3/18/2015. Chapter 19 Sorting and Searching SELECTION SORT SORTING AN ARRAY OF INTEGERS SORTING AN ARRAY OF INTEGERS FILE SELECTIONSORTER.

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1 Chapter 19 Sorting and Searching The Plan For Today AP Test Chapter 18 Quiz Corrections Chapter 18 Assignment Due Today Chapter : Selection Sort 19.2: Profiling the Selection Sort Algorithm 19.3: Analyzing to Performance of the Selection Sort Algorithm Ch18/19 Work Time SELECTION SORT Sorts an array by repeatedly finding the smallest element of the unsorted tail region and moving it to the front Slow when run on large data sets Example: sorting an array of integers Upcoming Exam 2 (Ch.11, 13, 18, 19) Wed. 3/25 SORTING AN ARRAY OF INTEGERS SORTING AN ARRAY OF INTEGERS Find the smallest and swap it with the first element Repeat Find the next smallest. It is already in the correct place When the unsorted portion is of length 1, we are done Find the next smallest and swap it with first element of unsorted portion FILE SELECTIONSORTER.JAVA (P.705) 02: This class sorts an array, using the selection sort 03: algorithm 04: */ 05: public class SelectionSorter 06: { 07: /** 08: Constructs a selection sorter. anarray the array to sort 10: */ 11: public SelectionSorter(int[] anarray) 12: { 13: a = anarray; 14: } 15: 16: /** 17: Sorts the array managed by this selection sorter. 18: */ FILE SELECTIONSORTER.JAVA 19: public void sort() 20: { 21: for (int i = 0; i < a.length - 1; i++) 22: { 23: int minpos = minimumposition(i); 24: swap(minpos, i); 25: } 26: } 27: 28: /** 29: Finds the smallest element in a tail range of the array. from the first position in a to compare the position of the smallest element in the 32: range a[from]... a[a.length - 1] 33: */ 34: private int minimumposition(int from) 35: { 1

2 FILE SELECTIONSORTER.JAVA 36: int minpos = from; 37: for (int i = from + 1; i < a.length; i++) 38: if (a[i] < a[minpos]) minpos = i; 39: return minpos; 40: } 41: 42: /** 43: Swaps two entries of the array. i the first position to swap j the second position to swap 46: */ 47: private void swap(int i, int j) 48: { 49: int temp = a[i]; 50: a[i] = a[j]; 51: a[j] = temp; 52: } 53: 54: private int[] a; 55: } FILE SELECTIONSORTTESTER.JAVA (P.706) 02: This program tests the selection sort algorithm by 03: sorting an array that is filled with random numbers. 04: */ 05: public class SelectionSortTester 06: { 07: public static void main(string[] args) 08: { 09: int[] a = ArrayUtil.randomIntArray(20, 100); 10: ArrayUtil.print(a); 11: 12: SelectionSorter sorter = new SelectionSorter(a); 13: sorter.sort(); 14: 15: ArrayUtil.print(a); 16: } 17: } 18: 19: FILE ARRAYUTIL.JAVA (P.707) 01: import java.util.random; 02: 03: /** 04: This class contains utility methods for array 05: manipulation. 06: */ 07: public class ArrayUtil 08: { 09: /** 10: Creates an array filled with random values. length the length of the array n the number of possible random values an array filled with length numbers between 14: 0 and n 1 15: */ 16: public static int[] randomintarray(int length, int n) 17: { FILE ARRAYUTIL.JAVA 18: int[] a = new int[length]; 19: for (int i = 0; i < a.length; i++) 20: a[i] = generator.nextint(n); 21: 22: return a; 23: } 24: 25: /** 26: Prints all elements in an array. a the array to print 28: */ 29: public static void print(int[] a) 30: { 31: for (int e : a) 32: System.out.print(e + " "); 33: System.out.println(); 34: } 35: 36: private static Random generator = new Random(); 37: } 38: FILE SELECTIONSORTTESTER.JAVA Output: Why do we need the temp variable in the swap method? What would happen if you simply assigned a[i] to a[j] and a[j] to a[i]? Dropping the temp variable would not work. Then a[i] and a[j] would end up being the same value. 2. What steps does the selection sort algorithm go through to sort the sequence ? 2

