1. EN.540.635 - Software Carpentry
Python – A Crash Course
Big O Notation

2. Functions!
Y = x
Y = log10(x)

3. Functions!
Y = x^2
Y = x * log10(x)

4. Functions!
Y = 2^x

5. How does a problem scale?
Useful to define some parameter describing how something scales
O notation – Upper bound
Ω notation – Lower bound
Θ notation – Exactly bound
We ignore constants
Question:
What does the Big O notation tell us?

6. Examples
Fit Functions 𝑦=4 ∗𝑥 𝑦= ∗𝑥 𝑦=4 ∗ log 10 4𝑥 𝑦= 𝑥 𝑦=x ∗ log 10 x+4 +x
Big O Notation
𝑂(𝑁)
𝑂 log 𝑁
𝑂 𝑁 4
𝑂 𝑁𝑙𝑜𝑔 𝑁
For more information, you can look at complexities here.

7. Sorting How can we sort the following array: Insertion 𝑂 𝑁 2
Merge 𝑂 𝑁𝑙𝑜𝑔 𝑁
Quick 𝑂 𝑁 2
Bubble 𝑂 𝑁 2
Radix 𝑂 𝑤𝑁 →O N , O Nlog N , worse
More 5 38 23 9 27 1

8. Group Project - Lazor

9. Group Project - Lazor
Block Types

10. Example Input File Next Few Slides
Group Project - Lazor
Example Input File Next Few Slides

11. Group Project - Lazor # This is a comment
# This example is for mad 1 in Lazor
# x = no block allowed
# o = blocks allowed
# A = fixed reflect block
# B = fixed opaque block
# C = fixed refract block
# Grid will start at top left being 0, 0
# Step size is by half blocks
# Thus, this leads to even numbers indicating
# the rows/columns between blocks, and odd numbers
# intersecting blocks.

12. Group Project - Lazor GRID START o o o o GRID STOP
# Here we specify that we have 2 reflect blocks
# and 1 refract block
A 2
C 1
# Now we specify that we have one lazer
# x, y, vx, vy
# NOTE! because 0, 0 is the top left, our axis
# are as follows:

13. Group Project - Lazor # __________\ +x # | / # | # \|/ +y # L 2 7 1 -1
# | /
# |
# \|/ +y # L
# Here we have the points that we need the lazers to intersect
P 3 0
P 4 3
P 2 5
P 4 7