My Youtube Channel: Programming Sessions

video production toolsI am planning to produce and share videos about programming and internet. In this purpose I ordered a microphone for recording audio and get a Cam Studio software for screen capturing. You can see my production environment on the right side. I also ordered an short intro video from a web site for $5.

In the early hours of today my first video is out on my YouTube Channel. It is about to setup a virtual machine and publish a web page on Google Cloud. I hope I will keep doing this regularly.

I think the recording of my voice is to be improved. Until I get a better microphone I will enter captions to help audiences understand better what I say.

Twelve Days of Christmas – An Obfuscated C Code

Today when I was cleaning my a decade-old mails of my early college years, I came up with a mail received from my programming instructor. Just like the file name (mystery.c) the content of the file was quite mystery. He might be expecting us (students) to put it on compiler and hit run.

Ekte bir C programi yolluyorum. Durumun vehametini anlamak acisindan faydali
olabilir. Merat etmeyin sinavda cikmayacak :)
erkan

Code

#include &lt;stdio.h&gt;</p>
<p style="text-align: justify;">main(t,_,a)
char *a;
{return!0&lt;t?t&lt;3?main(-79,-13,a+main(-87,1-_,
main(-86, 0, a+1 )+a)):1,t&lt;_?main(t+1, _, a ):3,main ( -94, -27+t, a
)&amp;&amp;t == 2 ?_&lt;13 ?main ( 2, _+1, "%s %d %dn" ):9:16:t&lt;0?t&lt;-72?main(_,
t,"@n'+,#'/*{}w+/w#cdnr/+,{}r/*de}+,/*{*+,/w{%+,/w#q#n+,/#{l,+,/n{n+
,/+#n+,/#;#q#n+,/+k#;*+,/'r :'d*'3,}{w+K w'K:'+}e#';dq#'l q#'+d'K#!/
+k#;q#'r}eKK#}w'r}eKK{nl]'/#;#q#n'){)#}w'){){nl]'/+#n';d}rw' i;# ){n
l]!/n{n#'; r{#w'r nc{nl]'/#{l,+'K {rw' iK{;[{nl]'/w#q#
n'wk nw' iwk{KK{nl]!/w{%'l##w#' i; :{nl]'/*{q#'ld;r'}{nlwb!/*de}'c
;;{nl'-{}rw]'/+,}##'*}#nc,',#nw]'/+kd'+e}+;
#'rdq#w! nr'/ ') }+}{rl#'{n' ')# }'+}##(!!/")
:t&lt;-50?_==*a ?putchar(a[31]):main(-65,_,a+1):main((*a == '/')+t,_,a
+1 ):0&lt;t?main ( 2, 2 , "%s"):*a=='/'||main(0,main(-61,*a, "!ek;dc
i@bK'(q)-[w]*%n+r3#l,{}:nuwloca-O;m .vpbks,fxntdCeghiry"),a+1);}

The output is a poem. I am not going to share it, just put it on compiler and hit run. You can find online c compilers with a little effort.

If you are interested, see this web page for more obfuscated codes like this.

How many colors are required to color a graph?

Selam.

Today I will talk about an interesting theorem in maths. It was my homework to prepare a paper summarizing “Four Color Theorem” in high school, many years later I am doing the same thing again.

Four Color Theorem

Here is a brief summary of Four Color Theorem from Wikipedia:

The theorem states that given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Two regions are called adjacent if they share a common boundary that is not a corner, where corners are the points shared by three or more regions [1].

In 1852 a South African mathematician and botanist Francis Guthrie claimed the theorem for the first time. Then in Fallacious proofs were given independently by Alfred Kempe in 1879 and Peter Guthrie Tait in 1880. Kempe’s proof was accepted for a decade until Heawood came.

Heawood’s Formula

The following image represents Percy John Heawood’s generalized formula where γ(g) (as known as the chromatic number) is the smallest number of colors needed to color the vertices of a graph so that no two adjacent vertices share the same color. Heawood’s formula also approved Gutherie’s theorem for g=0 (g is for genus, which has a value of 0 for planar space [5]). This result was finally obtained by Appel and Haken in 1977, who constructed a computer-assisted proof that four colors were sufficient. Then a shorter, independent proof was constructed by Neil Robertson.

Heawood-Conjecture-Formula
Heawood Conjecture Formula

In December 2004, Georges Gonthier verified Appel and Hakken’s proof by representing all 1,936 possible situations of generating a map using a computer program. Initially, their proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. Since then the proof has gained wider acceptance, although doubts remain. So, if you can find any planar map that can not be colored at least by four colors your name will be included in the chronology of this theorem. Good luck.

Featured Image

Map of provinces of Turkey can be colored using only four colors.

References

  1. http://en.wikipedia.org/wiki/Four_color_theorem
  2. http://mathworld.wolfram.com/Four-ColorTheorem.html
  3. http://mathworld.wolfram.com/HeawoodConjecture.html
  4. http://mathworld.wolfram.com/ChromaticNumber.html
  5. http://en.wikipedia.org/wiki/Genus_(mathematics)