3 PROFILING THE SELECTION SORT ALGORITHM We want to measure the time the algorithm takes to execute Exclude the time the program takes to load Exclude output time Create a StopWatch class to measure execution time of an algorithm It can start, stop and give elapsed time Use System.currentTimeMillis method Create a StopWatch object Start the stopwatch just before the sort Stop the stopwatch just after the sort Read the elapsed time (P.708) 02: A stopwatch accumulates time when it is running. You can 03: repeatedly start and stop the stopwatch. You can use a 04: stopwatch to measure the running time of a program. 05: */ 06: public class StopWatch 07: { 08: /** 09: Constructs a stopwatch that is in the stopped state 10: and has no time accumulated. 11: */ 12: public StopWatch() 13: { 14: reset(); 15: } 16: 17: /** 18: Starts the stopwatch. Time starts accumulating now. 19: */ 20: public void start() 21: { 22: if (isrunning) return; 23: isrunning = true; 24: starttime = System.currentTimeMillis(); 25: } 26: 27: /** 28: Stops the stopwatch. Time stops accumulating and is 29: is added to the elapsed time. 30: */ 31: public void stop() 32: { 33: if (!isrunning) return; 34: isrunning = false; 35: long endtime = System.currentTimeMillis(); 36: elapsedtime = elapsedtime + endtime - starttime; 37: } 38: 39: /** 40: Returns the total elapsed time. the total elapsed time 42: */ 43: public long getelapsedtime() 44: { 45: if (isrunning) 46: { 47: long endtime = System.currentTimeMillis(); 48: return elapsedtime + endtime - starttime; 49: } 50: else 51: return elapsedtime; 52: } 53: 54: /** 55: Stops the watch and resets the elapsed time to 0. 56: */ 57: public void reset() 58: { 59: elapsedtime = 0; 60: isrunning = false; 61: } 62: 63: private long elapsedtime; 64: private long starttime; 65: private boolean isrunning; 66: } FILE SELECTIONSORTTIMER (P.709) 01: import java.util.scanner; 02: 03: /** 04: This program measures how long it takes to sort an 05: array of a user-specified size with the selection 06: sort algorithm. 07: */ 08: public class SelectionSortTimer 09: { 10: public static void main(string[] args) 11: { 12: Scanner in = new Scanner(System.in); 13: System.out.print("Enter array size: "); 14: int n = in.nextint(); 15: 16: // Construct random array 17: 3

4 FILE SELECTIONSORTTIMER FILE SELECTIONSORTTESTER.JAVA 18: int[] a = ArrayUtil.randomIntArray(n, 100); 19: SelectionSorter sorter = new SelectionSorter(a); 20: 21: // Use stopwatch to time selection sort 22: 23: StopWatch timer = new StopWatch(); 24: 25: timer.start(); 26: sorter.sort(); 27: timer.stop(); 28: 29: System.out.println("Elapsed time: " 30: + timer.getelapsedtime() + " milliseconds"); 31: } 32: } 33: 34: Output: Enter array size: Elapsed time: milliseconds VARIOUS SIZE ARRAYS* VARIOUS SIZE ARRAYS n Milliseconds 10, ,000 3,051 30,000 6,846 40,000 12,188 50,000 19,015 60,000 27,359 *Obtained with a Pentium processor, 1.2 GHz, Java 5.0, Linux Figure 1: Time Taken by Selection Sort VARIOUS SIZE ARRAYS Doubling the size of the array more than doubles the time needed to sort it 3. Approximately how many seconds would it take to sort a data set of 80,000 values? Four times as long as 40,000 values, or about 50 seconds. 4. Look at the graph in Figure 1. What mathematical shape does it resemble? A parabola. 4

5 ANALYZING THE PERFORMANCE OF THE SELECTION SORT ALGORITHM In an array of size n, count how many times an array element is visited To find the smallest, visit n elements + 2 visits for the swap To find the next smallest, visit (n - 1) elements + 2 visits for the swap The last term is 2 elements visited to find the smallest + 2 visits for the swap ANALYZING THE PERFORMANCE OF THE SELECTION SORT ALGORITHM The number of visits: n (n - 1) (n - 2) This can be simplified to n 2 /2 + 5n/2-3 5n/2-3 is small compared to n 2 /2, so let's ignore it Also ignore the ½, it cancels out when comparing ratios ANALYZING THE PERFORMANCE OF THE SELECTION SORT ALGORITHM The number of visits is of the order n 2 Using big-oh notation: The number of visits is O(n 2 ) Multiplying the number of elements in an array by 2 multiplies the processing time by 4 Big-Oh notation "f(n) = O(g(n))" expresses that f grows no faster than g To convert to big-oh notation: locate fastest-growing term, and ignore constant coefficient 5. If you increase the size of a data set tenfold, how much longer does it take to sort it with the selection sort algorithm? It takes about 100 times longer. 6. How large does n need to be so that n 2 /2 is bigger than 5n/2-3? If n is 4, then n 2 /2 is 8 and 5n/2-3 is 7. 5