Linear and Binary Search

1
Linear and Binary Search

• Instructor Mainak Chaudhuri
• mainakc_at_cse.iitk.ac.in

2
Linear search

• class LinearAndBinarySearch
• public static void main (String arg)
• int size 20, key 23
• int array new intsize
• Initialize (array, size) // not shown
• PrintArray (array, size) // not shown
• System.out.println (Linear search
  result LinearSearch (array, key))
• System.out.println (Binary search
  result BinarySearch (array, 0, size-1,
  key))

3
Linear search

• public static int LinearSearch (int array,
  int key)
• int i
• for (i0iltarray.lengthi)
• if (arrayi key)
• return i
• return -1

4
Binary search

• public static int BinarySearch (int array,
  int start, int end, int key)
• // Pre-condition array is sorted
• // Caution binary search does not work
• // on unsorted arrays.
• int mid
• if (start gt end) return -1
• if (start end)
• if (key arraystart) return start
• else return -1
• // continued in next slide

5
Binary search

• mid (start end)/2
• if (key arraymid) return mid
• else if (key lt arraymid)
• return BinarySearch (array, start,
  mid-1, key)
• else
• return BinarySearch (array, mid1, end,
  key)
• // end class

6
Run time analysis

• Linear search in the worst case requires n
  comparisons
• Binary search in the worst case requires O(log n)
  comparisons
• Solution to T(n) T(n/2) O(1)
• Remember that binary search can be applied to
  sorted arrays only