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Algorithm cheatsheet by

Ciro Santilli 40 Updated 2025-07-16

Draft by Ciro Santilli with cross language input/output test cases: github.com/cirosantilli/algorithm-cheat

By others:

github.com/TheAlgorithms/Python

Alan Turing by

Ciro Santilli 40 Updated 2025-07-16

Michael J. Saylor by

Ciro Santilli 40 Updated 2025-07-16

twitter.com/saylor 2.6 M followers as of 2022. Because of Bitcoin? Or was he famous before that?
www.michael.com/ yes, he is Michael.com lol. When did he get the domain, and at what price? He's mildlly obsessed with domain names it seems: www.domainsherpa.com/saylor/. He also bought frank.com, mike.com. emma.com. This was between 1994 and 2000. He mentions that his email is saylor@strategy.com. strategy.com redirects to microstrategy.com as of 2022, so seems still valid.
We actually got a backlink from tvt.phishlabs.com to this page in August 2022, a phising security provider, presumably for showing his email here. This reminds Ciro of the All GitHub Commit Emails event!
A quick google for that address also leads to www.washingtonpost.com/wp-srv/liveonline/00/business/saylor0621.htm, a year 2000 profile page by the Washington Post, followed by a Q&A. In the Q&A, Michael himself gives his email in relation to Saylor Academy:
Kensington, Maryland: What has happened to your vision of an internet university? I believe it is an important initiative and it doesn't require $100 million to get started. We at the Rockefeller Foundation would like to become involved. How can we do this?
Michael Saylor: The internet university is alive and well. My goal is to initially roll out a cyber-libary of digital video that can be used by any for-profit or non-profit organization in order to accelerate the free education initiative. Eventually, people may just go direct to the web site.
I think the entire thing will unfold over about 10 years.
Send me an email if you would like to get involved. (saylor@strategy.com)
so it was already beyond leaked. Ciro did hit that email address seeking funding for OurBigBook.com, but no reply unfortunately. Maybe you gotta be part of the Rockefeller family to get a reply from these people? Well, at least this led to Ciro learning about the Rockefeller Foundation.

Elliptic-curve Diffie-Hellman by

Ciro Santilli 40 Updated 2025-07-16

The algorithm is completely analogous to Diffie-Hellman key exchange in that you efficiently raise a number to a power

n

times and send the result over while keeping

n

as private key.

The only difference is that a different group is used: instead of using the cyclic group, we use the elliptic curve group of an elliptic curve over a finite field.

Elliptic curves by Computerphile (2018)

Source. youtu.be/NF1pwjL9-DE?t=143 shows the continuous group well, but then fails to explain the discrete part.

Variant of Diffie-Hellman key exchange based on elliptic curve cryptography.

Prize by

Ciro Santilli 40 Updated 2025-07-16

Generally, prizes that pay big lumps of money to well established individuals are a bit useless, it would be better to pay smaller sums to struggling beginners in the field, of which there are aplenty.

The most important part about prizes should not be the money, nor the recognition, but rather explaining better what the laureates did. In this, most prizes fail. Thus Ciro Santilli's project idea: Project to explain each Nobel Prize better.

Ah, this list: en.wikipedia.org/wiki/List_of_prizes_known_as_the_Nobel_or_the_highest_honors_of_a_field

Git tips / It's not a tree, it's actually a DAG by

Ciro Santilli 40 Updated 2025-07-16

Every tree is a directed acyclic graph.

But not every directed acyclic graph is a tree.

Example of a tree (and therefore also a DAG):

5
|
4 7
| |
3 6
|/
2
|
1

Convention in this presentation: arrows implicitly point up, just like in a git log, i.e.:

1 is parent of 2
2 is parent of 3 and 6
3 is parent of 4

and so on.

Example of a DAG that is not a tree:

7
|\
4 6
| |
3 5
|/
2
|
1

This is not a tree because there are two ways to reach 7:

2, 3, 4, 7
2, 5, 6, 7

But we often say "tree" intead of "DAG" in the context of Git because DAG sounds ugly.

Example of a graph that is not a DAG:

6
^
|
3->4
^  |
|  v
2<-5
^
|
1

This one is not acyclic because there is a cycle 2, 3, 4, 5, 2.

