CS 211: Binary Search and Sorting

Transcription

1 CS 211: Binary Search and Sorting Chris Kauffman Week 13-2

2 Front Matter Deliverables P6 Up, Due Sunday Test Cases Later today Reading BJP: Ch 13 on Searching and Sorting Lab 13: Quiz/Task (Last one) Schedule Exam 2 back today 4/20 W13 Linear/Binary Search, Sorting 4/27 W14 Sorting, Stack/Queue 5/4 W15 Review Mon 5/4 12-1:15pm Last day for Sec 2 (Review) Tue 5/5 3-4:15pm Makeup day for Sec 4 (Review) Wed 5/6 2-4:30pm Special review office hours Thu 5/7 1:30-4:15pm Sec 4 (T/R) Final Exam Mon 5/11 10:30-1:15pm Sec 2 (M/W) Final Exam

3 Exam 2 Results Stat Val Count 95 Min Max Mean Median Stddev Range Count

4 Searching Arrays for Numbers Linear Search How does it work? What assumptions does it make? Is it fast? Can it be generalized? Binary Search How does it work? What assumptions does it make? Is it fast? Can it be generalized?

5 Binary Search: Iterative // Iterative // Use binary search to locate integer key in array a public static int binarysearch(int a[], int key){ int left=0, right=a.length-1; int mid = 0; while(left <= right){ mid = (left+right)/2; if(key == a[mid]){ return mid; else if(key < a[mid]){ right = mid-1; else{ left = mid+1; return -1;

6 Binary Search: Recursive // Easy-to-use recursive version which calls a helper public static int binarysearchr(int a[], int key){ return binarysearchr(a,key,0,a.length-1); // Helper method which does work of searching public static int binarysearchr(int a[], int key, int left, int right){ if(left > right){ return -1; int mid = (left+right)/2; if(key == a[mid]){ return mid; else if(key < a[mid]){ return binarysearchr(a,key,left,mid-1); else{ return binarysearchr(a,key,mid+1,right);

7 Generalizing Binary Search What would change in the following version? // Use binary search to locate String key in an array a public static int binarysearch(string a[], String key)

8 Generalized Searching and Sorting In the java library: interfaces Comparable / Comparator interface Comparable<T> Has function int compareto(t y) if(x.compareto(y) < 0){... x.compareto(y): Returns "x minus y" Negative for x before y 0 for equal Positive for x after y Note: Not always -1/0/+1: why not? interface Comparator<T> Has compare(t x,t y): Returns "x minus y" Neg/0/Pos numbers for ordering Comparator<String> cmp =...; if( cmp.compare(x,y) < 0){...

9 Generalized Binary Search Adapt String version of binary search to public static <T extends Comparable<T>> int binarysearch(t a[], T key){ Works with any Comparable thing: String, Integer, Person

10 Generalized Library methods Arrays and Collections methods use both of these to search and sort: sort() and binarysearch() From Arrays // Objects Must be comparable to one another public static int binarysearch(object[] a, Object key) // Use a comparator foor comparisons public static <T> int binarysearch(t[] a, T key, Comparator<? super T> c) // Uses compareto of comparable static void sort(object[] a) // Uses comparator static <T> void sort(t[] a, Comparator<? super T> c)

11 Comparable Exercise Person Write a class Person which implements the Comparable interface class Person implements Comparable<Person>{ public Person(String first, String last); public String tostring(); public int compareto(person other); Must have last method to satisfy Comparable interface Sort by last name then first name String already has a compareto so this is easy Try this with Generalized Binary Search

12 Speed Start thinking about the speed differences between Linear Search and Binary Search When is linear search better? When is binary search better?

13 Sort For binary search to work, must have sorted input How do I get ints or Strings or anything else sorted? What do you know so far about sorting? What you should know as Computer Scientist

14 Selection Sort Dead simple sorting Repeatedly look for the minimum element in right part of array Swap min element with last element of left part of array public static void selectionsort(int[] a) { for (int i = 0; i < a.length - 1; i++) { int smallest = i; for (int j = i + 1; j < a.length; j++) { if (a[j] < a[smallest]) { smallest = j; swap(a, i, smallest); public static void swap(int[] a, int i, int j) { int temp = a[i]; a[i] = a[j]; a[j] = temp;

15 Demonstration of Selection Sort a = [ 19, 8, 12, 2, 14, 6, 13, 7, 42, 11] Outer i = 0, smallest = 0 Inner j = 1, smallest = 1 j = 2, smallest = 1 j = 3, smallest = 3 j = 4, smallest = 3... j = 9, smallest = 3 swap(a, i,smallest) a = [ 2, 8, 12, 19, 14, 6, 13, 7, 42, 11] Outer i = 1, smallest = 1 Inner j = 2, smallest = 1 j = 3, smallest = 1 j = 4, smallest = 1 j = 5, smallest = 5... swap(a, i,smallest) a = [ 2, 6, 12, 19, 14, 8, 13, 7, 42, 11] Show the next few outers iterations

16 Insertion Sort Input/Output input: Array A output: Nothing side-effect: A is sorted Pseudocode Premise suppose A[0] to A[i-1] are sorted insert A[i] Shift elements until proper location is found Now A[0] to A[i] are sorted for i = 1 to length(a)-1 { m = i while( m > 0 and A[m-1] > A[m] ) { swap(a[m-1],a[m]) m = m - 1

17 Insertion Sort Pseudocode input: Array A output: Nothing side-effect: A is sorted for i = 1 to length(a)-1 { m = i while( m > 0 and A[m-1] > A[m] ) { swap(a[m-1],a[m]) m = m - 1 Visualize Try static void insertsort(int arr[])

18 How Long Will it Take? Input Array of length n We decided linear search can take n steps How about binary search? How about insertion sort? Can we do better?

19 Asymptotic Speed Array of size n Search Sort Linear search: O(n) Binary search: O(log n) Hash tables: O(1) Insertion sort: O(n 2 ) Merge sort: O(n log n) Quick sort: O(n log n) Radix sort: O(n)

20 Search and Sort Tons of CPU time is used searching and sorting stuff Many, many algorithms for both Different properties, particularly complexity CS 211: Start basic discussions CS 310: Framework for analysis CS 483: Analyze detailed aglorithms