Binary Search and Merge Sort

• The reason we have looked at recursion is to discuss recursive algorithms.
• Two of these are merge sort and binary search.
• Binary Search
  • A phone-book search.
  • Requires the array to be sorted.
  • Basic Idea

    • BSearch(data, start, end, key)
          if the start is greater than the end
              return false
          otherwise
              find the middle
              if the key is at the middle item return true.
              else if the key is less than the middle item , search the lower end of the array
              else  search the higher end of the array 

  • Performance of binary search is $O(log_2(n))$
  • This is much faster than $O(n)$
• Merge Sort
  • The idea is

  • MergeSort(data, start, end)
        Split the array into two parts.
        Sort the two smaller parts.
        Merge the two arrays 

  • Merge is not too bad

  • Merge(ary1, size1, ary2, size2, dest)
        while there is data in both ary1 and ary2
           append the smallest to dest
        If there is data left in ary1
           append this to dest
        If there is data left in ary2
           append this to dest
         

  • This is $O(n\times log_2(n))$
  • This is MUCH faster than $O(n^2)$