CSCI 51 Introduction to Programming March 12, 2009

Finding Pairs How do you pick which ones are pairs? Remember, a computer can only compare two things at a time.

Finding Pairs ind1ind2 Does Die at ind1 equal Die at ind2? int len = dice.getNumDice(); for (int ind1 = 0; ind1<len-1; ind1++) { // save face value of Die at ind1 for (int ind2 = ind1+1; ind<len; ind2++) { // save face value of Die at ind2 // compare face values -- if match -> print } length of array? 5

Equality Die die1 = dice.getDie(ind1); Die die2 = dice.getDie(ind2); if (die1.getFace() == die2.getFace()) if (die1.equals(die2)) public boolean equals (Die otherDie) { if (getFace() == otherDie.getFace()) { return true; } return false; } in Die class

New Stuff Searching arrays for a particular value –reference: Ch 11 Sorting arrays –makes searching for a particular value easier (and quicker) –reference: Ch 12

Searching Arrays Find one particular element in an array of many elements Find several particular elements in an array of many elements Complexity (How Long To Search?) –find a parking space - linear –look up a word in a dictionary - complex 500K+ words in OED – search - very complex over 3 trillion web pages

Linear Searching Given a test value and a list of values –list can be ordered or unordered –loop through the list repeatedly ask: Is this a match? quit when the answer is yes (use break stmt) –if you finish all items, there is no match Inefficient –worst time to search is ~ length –average time to search is ~ length/2 Relatively easy to program

// Linear search of unordered list of integers // unordered list int[] list = {17, 14, 9, 23, 18, 11, 62, 47, 33, 88}; // look for this value in the list int searchFor = 33; // Loop thru list until we find match int foundAt = -1; // where found (default) for (int index = 0; index < list.length; index++) { if (list[index] == searchFor) { foundAt = index; break;// jump out of the loop } // foundAt is now index of item “searchFor” // or -1 if not found

// Linear search of unordered list of Strings // unordered list String[] list = {“Bart”, “Homer”, “Marge”, “Lisa”, “Maggie”, “Millhouse”}; // look for this value in the list String searchFor = “Maggie”; // Loop thru list until we find match int foundAt = -1; // where found (default) for (int index = 0; index < list.length; index++) { if ( list[index].equals(searchFor) ) { foundAt = index; break;// jump out of the loop } // foundAt is now index of item ``searchFor’’ // or -1 if not found

Binary Search Requires ordered (sorted) list Set searchRange to the entire list Repeat: –pick a “test value” in the middle of searchRange –if test value == value searching for Stop! –if test value > value searching for searchRange = lower half of searchRange –if test value < value searching for searchRange = upper half of searchRange

Example Looking for 46 Trial

Notes on Binary Searches List must be ordered (sorted) –can maintain a list in ordered fashion Much more efficient than linear –in example, took 3 iterations instead of 13 –time ~ log 2 (listLength) –linear worst case ~ listLength average ~ listLength/2 –for 100K words: 17 iterations versus 50,000 More complex to program

Searching Things To Know Be able to recognize and write a linear search Understand its pros and cons Know the concepts of a Binary Search

Questions How many comparisons are needed to determine if the following items are in the list of 10 items? linear searchbinary searchnumber (49, 10, 17) (49, 85, 92, 98) (49, 10, 2) (3, if know list sorted)

Sorting Put elements of an array in some order –alphabetize names –order grades lowest to highest Three simple sorting algorithms –selection sort –insertion sort –bubble

Selection Sort Sorts by putting values directly into their final, sorted position For each position in the list, the selection sort finds the value that belongs in that position and puts it there

Selection Sort General Algorithm Scan the list to find the smallest value Exchange (swap) that value with the value in the first position in the list Scan rest of list for the next smallest value Exchange that value with the value in the second position in the list And so on, until you get to the end of the list

Selection Sort At Work SORTED!

Selection Sort Sorts in ascending order Can be changed to sort in descending order –look for max instead of min

Insertion Sort Like we’d actually sort things Insert each new item into an already sorted list Each unsorted element is inserted at the appropriate spot in the sorted subset until the list is ordered

Insertion Sort General Algorithm Sort the first two values (swap, if necessary) Repeat: –insert list’s next value into the appropriate position relative to the first ones (which are already sorted) Each time insertion made, number of values in the sorted subset increases by one Other values in array shift to make room for inserted elements

Insertion Sort At Work SORTED!

Insertion Sort Outer loop controls the index in the array of the next value to be inserted Inner loop compares the current insert value with values stored at lower indexes Each iteration of the outer loop adds one more value to the sorted subset of the list, until the entire list is sorted

Bubble Sort "bubble" –largest values bubble to the end –smallest values sink to the beginning Idea –go through the list and swap neighboring items if needed Pros –easy to understand and code Cons –horribly inefficient (listLength 2 )

Bubble Sort At Work SORTED!

Sort Implementations All three use double (nested) loops Selection and insertion –an outer loops scans all elements –an inner loop scans and switches/inserts as needed Bubble –an outer loop repeats until no swaps are needed –an inner loops scans and swaps as needed

Sorting Things To Know Be able to recognize and follow an insertion sort, selection sort, and bubble sort Understand their pros and cons Know that many other sorts exist with varying efficiency and programming difficulty Sorting animations (in Java of course!)

Question Given the operation of the following sort, identify the type of sort (selection, insertion, or bubble) original pass 1 pass 2 pass 3 pass 4 pass 5 SORTED

Question Given the operation of the following sort, identify the type of sort (selection, insertion, or bubble) original pass 1 pass 2 pass 3 pass 4 SORTED

Sorting Things Other Than Numbers characters –same as integers (compare with ) Strings –use the built-in compareTo method Other Objects –we write a compareTo method –use the compareTo method