Discrete Mathematics University of Kentucky CS 275 Spring ... - MGNet

Merge sort is a balanced binary tree method that first breaks a list up recursively
into two lists until each sublist has only one element. Then the sublists are
recombined, two at a time and sorted order, until only one sorted list remains.
Note: The height of the tree formed in merge sort is O(log 2 n) for n elements.
Notes:
10, 4, 7, 1
10, 4 7, 1
10 4 7 1
4, 10 1, 7
1, 4, 7, 10
• First three rows do the sublist splitting.
• Last two rows do the merging.
• There are two distinct algorithms at work.
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!
procedure merge_sort(L = " a
# i
if n > 1 then
m := 7n/28
!
L 1 := " a i
m
$
%
# &i=1
n
$
%
&i=m+1
n
$
% )
&i=1
!
L 2 := " a
# i
L := merge(merge_sort(L 1 ), merge_sort(L 2 ))
!
{L is now the sorted " a
# i
n
$
% }
&i=1
procedure merge(L 1 , L 2 : sorted lists)
L := /
while L 1 and L 2 are both nonempty
remove the smaller of the first element of L 1 and L 2 and append it to
end of L
if either L 1 or L 2 are empty, append the other list to the end of L
{L is the merged, sorted list}
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