Binary Search

• Binary search, as we have said in the past
  • Requires the data to be sorted.
  • Is faster than sequential search
• The big idea

  • Check the "middle" data 
        if that is what you are looking for, return
        else if the middle data is smaller than what you are looking for, search the top half
        else search the bottom half. 

• By the way, this is a recursive definition
  • How do you expect to search the "top" or "bottom" half?
• Try this with

  low  high   mid          0   1   2   3   4   5
                           0   5   8   9  10  15
  
  
  
  
  
      

• More formally

  BinarySearch(A, low, high, key)
  
   found ← false
   while low ≤ high and not found
      mid ← ( low + high) / 2    
      if A[mid] = key
           found ← true
      else if A[mid] < key
           low ← mid+1
      else
           high ← mid-1
   if not found
      mid ← high+1
   return mid