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Computer Science Fundamentals for Self-Taught P...
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PyCon 2014
April 11, 2014
Programming
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1.8k
Computer Science Fundamentals for Self-Taught Programmers by Justin Abrahms
PyCon 2014
April 11, 2014
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Transcript
Justin Abrahms Computer Science for the self taught programmer http://bit.ly/1gfszix
Who am I? • Justin Abrahms • Director of Product
Engineering at Quick Left • Author of Imhotep • @justinabrahms or github://justinabrahms
Overview • How I learn about Big O? • What
is Big O? • How is Big O done? • Resources and learned wisdom
None
A sane data model
Our data model
Our ACTUAL data model
What does N+1 Selects look like? entries = get_post_ids() final_list
= [] for entry_id in entries: entry = get_entry(entry_id) final_list.append(entry)
Questions • How did I miss this? • How did
this guy know about it and I didn’t? • How can I make sure this never happens again.
–Wikipedia (aka Inducer of Impostor Syndrome) In mathematics, big O
notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions.
–Me Big O is how programmers talk about the relation
of how much stuff is being done when comparing two pieces of code.
Google Study List Studied: • Data Structures • Algorithms •
System Design • Java Internals • Concurrency Issues
Google Study List Studied: • Data Structures! • Algorithms! •
System Design • Java Internals • Concurrency Issues These are Big O things
–Wikipedia A data structure is a particular way of storing
and organizing data in a computer so that it can be used efficiently.
–Wikipedia An algorithm is a step-by-step procedure for calculations
O(n)
What sorts of Big O are there? • O(1) —
Constant Time • O(log n) — Logarithmic Time • O(n) — Linear Time • O(n²) — Quadratic Time • O(n!) — Factorial Time
Intentionally left blank for people in the back
def get_from_list(idx, lst): return lst[idx] O(1)
def item_in_list(item, lst): for entry in lst: if entry ==
item: return True return False O(n)
Wait a second…
def item_in_list(item, lst): for entry in lst: if entry ==
item: return True return False O(n) — Broken Down
def item_in_list(item, lst): for entry in lst: O(n) if entry
== item: return True return False O(n) — Broken Down
def item_in_list(item, lst): for entry in lst: O(n) if entry
== item: O(1) return True return False O(n) — Broken Down
def item_in_list(item, lst): for entry in lst: O(n) if entry
== item: O(1) return True O(1) return False O(1) O(n) — Broken Down
def item_in_list(item, lst): for entry in lst: O(n) if entry
== item: O(1) return True O(1) return False O(1) O(n) — Broken Down =O(n) * O(1) + O(1)
Why don’t we say Big O of O(n) * O(1)
+ O(1)?
In non-“math-y” terms • If we plot our function, we
can also plot M * the big O and end up with a line that our function never crosses (for certain values of X)
Example O(n) * O(1) + O(1) Big O: To Plot:
?
Example O(n) * O(1) + O(1) Big O: To Plot:
x * ? O(n) always means x
Example O(n) * O(1) + O(1) Big O: To Plot:
x * 5 + 9 O(1) means pick any constant number
Example To Plot: x * 5 + 9
Example To Plot: x * 5 + 9
Example To Plot: x * 5 + 9
Is it O(1)? To Plot: x * 5 + 9
Is it O(n²)? To Plot: x * 5 + 9
Big O is an approximation of algorithmic complexity
def item_in_list(item, lst): for entry in lst: if entry ==
item: return True return False O(n)
What if the list is empty?
def item_in_list(item, lst): for entry in lst: if entry ==
item: return True return False O(n)
O(log n) The best example of O(log n) is binary
search.
O(log n) 1 2 3 4 5 6 7 8
9 10
O(log n) 1 2 3 4 5 6 7 8
9 10 4
O(log n) 1 2 3 4 5 6 7 8
9 10 4
O(log n) 1 2 3 4 5 6 7 8
9 10 4 == 6?
O(log n) 1 2 3 4 5 6 7 8
9 10 4 == 6? Nope.
O(log n) 1 2 3 4 5 6 7 8
9 10 4
O(log n) 1 2 3 4 5 6 7 8
9 10 4
O(log n) 1 2 3 4 5 6 7 8
9 10 4 == 3?
O(log n) 1 2 3 4 5 6 7 8
9 10 4 == 3? Nope.
O(log n) 1 2 3 4 5 6 7 8
9 10 4
O(log n) 1 2 3 4 5 6 7 8
9 10 4
O(log n) 1 2 3 4 5 6 7 8
9 10 4 == 4?
O(log n) 1 2 3 4 5 6 7 8
9 10 4 == 4? Yes!
def get_pairs(lst): pair_list = [] for i1 in lst: for
i2 in lst: pair_list.append([i1, i2]) return pair_list ! O(n²)
def get_pairs(lst): pair_list = [] O(1) for i1 in lst:
O(N) for i2 in lst: O(N) pair_list.append([i1, i2]) O(1) return pair_list O(1) ! O(n²)
def get_pairs(lst): pair_list = [] O(1) for i1 in lst:
O(N) for i2 in lst: O(N) pair_list.append([i1, i2]) O(1) return pair_list O(1) ! O(n²) = O(1) + O(n) * O(n) * O(1) + O(1)
O(n²) = O(1) + O(n) * O(n) * O(1) +
O(1)
O(n²) = O(1) + O(n) * O(n) * O(1) +
O(1)
O(n²) = O(1) + O(n) * O(n) * O(1) +
O(1) = O(n) * O(n) * O(1) + O(1) + O(1)
O(n²) = O(1) + O(n) * O(n) * O(1) +
O(1) = O(n) * O(n) * O(1) + O(1) + O(1) = x * x + 7 + 9 + 13
O(n²) = O(1) + O(n) * O(n) * O(1) +
O(1) = O(n) * O(n) * O(1) + O(1) + O(1) = x * x + 7 + 9 + 13 = x² + 29
O(n²) = x² + 29
O(n²) = x² + 29
O(n²) = x² + 29
O(n²) = x² + 29
Gotchas
The Big O of a function might not matter
Theoretical speed is different than practical speed.
This is probably not going to make your app faster.
Resources
Resources http://algorist.com/
Resources https://www.coursera.org/course/algo
Resources https://leanpub.com/computer-science-for-self-taught-programmers/
How do I write my code differently now?
Knowing Big-O doesn’t make you write your code differently.
Big O is… • useful in communicating about complexity of
code • basic arithmetic and algebra • used in talking about algorithms and data structures • not as hard as it originally sounds
Thanks • justin@abrah.ms • @justinabrahms • github.com/justinabrahms Credits: ! NYC
slide photo via flickr://Andos_pics