ECE 242 Spring 2003 Data Structures in Java

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ECE 242 Spring 2003Data Structures in Java

• http//rio.ecs.umass.edu/ece242
• Search
• Prof. Lixin Gao

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Todays Topics

• Applications
• Sequential Search
• Binary Search
• Implemented by while loop
• Implemented by recursion

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Applications

• Search is used everywhere in our daily life.
• Search telephone number in telephone book
• Search grade for Project 3 on ECE242 website
• Search course schedule on registration guide
• Search flight schedule on airline
• Anything else?
• Search is performed the most often in database

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Search
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A set of records are stored in array, linked
list, or others. Given a target key, find the
record(s) that have the same key.
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13
target
4
?
8
3
8
5
2
3
1
2
A
head
B
C
1
2
3
B
target
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Key
Find the student whose ID 8
ID
NAME
SCORE
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5
4
?
3
2
target
1
8
The key is the field in your record that is used
for searching. In the above example, student ID
is the key.
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Search Algorithm

• A step-by-step description of how to solve the
  search problem
• Some search algorithms
• sequential search
• binary search

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Sequential Search

• A simple search algorithm
• compare the target key to the key of records one
  by one starting from the first record
• Easy to implement for Array and Linked List

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Sequential Search For Array

• An Array db which stores integer numbers
• Searching 8 in this array
• If found, return index
• Otherwise, return 1

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Pseudo-code of Sequential Search For Array

• int SequentialSearch( int key, int db )
• int index
• for( index0 indexltdb.length index )
• if( dbindexkey )
• return index
• return 1

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5
13
target
4
?
8
3
8
5
2
3
1
2
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Sequential Search For Linked List

• Sequential Search also works for Linked List
• An Linked List db, in which each node stores a
  string
• Searching B in this list
• If found, return that node
• Otherwise, return null

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Pseudo-code of Sequential Searching For Linked
List

• DNode SequentialSearch( String key, SLList db )
  
• DNode probe db.head
• while ( probe!null )
• if( probe.value.equals(key) )
• return probe
• probe probe.next
• return null

B
target
A
head
B
C
1
2
3
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Complexity of Sequential Search

• Suppose there are n records
• In the best case, the target is the first entry.
  It only takes 1 step
• In the worst case, the target is the last entry,
  or it cannot be found. Sequential search has to
  scan all n records and takes totally n steps.
• Cost O(n)

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Binary Search

• If the records are sorted by the key, we can do
  better.
• Think about how you look up a word in English
  dictionary where the words are sorted
  alphabetically.
• Binary Search. (we mentioned it before)

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Binary Search

• If the target is present in the list, it must be
  one between low and high

A
B
C
M
X
Y
Z
middle12
high25
low0
Take a look at the middle one. middle
(lowhigh) / 2
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Binary Search Case 1

• Assume target is M

A
B
C
X
Y
Z
M
middle
high25
low0
If the target is the same as the key value in the
middle position, we have found the record.
Return the value of middle
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Binary Search Case 2

• Assume target is E

A
B
C
X
Y
Z
M
L
high11
low0
If target lt the key value in the middle position,
we know that it can not be found in the right
half. We only need to search in the left half.
high middle - 1
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Binary Search Case 3

• Assume target is P

A
B
C
X
Y
Z
N
M
high25
low13
If target gt the key value in the middle position,
we know that it can not be found in the left
half. We only need to search the right half.
low middle 1
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Pseudo-code of Binary Search

• int BinarySearch(char target, char array)
      int low0, high array.length-1,
  middle    while( lowlthigh)         middle
  (lowhigh)/2        if( arraymiddletarget
  )            return middle        else if(
  arraymiddlelttarget )            low middle
  1        else            high middle -
  1        return -1

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Sample Trace For Searching H

• Examples BinarySearchWhileLoop.java
• The Array is
• A B C D E F G H I J K L M N O P Q R S T
• Give me a search key H
• low0 high19 middle9 arraymiddleJ
• low0 high8 middle4 arraymiddleE
• low5 high8 middle6 arraymiddleG
• low7 high8 middle7 arraymiddleH
• Found at position 7

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Recursive Binary Search

• Main ideas compare the key value to the middle
  value
• equals, done
• less than, search the left half of the list only
• greater than, search the right half of the list
  only

M

Left half
Right half
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Code For Recursive Binary Search

• static int BinarySearch(char target, int low, int
  high, char array)
• if( targetltarraylow targetgtarrayhigh )
• return -1
• int middle (lowhigh)/2
• if( arraymiddletarget )
• return middle
• else if( arraymiddlegttarget )
• return BinarySearch(target, low,
  middle-1, array)
• else
• return BinarySearch(target,
  middle1, high, array)

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Sample Trace For Searching H

• Examples BinarySearchRecursive.java
• The Array is
• A B C D E F G H I J K L M N O P Q R S T
• Give me a search key H
• low0 high19 middle9 arraymiddleJ
• low0 high8 middle4 arraymiddleE
• low5 high8 middle6 arraymiddleG
• low7 high8 middle7 arraymiddleH
• Found at position 7

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Complexity For Binary Search

• Suppose there are n records
• In the best case, the target is the middle entry.
  It only takes 1 step
• In the worst case, it will take log2n 1 steps.
• Cost O(logN)

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What Happens In Linked List?

• Binary Search is easy to implement in Array
• What happens when searching in Linked List?
• Locate an element in linked list
• How can you get the middle node directly?
• Can not index linked list

head
A
B
C
D
E
middle node
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Motivation for Binary Tree

• In linked list, it is hard to implement binary
  search
• We need an index to each node
• Next class, we will talk about Binary Tree and
  Binary Search Tree

index
index
index
index
index
A
B
C
D
E