Searching Algorithms
The Search Problem
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 of the value in the data.
e.g., return index = 2
The Search Problem
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
Linear Search Algorithm
# Input: Array D, integer key
# Output: first index of key in D,
# or -1 if not found
For i = 0 to last index of D:
if D[i] equals key:
return i
return -1
Linear Search for Phone Numbers
# 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
Exercise
1.
Implement a class called Business that
includes fields for name, address, and phone
number, plus a constructor and accessor
methods.
2.
Create a class called YellowPages that stores a
set of Business objects in an array.
3.
Write a LinearSearch method for the
YellowPages class that finds the index of a
Business, given its phone number.
Binary Search
What happens if our array is huge?
Imagine finding a particular word on the Web
(approximately 100,000,000,000 documents)
Linear search would take a long time
Two common faster search techniques are:
Indexing (used on the Web and in databases)
Binary search
We’ll discuss binary search because it’s simpler, but you
can learn about indexing in later CIS classes
An Example Search Problem
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’.
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.
Binary Search: Normal Phone Book Use
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.
Binary Search Example
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:
-15
left
-7
-6
-2
D[mid] < key
Comparison:
0
8
mid
left
10
D[mid] = key!
29
mid
31
40
right
Binary Search Algorithm
# Input:
# Output:
Sorted Array D, integer key
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]:
right = middle -1
else:
left = middle + 1
return -1
// b/c D is sorted
You guessed it: Exercise
Implement a binary search method in your
Business class
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
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
Arrays.binarySearch
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);
Binary Search: What you should know
The requirements for it to work (array is
sorted)
How to simulate it on an example array
1.
2.
3.
4.
5.
That is, what sequence of indexes are compared
with the key for a specific input key?
Write the algorithm for it
Advantages and Disadvantages compared
with linear search
How to use Arrays.binarySearch()
Exercise
Modify your Business class so that the
Arrays.sort() method will work on it
What are the two things you need to do?
Declare that the class implements the
Comparable interface
Implement the compareTo() method
Make it sort the Businesses according to
phone number
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