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Sorting. Putting things in order. Searching and Sorting. Searching and sorting are two of the most used and most studied types of algorithms in computing In the early 70’s approximately 80% of computer usage was spent either sorting data or searching data Examples :
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Sorting Putting things in order
Searching and Sorting • Searching and sorting are two of the most used and most studied types of algorithms in computing • In the early 70’s approximately 80% of computer usage was spent either sorting data or searching data • Examples: • Searching for a login name or PIN from a database of IDs • Searching for a web site on the internet • Sorting a list of potential stock purchases based on some performance criterion • Bank statement with transactions sorted by date
Searching and Sorting • Many methods for searching/sorting; which is the “best”? • The one that is the quickest • The one that uses the least amount of memory • Can sort in ascending or descending order. • Sorting • Bubble sort • Insertion sort • Selection sort • Merge sort • Quick sort • Searching • Linear search • Binary search
Selection Sort public void selectionSort (int[] data) { for(inti=0; i<data.length; i++) { int min = indexOfMinimum(data, i); int temp = data[min]; data[min] = data[i]; data[i] = data[temp]; } } public intindexOfMinimum(int[] vals, inti) { int min = i; for (int j=i+1; j<vals.length; j++) { if (vals[j] < vals[min]) { min = j; } } return min; } int[] nums = {3, 18, -1, 12, 6, -2, 2}; selectionSort(nums);
Selection SortCan we modify to sort arrays of objects? public void selectionSort (int[] data) { for(inti=0; i<data.length; i++) { int min = indexOfMinimum(data, i); int temp = data[min]; data[min] = data[i]; data[i] = data[temp]; } } public intindexOfMinimum(int[] vals, inti) { int min = i; for (int j=i+1; j<vals.length; j++) { if (vals[j] < vals[min]) { min = j; } } return min; } String[] words = {“hello”, “jim”, “rams”, “packers”}; selectionSort(words);
Consider • How to sort a simple list? • Can we use the ‘array=based’ selection sort? void mergeSort(SimpleList<Integer> v) { if(v.size() < 2) return; SimpleList v1 = new SimpleList<Integer>(); SimpleList v2 = new SimpleList<Integer>(); v.reset(); int half = v.size()/2; while(v.hasNext()) { v1.add(v.next()); v.remove(); if(v.hasNext()) { v2.add(v.next()); v.remove(); } } mergeSort(v1); mergeSort(v2); merge(v1, v2, v); } void merge(SimpleList<Integer> v1, SimpleList<Integer> v2, SimpleList<Integer> result) { v1.reset(); v2.reset(); result.reset(); while(v1.hasNext() && v2.hasNext()) { Integer n1 = v1.next(); Integer n2 = v2.next(); if(n1 < n2) { result.add(n1); v1.remove(); v2.add(n2); } else { result.add(n2); v2.remove(); v1.add(n1); } } while(v1.hasNext()) { result.add(v1.next()); v1.remove(); } while(v2.hasNext()) { result.add(v2.next()); v2.remove(); } }
Subclassing and sorting public class SortedListextends SimpleList<Integer> { public SortedList() { super(); } public boolean add(Integer v) { int smaller = firstItemSmaller(v); if(smaller != null) { remove(); super.add(v); super.add(smaller); } else { super.add(v); } return true; } private Integer firstItemSmaller(Integer v) { reset(); while(hasNext()) { Integer val = next(); if(val < v) return val; } return null; } } SordedList list = new SortedList(); for(inti=0; i<10; i++) { int random = (int)(Math.random() * 100); list.add(random); }
Consider searching a sorted array • How to best ‘find’ an item in the array? public intindexOf(int[] data, intval) { for(inti=0; i<data.length; i++){ if(data[i] == val) return i; } return -1; } • public intindexOf(int[] data, intval) { • int min = 0; • int max = data.length-1; • while(min <= max) { • int mid = (min + max)/2; • if(data[mid] == val) return mid; • else if(data[mid] < val) min = mid; • else max = mid; • } • return -1; • }
Insertion Sort public void insertionSort (int[] x) { for (inti=1; i<x.length; i++) { intcurrentValue= x[i]; int j = i-1; while (j>=0 && x[j]>currentValue) { x[j+1] = x[j]; j--; } x[j+1] = currentValue; } }
Summary • Bubble Sort • Never useful! Don’t ever write another bubble sort routine! • Selection Sort • Somewhat slower than insertion sort. Don’t use it! • Insertion Sort • Very goodwhen an array is “almost sorted” already • Should be used in some applications and may beat quicksort! • Quick Sort • The best general purpose sorting routine. Use it! • Merge Sort • The best way to sort lists or vectors. • Generic Sorting • Use the Comparable and/or Comparator interfaces