Git tips / git rebase 101 by

Ciro Santilli 40 Updated 2025-07-16

Server-side rendering by

Ciro Santilli 40 Updated 2025-07-16

ASML Holding by

Ciro Santilli 40 Updated 2025-07-16

As of 2020 leading makers of the most important fab photolithography equipment.

ASML: TSMC's Critical Supplier by Asianometry (2021)

Source.

Video 2.

How ASML Won Lithography by Asianometry (2021)

Source.

First there were dominant Elmer and Geophysics Corporation of America dominating the market.

Then a Japanese government project managed to make Nikon and Canon Inc. catch up, and in 1989, when Ciro Santilli was born, they had 70% of the market.

youtu.be/SB8qIO6Ti_M?t=240 In 1995, ASML had reached 25% market share. Then it managed the folloging faster than the others:

TwinScan, reached 50% market share in 2002
Immersion litography
EUV. There was a big split between EUV vs particle beams, and ASML bet on EUV and EUV won.
youtu.be/SB8qIO6Ti_M?t=459 they have an insane number of software engineers working on software for the machine, which is insanely complex. They are big on UML.
youtu.be/SB8qIO6Ti_M?t=634 they use ZEISS optics, don't develop their own. More precisely, the majority owned subsidiary Carl Zeiss SMT.
youtu.be/SB8qIO6Ti_M?t=703 IMEC collaborations worked well. Notably the ASML/Philips/ZEISS trinity

www.youtube.com/watch?v=XLNsYecX_2Q ASML: Chip making goes vacuum with EUV (2009) Self promotional video, some good shots of their buildings.

Photomask by

Ciro Santilli 40 Updated 2025-07-16

Asianometry by

Ciro Santilli 40 Updated 2025-07-16

www.youtube.com/channel/UC1LpsuAUaKoMzzJSEt5WImw

Very good channel to learn some basics of semiconductor device fabrication!

Focuses mostly on the semiconductor industry.

youtu.be/aL_kzMlqgt4?t=661 from Video "SMIC, Explained by Asianometry (2021)" from mentions he is of Chinese ascent, ancestors from Ningbo. Earlier in the same video he mentions he worked on some startups. He doesn't appear to speak perfect Mandarin Chinese anymore though based on pronounciation of Chinese names.

asianometry.substack.com/ gives an abbreviated name "Jon Y".

Reflecting on Asianometry in 2022 by Asianometry (2022)

Source. Mentions his insane work schedule: 4 hours research in the morning, then day job, then editing and uploading until midnight. Appears to be based in Taipei. Two videos a week. So even at the current 400k subs, he still can't make a living.

Web crawling by

Ciro Santilli 40 Updated 2025-07-16

Integrated circuit by

Ciro Santilli 40 Updated 2025-08-08

It is quite amazing to read through books such as The Supermen: The Story of Seymour Cray by Charles J. Murray (1997), as it makes you notice that earlier CPUs (all before the 70's) were not made with integrated circuits, but rather smaller pieces glued up on PCBs! E.g. the arithmetic logic unit was actually a discrete component at one point.

The reason for this can also be understood quite clearly by reading books such as Robert Noyce: The Man Behind the Microchip by Leslie Berlin (2006). The first integrated circuits were just too small for this. It was initially unimaginable that a CPU would fit in a single chip! Even just having a very small number of components on a chip was already revolutionary and enough to kick-start the industry. Just imagine how much money any level of integration saved in those early days for production, e.g. as opposed to manually soldering point-to-point constructions. Also the reliability, size an weight gains were amazing. In particular for military and spacial applications originally.

A briefing on semiconductors by Fairchild Semiconductor (1967)

Source.

Uploaded by the Computer History Museum. There is value in tutorials written by early pioneers of the field, this is pure gold.

Shows:

photomasks
silicon ingots and wafer processing

Scientific software by

Ciro Santilli 40 Updated 2025-07-16

System on a chip by

Ciro Santilli 40 Updated 2025-07-16

Ciro Santilli 40 Updated 2025-07-16

The only two truly relevant RTL languages as of 2020 are: Verilog and VHDL. Everything else compiles to those, because that's all that EDA vendors support.

Much like a C compiler abstracts away the CPU assembly to:

increase portability across ISAs
do optimizations that programmers can't feasibly do without going crazy

Compilers for RTL languages such as Verilog and VHDL abstract away the details of the specific semiconductor technology used for those exact same reasons.

The compilers essentially compile the RTL languages into a standard cell library.

