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Merge original( a)
Merge sort is an algorithm that sorts a list by dividing it into halves and then merging the sorted halves together. It works by first splitting the list into individual elements, then repeatedly merging the sorted pairs into larger sorted groups until the entire list is sorted. The algorithm runs in O(n log n) time since each merge takes linear time and there are log n levels of merging.
Merge original( a)
- 1.
- 2. Merge sort hasa secret sauce - it’s how you mix lists 2 5 7 1 3 8 Sorted list A Sorted list B Merged List Merge sort
- 3. 2 5 71 3 8 Sorted list A Sorted list B Merged List To merge two sorted lists begin at the beginning of each Merge sort secret sauce
- 4. 2 5 71 3 8 Sorted list A Sorted list B Merged List You have two markers (red)for for each list. Merge sort secret sauce
- 5. 2 5 71 3 8 Sorted list A Sorted list B Merged List The next item in the merged list is the lower of the two Merge sort secret sauce
- 6. 2 5 71 3 8 1 Sorted list A Sorted list B Merged List The next item in the merged list is the lower of the two Merge sort secret sauce
- 7. 2 5 71 3 8 1 2 Sorted list A Sorted list B Merged List If you use a marker you move it forward and try again Merge sort secret sauce
- 8. 2 5 71 3 8 1 2 3 Sorted list A Sorted list B Merged List The next item in the merged list is the lower of the two Merge sort secret sauce
- 9. 2 5 71 3 8 1 2 3 5 Sorted list A Sorted list B Merged List Merge sort secret sauce
- 10. 2 5 71 3 8 1 2 3 5 7 Sorted list A Sorted list B Merged List Merge sort secret sauce
- 11. 2 5 71 3 8 1 2 3 5 7 8 Sorted list A Sorted list B Merged List When one list is used you can just use up all of the other Merge sort secret sauce
- 12. 2 5 13 4 7 8 1 2 3 5 7 8 Sorted list A Sorted list B Merged List List don’t even have to be the same length to work! Merge sort secret sauce
- 13. Once you knowhow to merge two sorted lists the rest is easy
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- 16. Split each listinto two again
- 17. Split each listinto two again, and again
- 18. Split each listinto two again, and again
- 19. Until each listhas one item in it
- 20. Each one itemlist is ‘sorted’
- 21. Now move backand look at the pairs
- 22. Merge the pairsas first described...
- 23. ... to makesorted pairs
- 24. Now merge pairslists keeping them sorted
- 25. Merge pairs oflists together...
- 26. Merge pairs oflists together...
- 27. Finally we getback to the first two lists...
- 28.
- 29. Leaving the originallist sorted
- 30.
- 31. 2 5 13 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) times Making algorithm Order (N log(N))
- 32. 2 5 13 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) times Making algorithm Order (N log(N)) Pity you need extra space to ‘merge’ into otherwise it would be pretty neet
Editor's Notes
- #15 Lets begin with a list to sort
- #16 Lets begin with a list to sort
- #17 Lets begin with a list to sort
- #18 Lets begin with a list to sort
- #19 Lets begin with a list to sort
- #20 Lets begin with a list to sort
- #21 Lets begin with a list to sort
- #22 Lets begin with a list to sort
- #23 Lets begin with a list to sort
- #24 Lets begin with a list to sort
- #25 Lets begin with a list to sort
- #26 Lets begin with a list to sort
- #27 Lets begin with a list to sort
- #28 Lets begin with a list to sort
- #29 Lets begin with a list to sort
- #30 Lets begin with a list to sort