Merge sort

Merge sort has a secret sauce - it’s how you mix lists

2 5 7 1 3 8Sorted list A Sorted list B

Merged List

Merge sort

2 5 7 1 3 8Sorted list A Sorted list B

Merged ListTo merge two sorted lists begin at the

beginning of each

Merge sort secret sauce

2 5 7 1 3 8Sorted list A Sorted list B

Merged List

You have two markers (red)for for each list.

Merge sort secret sauce

2 5 7 1 3 8Sorted list A Sorted list B

Merged ListThe next item in the merged list is the lower

of the two

Merge sort secret sauce

2 5 7 1 3 8

1

Sorted list A Sorted list B

Merged ListThe next item in the merged list is the lower

of the two

Merge sort secret sauce

2 5 7 1 3 8

1 2

Sorted list A Sorted list B

Merged ListIf you use a marker you move it forward and

try again

Merge sort secret sauce

2 5 7 1 3 8

1 2 3

Sorted list A Sorted list B

Merged ListThe next item in the merged list is the lower

of the two

Merge sort secret sauce

2 5 7 1 3 8

1 2 3 5

Sorted list A Sorted list B

Merged List

Merge sort secret sauce

2 5 7 1 3 8

1 2 3 5 7

Sorted list A Sorted list B

Merged List

Merge sort secret sauce

2 5 7 1 3 8

1 2 3 5 7 8

Sorted list A Sorted list B

Merged ListWhen one list is used you can just use up all of

the other

Merge sort secret sauce

2 5 1 3 4 7 8

1 2 3 5 7 8

Sorted list A Sorted list B

Merged ListList don’t even have to be the same length to

work!

Merge sort secret sauce

Once you know how to merge

two sorted lists the rest is easy

Begin with unsorted list

Split into two

Split each list into two again

Split each list into two again, and again

Split each list into two again, and again

Until each list has one item in it

Each one item list is ‘sorted’

Now move back and look at the pairs

Merge the pairs as first described...

... to make sorted pairs

Now merge pairs lists keeping them sorted

Merge pairs of lists together...

Merge pairs of lists together...

Finally we get back to the first two lists...

Which we merge

Leaving the original list sorted

Your done!

2 5 1 3 8 7 4

1 2 3 5 7 8

Sorted list A Sorted list B

Merge sort secret sauce

Merging lists takes as long as the list (order(N))

You do this log(N) timesMaking algorithm Order (N log(N))

2 5 1 3 4 7 8

1 2 3 4 5 7

Sorted list A Sorted list B

Merge sort secret sauce

Merging lists takes as long as the list (order(N))

You do this log(N) timesMaking algorithm Order (N log(N))

Pity you need extra space to ‘merge’ into otherwise it would be pretty neet