Merge Sort (10.7)

















How does Merge Sort work?

	if the size of the List is at least 2
	    split the List into the left half and the right half
	    recursively sort left
	    recursively sort right
	    merge left and right into one List
	end if



What are the contents of the left half and the right half
after the recursive calls sort each half.

	8 5 2 7 7 6 3 4



How do you merge the two sorted halves?
Show the steps of merging the two sorted halves.

















Show the steps of Merge Sort on the List.
Give the Lists after each split and merge step.

	8 5 2 7 7 6 3 4

















Classwork
You may work with a partner.

Show the steps of Merge Sort on the List.
Give the Lists after each split and merge step.

	8 5 4 6 2 3 4 1

















Merge Sort Code


mergeSort ( list ) {

  if ( list.size > 1 ) {

    split( list, left, right );

    mergeSort( left );
    mergeSort( right );

    merge( left, right, list );

  }

}

split ( list, left, right ) {

  for each item in the left half of list
     add the item to left

  for each item in the right half of list
     add the item to right

}

merge( left, right, list ) {

  while both left and right have more items
    if the left item is less than the right item
      add the left item to list
    else
      add the right item to list

  while left has more items
    add the left item to list

  while right has more items
    add the right item to list

}



What's the running time for split?

What's the running time for merge?

What's the running time for Merge Sort?

Does the running time for Merge Sort depend on
the kind of input you give it?

DEMO	(merge sort running time on sorted, reverse, random data)

















Visualizing The Merge Sort Running Time


How can you see the Merge Sort running time visually?

How much merging work does Merge Sort do at each level?

How many levels can Merge Sort recurse before hitting the base case?