Merge sort

G R Lockwood, 2006 1
Sorting a Sequence With Merge SortSorting a Sequence With Merge Sort
 Sort the sequence 6, 5, 8, 3, 2, 7, 1Sort the sequence 6, 5, 8, 3, 2, 7, 1
using merge sortusing merge sort

 Split the sequenceSplit the sequence
atat mm==((ii++jj)/2)/2
 ii=1,=1, jj=7,=7, mm=4=4
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 Make a recursiveMake a recursive
call to merge sortcall to merge sort
 mm :=:= ((ii++jj)/2)/2==
2.52.5=2=2
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 Now sorting thisNow sorting this
partpart
 ii=1,=1, jj=2,=2, mm=1 and=1 and
make a recursivemake a recursive
callcall
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 Sequence of lengthSequence of length
1 is already sorted,1 is already sorted,
so returnso return
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1 is sorted1 is sorted
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 Return control andReturn control and
merge these 2 sub-merge these 2 sub-
sequences intosequences into
correct ordercorrect order
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 Now sort theNow sort the
second part of thissecond part of this
subsequencesubsequence
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 Merge these twoMerge these two
into correct orderinto correct order
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 Return control toReturn control to
previous call.previous call.
 Now merge theseNow merge these
two sub-sequencestwo sub-sequences
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 The recursive callThe recursive call
at line 7 is nowat line 7 is now
completedcompleted
 First part ofFirst part of
sequence is nowsequence is now
fully sortedfully sorted
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 Control nowControl now
returns to the veryreturns to the very
first call of mergefirst call of merge
sortsort
 A recursive call isA recursive call is
now made on thenow made on the
second part of thesecond part of the
sequencesequence
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 ii=5,=5, jj=7,=7, mm=6=6
 Split sequence atSplit sequence at
item 6item 6
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call to sort thesecall to sort these
two itemstwo items
 Split sequence atSplit sequence at
item 5item 5
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 Make anotherMake another
recursive call onrecursive call on
the first part of thisthe first part of this
subsequencesubsequence
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call on second partcall on second part
of sequenceof sequence
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 Now merge these 2Now merge these 2
sub-sequencessub-sequences
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call with thecall with the
remaining elementremaining element
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sub-sequences intosub-sequences into
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 Return to the firstReturn to the first
callcall
sub-sequences intosub-sequences into
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 Merge sort isMerge sort is
completedcompleted
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Merge sort

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