1. Insertion Sort

2. Insertion Sort
Insertion Sort works by taking the first two elements of the list, sorting them, then taking the third one, and sorting that into the first two, then taking the fourth element and sorting that into the first three, etc.

3. Insertion Sort
Let’s look at an example:

4. Insertion Sort 44 23 1 42 2 33 3 16 4 54 5 6 34 7 18
Age

5. Insertion Sort 44 23 1 42 2 33 3 16 4 54 5 6 34 7 18
Age

6. Insertion Sort 23 44 1 42 2 33 3 16 4 54 5 6 34 7 18
Age

7. Insertion Sort 23 44 1 42 2 33 3 16 4 54 5 6 34 7 18
Age

8. Insertion Sort 23 44 1 42 2 33 3 16 4 54 5 6 34 7 18
Age

9. Insertion Sort 23 42 1 44 2 33 3 16 4 54 5 6 34 7 18
Age

10. Insertion Sort 23 42 1 44 2 33 3 16 4 54 5 6 34 7 18
Age

11. Insertion Sort 23 42 1 44 2 33 3 16 4 54 5 6 34 7 18
Age

12. Insertion Sort 23 33 1 42 2 44 3 16 4 54 5 6 34 7 18
Age

13. Insertion Sort 23 33 1 42 2 44 3 16 4 54 5 6 34 7 18
Age

14. Insertion Sort 23 33 1 42 2 44 3 16 4 54 5 6 34 7 18
Age

15. Insertion Sort 16 23 1 33 2 42 3 44 4 54 5 6 34 7 18
Age

16. Insertion Sort 16 23 1 33 2 42 3 44 4 54 5 6 34 7 18
Age

17. Insertion Sort 16 23 1 33 2 42 3 44 4 54 5 6 34 7 18
Age

18. Insertion Sort 16 23 1 33 2 42 3 44 4 54 5 6 34 7 18
Age

19. Insertion Sort 16 23 1 33 2 42 3 44 4 54 5 6 34 7 18
Age

20. Insertion Sort 16 23 1 33 2 42 3 44 4 54 5 6 34 7 18
Age

21. Insertion Sort 16 23 1 33 2 34 3 42 4 44 5 6 54 7 18
Age

22. Insertion Sort 16 23 1 33 2 34 3 42 4 44 5 6 54 7 18
Age

23. Insertion Sort 16 23 1 33 2 34 3 42 4 44 5 6 54 7 18
Age

24. Insertion Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

25. Insertion Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

26. Insertion Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

27. Insertion Sort
How do we move the elements into their correct position (we’ll call this the “Insertion Sort move”)?

28. Insertion Sort Age We store 34 in CURRENT. 16 1 23 33 2 42 3 44 4 54 516 1 23 33 2 42 3 44 4 54 5 6 34 7 18
Age
Current: 34

29. Insertion Sort
Next we move what value is in the previous position to 34 into that location. 16 1 23 33 2 42 3 44 4 54 5 6 34 7 18
Age
Current: 34

30. Insertion Sort
Next we move what value is in the previous position to 34 into that location. 16 1 23 33 2 42 3 44 4 54 5 6 54 7 18
Age
Current: 34

31. Insertion Sort Age And we do that again. 16 1 23 33 2 42 3 44 4 44 5 616 1 23 33 2 42 3 44 4 44 5 6 54 7 18
Age
Current: 34

32. Insertion Sort Age And again. 16 1 23 33 2 42 3 42 4 44 5 6 54 7 1816 1 23 33 2 42 3 42 4 44 5 6 54 7 18
Age
Current: 34

33. Insertion Sort Age And then we move CURRENT into the correct position.16 1 23 33 2 42 3 42 4 44 5 6 54 7 18
Age
Current: 34

34. Insertion Sort Age And then we move CURRENT into the correct position.16 1 23 33 2 42 3 42 4 44 5 6 54 7 18
Age
Current: 34

35. Insertion Sort Age And then we move CURRENT into the correct position.16 1 23 33 2 34 3 42 4 44 5 6 54 7 18
Age

36. Insertion Sort
The element being added in each time is just to the left of the sorted list.
So, if the next element is called CURRENT, the largest element in the sorted list is CURRENT – 1.
So we’ll know if the next element is largest if it is bigger than CURRENT – 1.
Sorted sub-list
Next
element
CURRENT

37. Insertion Sort Structured English:
FOR each element from the second TO the end of the list
DO Remember the current position and value
WHILE the previous element is bigger than current
DO Move the previous element into current’s position
END WHILE
We’ve reached the position in the list that current should be
Put it in
END FOR
NOTE: The Previous
Element is the end of
the sorted sub-list

38. Insertion Sort
PROGRAM InsertionSort: Integer Array[8] <- {44,23,42,33,16,54,34,18}; FOR Index IN 1 TO N DO current = Array[index]; pos = index; WHILE (pos > 0 and Array[pos – 1] > current) DO Array[pos] <- Array[pos - 1]; pos = pos - 1; ENDWHILE; Array[pos] = current; ENDFOR; END.
NOTE: If you have
reached the start of
the list, STOP!

39. Insertion Sort Complexity of Insertion Sort
Best-case scenario complexity = O(N)
Average complexity = O(N2)
Worst-case scenario complexity = O(N2)

40. etc.