Searching Arrays

1
Searching Arrays

• ANSI-C

2
Searching

• Searching looking for something
• Searching an array is particularly common
• Goal determine if a particular value is in the
  array
• If the entries in the array are not in order
• start at the beginning and look at each
• element to see if it matches

3
Linear Search

• / If x appears in table0..length-1, return its
• position in the table, i.e.,
• return k so that tablekentry. If entry not
• found, return -1
• /
• int lsearch (int table , int length, int entry)
  
• int index 0
• while (index lt length tableindex ! entry)
  index index 1
• if (index gt length )
• index -1
• return index

4
Binary search

• Can we do better?
• "Binary search" works if the array is sorted
• The strategy in this case is
• 1. Look for the target in the middle.
• 2. If you dont find it, you can ignore half of
  the array, and repeat the process with the other
  half.
• Example Find first page of Pizza
• listings in the yellow pages

5
Binary Search

• / If entry appears in table0..length-1, return
  its
• location, i.e. return k so that
  tablekentry.
• If entry not found, return -1
• /
• int bsearch (int table , int length, int entry)
  
• int left
• int right
• int middle
• while ( _______________ )
• middle (left right) / 2
• if (tablemiddle lt entry)
• left middle 1
• else
• right middle - 1
• _________________

6
Binary Search

• / If entry appears in table0..length-1, return
  its
• location, i.e. return k so that
  tablekentry.
• If entry not found, return -1
• /
• int bsearch (int table , int length, int entry)
  
• int left 0
• int right length 1
• int middle
• while ( left lt right)
• middle (left right) / 2
• if (tablemiddle lt entry)
• left middle 1
• else
• right middle - 1
• _________________

7
Binary Search

• / If entry appears in table0..length-1, return
  its
• location, i.e. return k so that
  tablekentry.
• If entry not found, return -1
• /
• int bsearch (int table , int length, int entry)
  
• int left 0
• int right length 1
• int middle
• int k -1
• while ( left lt right)
• middle (left right) / 2
• if (tablemiddle lt entry)
• left middle 1
• else
• right middle - 1
• if ( left lt length tableleft entry )
• k left
• return k

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Is it worth the trouble?

• Suppose you had 1000 elements
• Linear search would require maybe 500 comparisons
  on average
• Binary search
• after 1st compare, throw away half, leaving 500
  elements to be searched.
• after 2nd compare, throw away half, leaving 250.
• Then 125, 63, 32, 16, 8, 4, 2, 1 are left.
• After at most 10 steps, youre done!
• What if you had 1,000,000 elements??