5/31/2006. Last Time. Announcements. Today. Variable Scope. Variable Lifetime. Variable Scope - Cont. The File class. Assn 3 due this evening.

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1 Last Time Announcements The File class. Back to methods Passing parameters by value and by reference. Review class attributes. An exercise to review File I/O, look at passing by reference and the use of class attributes. Assn 3 due this evening. Final Exam on June 15, 9am. Room TBA. Lecture exercise solution from Tuesday is posted. Assn 4 posted later today. ing String s! Spring 2006 CISC101 - Prof. McLeod 1 Spring 2006 CISC101 - Prof. McLeod 2 Today Variable scope and lifetime. (leftover from Tuesday) ing Variable Scope A variable can be declared in five different places, all within a class, from innermost to outermost: Inside a block ({}), which is contained within a method. Inside a for statement. Inside a method, but not inside another block. Inside a parameter list. Inside a class, at the same level as the methods. A variable is not known outside its scope - it is as if the variable were not even declared. Spring 2006 CISC101 - Prof. McLeod 3 Spring 2006 CISC101 - Prof. McLeod 4 Variable Scope - Cont. Remember: That it is wasteful to declare a variable inside a loop. If a loop counter is declared in the for statement itself, it is not available outside the loop. If you try to access the value of a variable outside its scope, you will get an error. The same variable name cannot be used twice in the same scope. So you cannot declare the same variable name in an inner block, when it already exists in an outer block. The same variable name can be used in separate (not overlapping) scopes. - Be careful with this as it can cause confusion! Variable Lifetime Also called duration. When the execution of a program moves out of the scope of a non-static variable, it s lifetime is over. In Java, it is garbage collected automatically. A static variable or method persists in memory after its first use and is not garbage collected until the program is complete. Only class attributes and methods can be called static. Spring 2006 CISC101 - Prof. McLeod 5 Spring 2006 CISC101 - Prof. McLeod 6 1

2 ing - Overview Suppose you have a collection of things why would you want to sort them? Imagine a telephone book that was not in order! The first step in sorting is to select the criteria used for the sort and the direction of the sort. It could be ascending numeric order, or alphabetic order by last name, etc. Spring 2006 CISC101 - Prof. McLeod 7 Spring 2006 CISC101 - Prof. McLeod 8 The next step is to decide which of the dozens of available sorting algorithms is most appropriate. Issues: How large is the dataset? What will be critical: memory usage or execution time? Is it necessary that a new element be inserted in order or can it be added at the end and the sort deferred? How often will the algorithm be asked to sort a dataset that is already in order, except for a few newly added elements? Or, will it always have to re-sort a completely disordered dataset? Will the dataset initially be in random order or will it have some order to start with? Spring 2006 CISC101 - Prof. McLeod 9 Spring 2006 CISC101 - Prof. McLeod 10 If the dataset is small (< 1000?) then it is often just as easy to stick with a simple sorting algorithm since it will be easier to code and debug, and not too memory intensive. ing algorithms can be compared on the basis of: The number of comparisons for a dataset of size n, The number of data movements ( swaps ) necessary, and How these measures change with n (Analysis of Complexity ). Spring 2006 CISC101 - Prof. McLeod 11 Often need to consider the above values for best case (data almost in order), average case (random order), and worst case (reverse order). Some algorithms behave the same regardless of the state of the data, and others do better depending on how well the data is initially ordered. Spring 2006 CISC101 - Prof. McLeod 12 2

3 If sorting simple values like integers or key values, then comparisons are easy to carry out and the comparison efficiency of the algorithm may not be as important as the number of data movements. However, if strings or objects are being compared then the number of comparisons would be better kept to a minimum. Finally, the only real measure of what algorithm is the best is an actual measure of elapsed time. The initial choice can be based on theory alone, but the final choice for a time-critical application must be by actual experimental measurement. Spring 2006 CISC101 - Prof. McLeod 13 I will be presenting code samples that sort arrays of integers (int[] A) into ascending order because this is easiest to understand. However the logic of the algorithm can be applied directly to arrays or lists of objects, provided the search criteria are specified. Descending order usually only requires that you change the comparison from > to <. Spring 2006 CISC101 - Prof. McLeod 14 Aside: ing Code on Slides The code I will show is fairly compact (to run quickly and fit on a slide!). Coding style may be a bit compromised It uses A for the variable name for an array of ints that s normally not a great variable name to use but it is short! There are many ways of expressing these algorithms in code, but you can always tell which algorithm it is! Spring 2006 CISC101 - Prof. McLeod 15 Simple ing Algorithms Insertion Probably the most instinctive kind of sort: Find the location for an element and move all others up one, and insert the element. Pseudocode: Loop through array from i=1 to array.length-1, selecting element at position i = temp. Locate position for temp (position j, where j <= i), and move all elements above j up one location Put temp at position j. Spring 2006 CISC101 - Prof. McLeod 16 Simple ing Algorithms Insertion Cont. public static void insertion (int[] A) { int temp; int i, j; for (i=1; i < A.length; i++) { temp = A[i]; for (j=i; j>0 && temp < A[j-1]; j--) A[j] = A[j-1]; A[j] = temp; } // end for } // end insertion Spring 2006 CISC101 - Prof. McLeod Spring 2006 CISC101 - Prof. McLeod 18 3

