3.2 insertion sort

Insertion Sort: Idea

Idea: sorting cards.
− 8 | 5 9 2 6 3
− 5 8 | 9 2 6 3
− 5 8 9 | 2 6 3
− 2 5 8 9 | 6 3
− 2 5 6 8 9 | 3
− 2 3 5 6 8 9 |

Insertion Sort: Idea
1. We have two group of items:
 sorted group, and
 unsorted group
1. Initially, all items in the unsorted group
and the sorted group is empty.
 We assume that items in the unsorted
group unsorted.
 We have to keep items in the sorted group
sorted.
1. Pick any item from, then insert the item
at the right position in the sorted group to

40 2 1 43 3 65 0 -1 58 3 42 4
2 40 1 43 3 65 0 -1 58 3 42 4
1 2 40 43 3 65 0 -1 58 3 42 4
40
Insertion Sort: Example

1 2 3 40 43 65 0 -1 58 3 42 4
1 2 40 43 3 65 0 -1 58 3 42 4
1 2 3 40 43 65 0 -1 58 3 42 4

1 2 3 40 43 65 0 -1 58 3 42 4
1 2 3 40 43 650 -1 58 3 42 4
1 2 3 40 43 650 58 3 42 41 2 3 40 43 650-1

1 2 3 40 43 650 58 3 42 41 2 3 40 43 650-1
1 2 3 40 43 650 58 42 41 2 3 3 43 650-1 5840 43 65
1 2 3 40 43 650 42 41 2 3 3 43 650-1 5840 43 65
1 2 3 40 43 650 421 2 3 3 43 650-1 584 43 6542 5840 43 65

Insertion Sort: Analysis

Running time analysis:
− Worst case: O(N2
)
− Best case: O(N)

A Lower Bound

Bubble Sort, Selection Sort, Insertion
Sort all have worst case of O(N2
).

Turns out, for any algorithm that
exchanges adjacent items, this is the
best worst case: Ω(N2
)

In other words, this is a lower bound!

How many squares can you create in this figure by connecting any 4
dots (the corners of a square must lie upon a grid dot?
TRIANGLES:
How many triangles are located in the image below?

There are 11 squares total; 5 small, 4 medium, and 2 large.
27 triangles. There are 16 one-cell triangles, 7 four-cell triangles, 3 nine-cell triangles, and
1 sixteen-cell triangle.

3.2 insertion sort

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3.2 insertion sort