Sorting and Searching

Sorting and Searching Pepper

Common Collection and Array Actions • Sort in a certain order • Max • Min • Shuffle • Search • Sequential (contains) • Binary Search – • assumes sort, faster

Static Method Tools Classes • Arrays • binarySearch (array, value) • sort(array) • Collections • binarySearch (list, value) • shuffle(list) • sort(list) • max(list) • min(list)

Sorting – need order • Comparable interface • Only one order – chosen as natural order • Implemented inside order • Implements Comparable<T> • int compareTo (SelfType o) • int compareTo (Object o) • Compare this item to the parm • Used automatically by Collections sort • Used automatically by TreeMap and TreeSet

Sorting – Custom Order • Comparator • Custom order • Independent of the object's definition • Uses 2 objects and compares them • int compare (Selftype s1, Selftype s2) • No this • just 2 input objects to compare • Implements comparator<T> • Outside the class being sorted • Why • Collections sort can use it • TreeSet can use it • TreeMap can use it

The Comparator Interface • Syntax to implement • public class lengthCom implements Comparator<String>{ • public int compare(String s1, String s2){ • Return s1.length() = s2.length(); }} • Sorted list: dog, cat, them, bunnies

How to use the Comparator • Collections sort can take in a comparator • Passed to methods as an extra parm • Object passed into Collections.sort • Ex: Collections.sort(myarray, new myArraySorter()) • Use • Arrays.sort(stringArray, new lengthCom()); • Collections.sort(stringList, new lengthCom()); • new TreeSet<String> (new lengthCom());

Stock Comparators • String • CASE_INSENSITIVE_ORDER • Collections • reverseOrder() – returns comparator • reverseOrder(comparator object) • Returns opposite order of comparator • Use • Collections.sort(myStringList, CASE_INSENSITIVE_ORDER) • Collections.sort(myStringList, Collections.reverseOrder(new lengthCom()))

Searching and Sorting • Complexity measuring • Search algorithms • Sort algorithms

Complexity Measurements • Empirical – log start and end times to run • Over different data sets • Algorithm Analysis • Assumed same time span (though not true): • Variable declaration and assignment • Evaluating mathematical and logical expressions • Access or modify an array element • Non-looping method call

How many units – worst case: • Sample code – find the largest value var M = A[ 0 ]; //lookup 1, assign 1 for ( var i = 0; i < n; i++) { // i = o 1; test 1 // retest 1; i++ 1; if ( A[ i ] >= M ) { // test 1 ; lookup 1 M = A[ i ];}} // lookup 1, assign 1 4 + 2n + 4n F(n) = 4 + 2n + 4n = 4 + 6n Fastest growing term with no constant: F(n) = n (n is your array size) http://discrete.gr/complexity/

Practice with asymptote finding – no constant • f( n ) = n2 + 3n + 112 gives f( n ) = n2 • f( n ) = n + sqrt(n) gives f( n ) = n • F(n) = 2n + 12 gives f(n) = 2n • F(n) = 3n + 2n gives f(n) = 3n • F(n) = 3n + 2n gives f(n) = 3n • Just test with large numbers

Practice with asymptote finding (dropping constant) • f( n ) = 5n + 12 gives f( n ) = n. • Single loop will be n; • called linear • f( n ) = 109 gives f( n ) = 1. • Need a constant 1 to show not 0 • Means no repetition • Constant number of instructions

Determining f(n) for loops for (i = 0; i < n; i++) for (j = 0; j < n; j++) for (k = 0; k < n; k++) System.out.println(a[i][j][k]);}}} F(n) = n3

Big O Notation – Growth Rate • F(n) = n3 gives Big O Notation of O( n3 ) • Which will be slower than O(n) • Which will be slower than O(1)

Searching • Sequential : • Go through every item once to find the item • Measure worst case • 0(N)

Binary Search • First Sorted • Dictionary type search – keep looking higher or lower • Takes 0 seconds, but cannot be O(1) because it has a loop • As input grows, number of times to divide min-max range grows as: • 2repetitions is approximately the Number of elements in the array • So, repetitions = log2N - O(log2 N)

Binary Search code public static int findTargetBinary(int[] arr, int target){ int min = 0; int max = arr.length - 1; while( min <= max) { int mid = (max + min) / 2; if (arr[mid] == target){ return mid; } else if (arr[mid] < target) { min = mid + 1; } else { max = mid - 1; } } return -1; }

Selection Sort • Find the smallest value's index • Place the smallest value in the beginning via swap • Repeat for the next smallest value • Continue until there is no larger value • Go through almost every item in the array for as many items as you have in the array • Complexity: O (N2)

Bubble Sort • Initial algorithm Check every member of the array against the value after it; if they are out of order swap them. As long as there is at least one pair of elements swapped and we haven’t gone through the array n times: If the data is in order, it can be as efficient as O(n) or as bad as O(n2)

Merge Sort • Two sorted subarrays can quickly be merged into a sorted array. • Divide the array in half and sort the halves. • Merge the halves. • Picture: http://www.java2novice.com/java-sorting-algorithms/merge-sort/ • Video: http://math.hws.edu/TMCM/java/xSortLab/

Merge Sort Complexity • Split array in half repeatedly until each subarray contains 1 element. • 2repetitions is approximately the Number of elements in the array • So, repetitions of division= log2N • O(log N) • At each step, do a merge, go through each element once • O(N) • Together: O (N log2 N)

Comparison speed • Sequential Search - O(N) • Binary Search - O(log2 N) • Selection Sort - O(N2) • Bubble Sort - O(N2) • Merge Sort - O (N log2 N) • https://www.ics.uci.edu/~eppstein/161/960116.html

Summary • Relative complexity – O Notation • Arrays and Collections class • Different Search methods • Sequential Search – keep looking one by one • Binary Search – dictionary type split search • Different Sort methods • Selection Sort – look through all to find smallest and put it at the beginning – repeatedly • Bubble Sort – continual swapping pairs – repeatedly • Merge Sort - continually divide and sort then merge

Sorting and Searching