1. Search - CIS 1068 Program Design and Abstraction
Zhen Jiang
CIS Dept.
Temple University
1050 Wachman Hall, Main Campus
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2. 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
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3. 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)
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4. 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
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5. 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
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6. For instance Price is right (click on this link to try)
To see if you can get the price quickly…
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7. 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
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8. # 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
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9. 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.
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10. 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!
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11. 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
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12. 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.
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13. 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.
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14. 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
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15. 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
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16. 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); }
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17. 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)); }
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18. Implement a binary search method in your Business class
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19. 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
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20. 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)
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21. Little O notation T(n) = o(n2) tells that T grows much slower than n2.
T(n) = o(g(n))
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22. 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:
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23. 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:
******
* *
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24. 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: * **
***
****
*****
******
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25. 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);
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26. 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 ( )
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