4 This one works by selecting the smallest element and then putting it in its proper location. Pseudocode: Loop through the array from i=0 to one element short of the end of the array. Select the smallest element in the array range from i plus one to the end of the array. Swap this value with the value at position i. First, a swap method that will be used by this and other sorts: public static void swap(int[] A, int pos1, int pos2) { int temp = A[pos1]; A[pos1] = A[pos2]; A[pos2] = temp; } // end swap Spring 2006 CISC101 - Prof. McLeod 19 Spring 2006 CISC101 - Prof. McLeod 20 public static void selection(int[] A) { int i, j, least; for (i = 0; i < A.length-1; i++) { least = i; for (j = i+1; j < A.length; j++) if (A[j] < A[least]) least = j; if (i!= least) swap(a, least, i); } // end for } // end selection Spring 2006 CISC101 - Prof. McLeod Spring 2006 CISC101 - Prof. McLeod 22 Cont. The selection sort is swap efficient, and the insertion sort can be efficient for datasets that are mostly in order. Is best envisioned as a vertical column of numbers as bubbles. The larger bubbles gradually work their way to the top of the column, with the smaller ones pushed down to the bottom. Pseudocode: Loop through array from i=0 to length of array. Loop down from the last element in the array to i. - Swap adjacent elements if they are in the wrong order. Spring 2006 CISC101 - Prof. McLeod 23 Spring 2006 CISC101 - Prof. McLeod 24 4

5 Cont. public static void bubble(int[] A) { int i, j; Cont. Note that both the comparison and the swap are inside the inner loop (yuk!). for (i=0; i < A.length; i++) for (j = A.length-1; j > i; j--) if (A[j] < A[j-1]) swap(a, j, j-1); } // end bubble Spring 2006 CISC101 - Prof. McLeod 25 Spring 2006 CISC101 - Prof. McLeod 26 A Slight Improvement public static void bubble(int[] A) { int i, j; boolean isdone = false; for (i=0; i < A.length &&!isdone; i++) { isdone = true; for (j = A.length-1; j > i; j--) if (A[j] < A[j-1]) { swap(a, j, j-1); isdone = false; } } } // end bubble Cont. Possibly the simplest sorting algorithm to code. (If you have to commit one to memory, this is it!) Also the slowest sorting algorithm! On average, bubble sort makes n times more moves than selection or insertion sort. Spring 2006 CISC101 - Prof. McLeod 27 Spring 2006 CISC101 - Prof. McLeod Comparing s Based on sorting a given number of int values between 0 and 1,000,000, on my laptop (a Pentium 4 with XP, using Eclipse). Timings obtained with System.currentTimeMillis() (see code) Spring 2006 CISC101 - Prof. McLeod 29 Spring 2006 CISC101 - Prof. McLeod 30 5

6 Time (msec ing Execution Times With Random Data Dataset Size Insertion Selection Bubble Best is insertion followed by selection, and worst is bubble sort. The sorting times actually increase as the square of the size of the dataset. With more experiments: Bubble sort is always the worst!! Insertion sort works best with data that is almost in order, but not quite as well as selection sort for reverse order data. Selection sort does not care about the state of the data. Spring 2006 CISC101 - Prof. McLeod 31 Spring 2006 CISC101 - Prof. McLeod 32 Remember our bin sort from assignment 2? How does it measure up? ing Execution Times With Random Data And, let us include another algorithm called Quicksort used by Arrays.sort(). (More about Arrays.sort() in a moment ) Time (msec Insertion Selection Bubble Binsort Quicksort Dataset Size Spring 2006 CISC101 - Prof. McLeod 33 Spring 2006 CISC101 - Prof. McLeod 34 Aside - ing in java.util That s a very dramatic difference! What is going on here? Any ideas as to why binsort is so fast? What is the limitation of binsort why not use it to sort everything? What about this other sort Quicksort? Spring 2006 CISC101 - Prof. McLeod 35 Java provides canned sorting methods for arrays. The java.util.arrays class has static methods for arrays of each of the primitive types (except boolean). For example, the methods for arrays of integers are: public static void sort(int[] a) public static void sort(int[] a, int first, int last) Spring 2006 CISC101 - Prof. McLeod 36 6

7 ing in java.util Cont. The latter method call is used to sort a range in the array a. So, a command like Arrays.sort(A); will sort the array A in ascending order. (Assuming you have done an import java.utils.arrays; ) Spring 2006 CISC101 - Prof. McLeod 37 ing in java.util Cont. You are not responsible for this: All of these Arrays.sort() sorting methods utilize a Quicksort algorithm. Quicksort is a recursive algorithm. Its speed of execution increases as nlog(n), where n is the size of the dataset (as opposed to n 2 for out simple sorts, or n for binsort). See the next slide for a Quicksort method: Spring 2006 CISC101 - Prof. McLeod 38 public static void quick (int[] A, int first, int last) { int lower = first + 1; int upper = last; swap(a, first, (first+last)/2); int pivot = A[first]; while (lower <= upper) { while (A[lower] < pivot) lower++; while (A[upper] > pivot) upper--; if (lower < upper) swap(a, lower++, upper--); else lower++; } swap(a, upper, first); if (first < upper - 1) quick(a, first, upper-1); if (upper + 1 < last) quick(a, upper+1, last); } // end quick(subarrays) Spring 2006 CISC101 - Prof. McLeod 39 ing Animations For a collection of animation links see: Here are a couple that I liked: Spring 2006 CISC101 - Prof. McLeod 40 7