Examples of companies that work at this level include:

Intel. Intel also has semiconductor fabrication plants however.
Arm which does not have fabs, and is therefore called a "fabless" company.

SymPy by

Ciro Santilli 40 Updated 2025-07-16

This is the dream cheating software every student should know about.

It also has serious applications obviously. www.sympy.org/scipy-2017-codegen-tutorial/ mentions code generation capabilities, which sounds super cool!

The code in this section was tested on sympy==1.8 and Python 3.9.5.

Let's start with some basics. fractions:

from sympy import *
sympify(2)/3 + sympify(1)/2

outputs:

7/6

Note that this is an exact value, it does not get converted to floating-point numbers where precision could be lost!

We can also do everything with symbols:

from sympy import *
x, y = symbols('x y')
expr = x/3 + y/2
print(expr)

outputs:

x/3 + y/2

We can now evaluate that expression object at any time:

expr.subs({x: 1, y: 2})

outputs:

4/3

How about a square root?

x = sqrt(2)
print(x)

outputs:

sqrt(2)

so we understand that the value was kept without simplification. And of course:

sqrt(2)**2

outputs 2. Also:

sqrt(-1)

outputs:

I is the imaginary unit. We can use that symbol directly as well, e.g.:

I*I

gives:

-1

Let's do some trigonometry:

cos(pi)

gives:

-1

and:

cos(pi/4)

gives:

sqrt(2)/2

The exponential also works:

exp(I*pi)

gives;

-1

Now for some calculus. To find the derivative of the natural logarithm:

from sympy import *
x = symbols('x')
print(diff(ln(x), x))

outputs:

1/x

Just read that. One over x. Beauty. And now for some integration:

print(integrate(1/x, x))

outputs:

log(x)

OK.

Let's do some more. Let's solve a simple differential equation:

y''(t) - 2y'(t) + y(t) = sin(t)

Doing:

from sympy import *
x = symbols('x')
f, g = symbols('f g', cls=Function)
diffeq = Eq(f(x).diff(x, x) - 2*f(x).diff(x) + f(x), sin(x)**4)
print(dsolve(diffeq, f(x)))

outputs:

Eq(f(x), (C1 + C2*x)*exp(x) + cos(x)/2)

which means:

f (x) = C_{1} + C_{2} x e^{x} + cos (x) /2

(1)

To be fair though, it can't do anything crazy, it likely just goes over known patterns that it has solvers for, e.g. if we change it to:

diffeq = Eq(f(x).diff(x, x)**2 + f(x), 0)

it just blows up:

NotImplementedError: solve: Cannot solve f(x) + Derivative(f(x), (x, 2))**2

Sad.

Let's try some polynomial equations:

from sympy import *
x, a, b, c = symbols('x a b c d e f')
eq = Eq(a*x**2 + b*x + c, 0)
sol = solveset(eq, x)
print(sol)

which outputs:

FiniteSet(-b/(2*a) - sqrt(-4*a*c + b**2)/(2*a), -b/(2*a) + sqrt(-4*a*c + b**2)/(2*a))

which is a not amazingly nice version of the quadratic formula. Let's evaluate with some specific constants after the fact:

sol.subs({a: 1, b: 2, c: 3})

which outputs

FiniteSet(-1 + sqrt(2)*I, -1 - sqrt(2)*I)

Let's see if it handles the quartic equation:

x, a, b, c, d, e, f = symbols('x a b c d e f')
eq = Eq(e*x**4 + d*x**3 + c*x**2 + b*x + a, 0)
solveset(eq, x)

Something comes out. It takes up the entire terminal. Naughty. And now let's try to mess with it:

x, a, b, c, d, e, f = symbols('x a b c d e f')
eq = Eq(f*x**5 + e*x**4 + d*x**3 + c*x**2 + b*x + a, 0)
solveset(eq, x)

and this time it spits out something more magic:

ConditionSet(x, Eq(a + b*x + c*x**2 + d*x**3 + e*x**4 + f*x**5, 0), Complexes)

Oh well.

Let's try some linear algebra.

m = Matrix([[1, 2], [3, 4]])

Let's invert it:

m**-1

outputs:

Matrix([
[ -2,    1],
[3/2, -1/2]])

Microarchitecture by

Ciro Santilli 40 Updated 2025-07-16

Nobel Foundation by

Ciro Santilli 40 Updated 2025-07-16

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