, every element has a next element. The next() method serves two purposes. If called immediately after a call to remove(), then it resets the last field (line 56), which the remove() method leaves null. Otherwise, it simply advances the preLast and last pointers (lines 58 59). The purpose of the remove() method at line 64 is to delete the last element accessed by the next() method. Normally, it does that simply by resetting one link the preceding node s next field (line 71). But it also has several special cases to handle. If its invocation does not immediately follow a call to next(), then it s in an illegal state, and thus throws an IllegalStateException at line 66. If the list has only one element, then removing it should leave the list in its original empty state by nullifying its preLast field (line 69). In that case, the Ring class s end field is also nullified. If the element being deleted is the one referenced by the Ring class s end field, then that field is reset to the element s predecessor at line 74. Finally, last is nullified at line 76 to mark the fact that the next() method was not the last one called in the iterator.
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Figure 7.3 The last and preLast references in the RingIterator class
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Figure 7.3 illustrates how the last and preLast pointers work in an iterator on a Ring list. This shows the state of the list immediately after a call to next() has returned the element C. An immediate call to remove() would delete the C node by resetting the B node s next reference to point to the D node, as shown in Figure 7.4.
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Figure 7.4 After a call to it.remove()
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Note the efficiency of this operation: To delete C, only one link has to be reset, and one link is nullified.
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[CHAP. 7
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APPLICATION: THE JOSEPHUS PROBLEM This problem is based upon a report by the historian Joseph ben Matthias (Josephus) on the outcome of a suicide pact that he had made between himself and 40 soldiers as they were besieged by superior Roman forces in 67 A.D. Josephus proposed that each man slay his neighbor. This scheme necessarily leaves one to kill himself. Josephus cleverly contrived to be that one, thus surviving to tell the tale. The solution to the problem is generated by the Josephus program in Example 7.6. It uses the Ring class from Example 7.5 on page 136. EXAMPLE 7.6 The Josephus Problem
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public class Josephus { public static final int SOLDIERS = 8; public static final String ALPHA = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; public static void main(String[] args) { Ring<String> ring = new Ring<String>(); for (int i=0; i<SOLDIERS; i++) { ring.add(ALPHA.substring(i, i+1)); } System.out.println(ring); Iterator<String> it = ring.iterator(); String killer = it.next(); while (ring.size() > 1) { String victim = it.next(); System.out.println(killer + " killed " + victim); it.remove(); killer = it.next(); } System.out.println("The lone survivor is " + it.next()); } }
Here is the output from a run for 11 soldiers:
[A, B, C, D, E, F, G, H, I, J, K] A killed B C killed D E killed F G killed H I killed J K killed A C killed E G killed I K killed C G killed K The lone survivor is G
This output shows the solution, which is illustrated Figure 7.5 The solution to the Josephus problem in Figure 7.5. The Ring list is instantiated at line 6 and loaded at lines 7 9. The iterator it is obtained from the iterator() method at line 11. After advancing past A at line 12, it advances past B at line 14, removes B at line 16, and then advances past C at line 17. The while loop continues until only one soldier remains. Each iteration advances it past two elements, naming them killer and victim, and removes the victim node.
CHAP. 7]
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