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CS100J Lecture 12

CS100J Lecture 12. Previous Lecture Java Constructs arrays and indexing increment and decrement for -statements Lewis and Loftus, Sections 3.8 and 6.1-6.2 This Lecture Java constructs for ( initialized-declaration ; … ) throw Programming Concepts Alternative class implementations

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CS100J Lecture 12

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  1. CS100J Lecture 12 • Previous Lecture • Java Constructs • arrays and indexing • increment and decrement • for-statements • Lewis and Loftus, Sections 3.8 and 6.1-6.2 • This Lecture • Java constructs • for( initialized-declaration; … ) • throw • Programming Concepts • Alternative class implementations • Use of an array for maintaining a list of items • Exception handling Lecture 12

  2. Motivating Example • In many applications, we need to maintain an unordered list of natural numbers, where each natural number may occur more than once. • Such a list is called a “multi-set” of natural numbers. • For example, the set of grades obtained on an exam is such a multi-set. • Specification of classNatMultiset //Construct NatMultiset of items <= maxValue. public NatMultiset(int maxValue) // Insert item into multiset. public void insert(int item) // Is item in multiset? public boolean isElement(int item) // Delete item from multiset. public void delete(int item) // Multiplicity of item in multiset. public int multiplicity(int item) Lecture 12

  3. Frequencies of Grades, revisited int grade; // the grade being processed. // Let histogram be represented by a NatMultiset. NatMultiset hist = new NatMultiset(100); /* “Process” grades until (but not including) a stopping signal of -1. */ grade = in.readInt(); while (grade != -1 ) { hist.insert(grade); grade = in.readInt(); } /* Print histogram. */ System.out.println(”Grade Frequency”); for ( grade = 0; grade<=100; grade++ ) System.out.println( grade + ” ” + hist.multiplicity(grade) ); Lecture 12

  4. First Implementation of natMultset maxValue freq • Representation Invariant: For each k in the range 0..maxValue, the frequency of item k in the multiset is freq[k]. maxValue 0 . . . publicclass NatMultiset { /* For each k in range 0..maxValue, frequency of k in multiset is freq[k]. */ private int maxValue; private int[] freq; /* methods */ . . . } Lecture 12

  5. Constructor NatMultiset (Version 1) /* Construct a NatMultiset for elements in the range 0 through maxValue. */ public NatMultiset( int maxValue ) { this.maxValue = maxValue; freq = new int[maxValue+1]; for (int k = 0; k <= maxValue; k++) freq[k]=0; } Running time: Proportional to maxValue Lecture 12

  6. Method insert (Version 1) /* Insert item into the multiset; throw RuntimeException if item out of range. */ publicvoid insert(int item) { if ( item < 0 || item > maxValue ) thrownew RuntimeException( ”NatMultiset: item out of range” ); else freq[item]++; } Running time: Constant time Exceptions: new RuntimeException(String msg)constructs an object that contains messagemsg. [In the absence of a user-defined catch,] throw terminates execution, and prints the message contained in theRuntimeException object. Lecture 12

  7. Method isElement (Version 1) /* Return true if the multiset contains 1 or more instances of item. Throw RuntimeException if item out of range. */ public boolean isElement(int item) { if ( item < 0 || item > maxValue ) thrownew RuntimeException( ”NatMultiset: item out of range” ); elsereturn freq[item] != 0; } Running time: Constant time Lecture 12

  8. Method delete (Version 1) /* Delete one instance of item from the multiset, if there is one. RuntimeException if item out of range. */ publicvoid delete(int item) { if ( item < 0 || item > maxValue ) thrownew RuntimeException( ”NatMultiset: item out of range” ); elseif (freq[item] > 0) freq[item]--; } Running time: Constant time Lecture 12

  9. Method multiplicity (Version 1) /* Return the number of occurrences of item in the multiset. RuntimeException if item out of range. */ publicint multiplicity(int item) { if ( item < 0 || item > maxValue ) thrownew RuntimeException( ”NatMultiset: item out of range” ); elsereturn freq[item]; } Running time: Constant time Lecture 12

  10. Motivation for a Different Implementation • Suppose instead of grading in the range 0..100, we were to grade in the range 0..100,000, but there are no more than 350 students in the class. • Then the declaration // Let histogram be represented by an NatMultiset. NatMultiset hist = new NatMultiset(100000); would lead to an array of length 100,001. • Shortcomings: • Large amount of space • Space utilization is very sparse • The multiplicity “read-out” takes on the order of a 100,001 steps to look at each element of the array. • Because class NatMultiset provides information hiding, its implementation can be changed without affecting its client’s code. Lecture 12

  11. Second Implementation of natMultset currentSize maxSize list • Representation Invariant: The multiset elements are list[0..currentSize-1], where currentSize <= maxSize. currentSize maxSize 0 . . . ? ? ? ? ? ? publicclass NatMultiset { /* The multiset elements are list[0..currentSize-1], where currentSize <= maxSize. */ private int currentSize; private int maxSize = _______________ ; private int[] list; } Lecture 12

  12. Constructor NatMultiset (Version 2) /* Construct a NatMultiset for elements in the range 0 through maxValue. */ public NatMultiset( int maxValue ) { list = new int[maxSize______]; currentSize = 0; // Note: maxValue is ignored // in this implementation. } Running time: Proportional to maxSize Lecture 12

  13. Method insert (Version 2) /* Insert item into the multiset; throw RuntimeException if out of space. */ publicvoid insert(int item) { if ( currentSize==maxSize ) thrownew RuntimeException( "NatMultiset: too many distinct elements” ); else { list[currentSize] = item; currentSize++; } } Running time: Constant time Lecture 12

  14. Method isElement (Version 2) /* Return true if the multiset contains 1 or more instances of item. */ public boolean isElement(int item) { int k; /* Let k be index of leftmost occurrence of item in list, or currentSize if item isn't in list. */ list[currentSize] = item; k = 0; while ( list[k] != item ) k++; return k != currentSize; } Running time: Worst case proportional to currentSize Lecture 12

  15. Method delete (Version 2) /* Delete one instance of item from the multiset, if there is one. */ publicvoid delete(int item) { int k; /* Let k be index of leftmost occurrence of item in list, or currentSize if item isn't in list. */ list[currentSize] = item; k = 0; while (list[k] != item) k++; if ( k!=currentSize ) { list[k] = list[currentSize-1]; currentSize--; } } Running time: Worst case proportional to currentSize Lecture 12

  16. Method multiplicity (Version 2) /* Return the number of occurrences of item in the multiset. */ publicint multiplicity(int item) { if ( item < 0 || item >= maxValue ) thrownew RuntimeException( ”NatMultiset: item out of range” ); else { int count = 0; for (int k=0; k < currentSize; k++) if ( list[k]==item ) count++; return count; } } Running time: Proportional to currentSize Lecture 12

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