Search - CIS 1068 Program Design and Abstraction Zhen Jiang CIS Dept. Temple University 1050 Wachman Hall, Main Campus Email: zhen.jiang@temple.edu 4/19/2017

Table of Contents Introduction to searching problem Problem statement Linear search algorithm Binary search Binary search algorithm How much fast is binary search? Search mechanics in java Summary 4/19/2017

The Search Problem Considering e.g., String str= “hello”; a sequence of characters that are contained in a string e.g., String str= “hello”; and a particular character in another string, e.g., String str2 = “l”; Find 1st appearance of such a character in the original group e.g., return str.indexOf(str2) 4/19/2017

Problem Statement Given a set of data e.g., int [] arr = {10, 2, 7, 9, 7, 4}; and a particular value, e.g., int val = 7; Find the first index/position of the value in the data. e.g., return index = 2 4/19/2017

Problem Statement, revisited: Input: A set of data (an array, ArrayList, LinkedList, …) A single data element Output: Position of the data element in the data set, or -1 if the element does not appear in the data set 4/19/2017

For instance Price is right (click on this link to try) To see if you can get the price quickly… 4/19/2017

Linear Search Algorithm (p541) # Input: Array D, integer key # Output: first index of key in D, # or -1 if not found # also called sequential search For i = 0 to last index of D: if D[i] equals key: return i return -1 4/19/2017

# Input: Array D of Business objects, # phone number key # Output: first index where key’s phone # number matches D, or -1 if not found Business: phone # address name For i:= 0 to end of D: if D[i].phone matches key: return i return -1 4/19/2017

Implement a class called Business that includes fields for name, address, and phone number, plus a constructor and accessor methods. Create a class called YellowPages that stores a set of Business objects in an array. Write a LinearSearch method for the YellowPages class that finds the index of a Business, given its phone number. 4/19/2017

Binary Search Imagine finding the price among the range up to $100,000,000 Linear search would take a long time Random guess is even worse! 4/19/2017

Two common search techniques are: Indexing (used on the Web and in databases) Imagine flipping through the Yellow Pages, looking for a pizza place near you. It’s pretty easy – you just flip to the section for ‘P’, then look for ‘Pi’, then ‘Piz’, …, ‘Pizza’. We can learn about indexing in later CIS classes Binary search We’ll discuss binary search because it’s simpler 4/19/2017

Now imagine doing the reverse: find the name of a business given just their phone number. What algorithm will find the number in the phone book? Answer: you need to use (some version of) linear search! Ugh. 4/19/2017

Normally, when you search the phone book, you implicitly use the fact that it’s sorted: The smallest element (alphabetically first element) appears first. Then the next smallest, … Then the biggest (alphabetically last) element. Binary search does the same thing, and it only works if your data (array) is sorted. 4/19/2017

29 -15 -7 -6 -2 8 10 29 31 40 left mid left mid right Step 1: Define left and right boundaries for searching Step 2: Define middle of the search region Repeat! Step 3: Compare the middle with our key Find key: 29 Comparison: D[mid] < key Comparison: D[mid] = key! -15 -7 -6 -2 8 10 29 31 40 left mid left mid right 4/19/2017

Binary Search Algorithm # Input: Sorted Array D, integer key # Output: first index of key in D, or -1 if not found left = 0, right = index of last element while left <= right: middle = index halfway between left, right if D[middle] matches key: return middle else if key comes before D[middle]: // b/c D is sorted right = middle -1 else: left = middle + 1 return -1 4/19/2017

public static int bs(int [ ] n, int first, int last, int v){ int middle; if (first > last) return -1; middle = (first + last)/2; if(n[middle] = = v) return middle; else if ( n[middle] < v) return bs(n, middle+1, last, v); else return bs(n, first, middle-1, v); } 4/19/2017

Find out what will be the print out results of the following program and trace the position (subscript value) of each access of the array n (i.e., the value of variable middle). public class ArrayRecursive { public static void main(String [ ] args){ int [ ] n = {101, 142, 147, 189, 199, 207, 222, 234, 289, 296, 310, 319, 388, 394, 417, 429, 447, 521, 536, 600}; System.out.println( “bs(”+102+“)=”+bs(n, 0, n.length-1, 102)); System.out.println( “bs(”+296+“)=”+bs(n, 0, n.length-1, 296)); System.out.println( “bs(”+289+“)=”+bs(n, 0, n.length-1, 289)); } 4/19/2017

Implement a binary search method in your Business class 4/19/2017

How much faster is binary search? Way, way faster Assuming the array is already sorted But precisely how much? For an array of size: Linear search might visit: Binary search might visit: 24 = 16 elements 4+1 = log2(16)+1 28 = 256 256 elements 8+1 = log2(256)+1 212 = 4096 4096 elements 12+1 = log2(4096)+1 2n = m elements m elements n + 1 = log2(m) + 1 4/19/2017

Big O notation Analyzing algorithms/processes for efficiency Fast? T(n) = O(n2) tells the order of n2 time complexity. n∞ T(n) = O(g(n)) c1g(n) ≤ T(n) ≤ c2g(n) Linear search T(n) and binary search T(log n) 4/19/2017

Little O notation T(n) = o(n2) tells that T grows much slower than n2. T(n) = o(g(n)) 4/19/2017

Code: Output: n=keyboard.nextInt(); // try 5! for (int i = 1; i <= n; i++) { for (int j = 1; j <= 10; j++) { System.out.print((i * j) + " "); } System.out.println(); Output: 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 20 3 6 9 12 15 18 21 24 27 30 4 8 12 16 20 24 28 32 36 40 5 10 15 20 25 30 35 40 45 50 4/19/2017

Code: Output: ****** * * n=keyboard.nextInt(); // try 6! for (i = 1; i<=n; i++) System.out.print(“*”); System.out.println(“”); for (i = 1; i <= n-2; i++) { System.out.print(“*”); for (int j = 1; j <= n-2; j++) System.out.print(“ ”); System.out.println(“*”); } Output: ****** * * 4/19/2017

Code: Output: n=keyboard.nextInt(); // try 6! for (int i = 1; i <= n; i++) { for (int j = 1; j <= i; j++) { System.out.print("*"); } System.out.println(); Output: * ** *** **** ***** ****** 4/19/2017

Java Mechanics in Java The Java class Arrays has numerous helpful methods built in, including a binary search method: public static int binarySearch(int[] a, int key): Searches the specified array of ints for the specified value using the binary search algorithm. Example: int index = Arrays.binarySearch(arr, 29); 4/19/2017

Summary The requirement for it to work (array is pre-sorted) How to simulate it on an example array That is, what sequence of indexes are compared with the key for a specific input key? Write the binary search algorithm for it Advantages and disadvantages compared with linear search (also called sequential search) How to use Arrays.binarySearch ( ) 4/19/2017