Symmetry clear solution for Counting Tiles by veky - python coding challenges

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Symmetry solution in Clear category for Counting Tiles by veky
def checkio(radius):
    ran,solid,total=range(int(radius)+1),0,0
    for x in ran:
        for y in ran:
            solid+=abs(x+y*1j+1+1j)<=radius
            total+=abs(x+y*1j)
                        June 1, 2013

                        
                            Comments:
                            
                                
                                    gflegar
 on Jan. 28, 2014, 10:38 a.m.

                                    <p>Same idea as mine. Just more readable :)</p>

                                
                            
                                
                                    veky
 on Jan. 28, 2014, 11:13 a.m.

                                    <p>I'm getting old, obviously. :-D</p>

                                
                            
                                
                                    glebmikh
 on March 3, 2015, 3:40 p.m.

                                    <p>Very cool! Could you explain 1j stuff?) Thanks</p>

                                
                            
                                
                                    veky
 on July 20, 2015, 2:05 p.m.

                                    <p>Sorry, I don't know how I missed this. 1j is the imaginary unit, x+y*1j is a complex number with real part x and imaginary part y. It represents a point (x,y) in the plane. In the same way, x+y*1j+1+1j represents a point (x+1,y+1). abs() gives the distance from origin. Is it clearer now?</p>

                                
                            
                                
                                    veghadam1991
 on Oct. 13, 2015, 5:35 p.m.

                                    <p>Hmmm... with complex number. Clear and very creative too! Amazing! I like your solutions. :D Since when do you program in Python and any other languages?</p>

                                
                            
                                
                                    veky
 on Oct. 13, 2015, 8:06 p.m.

                                    <p>Thanks. Many people forget Python has native support for complexes.</p>

<p>I program for about 30 years, and have written a nontrivial amount of code in various BASICs, Pascal, HP RPL, C, C++, Wolfram Language, Perl and of course Python; and a trivial amount of code in 6502 assembler, FORTH, Java, batch language, ksh, Haskell, Prolog, Scheme, and various other languages, some of whom I designed. :-)</p>

<p>Python is the only language I use professionally, and I started to use it when Python3 came out (about 6 years ago) - but for a long time it was just another language. About 2.5 years ago I started to really appreciate its strengths, and realized it really clicks with my deep convictions about coding.</p>

                                
                            
                                
                                    piter239
 on April 26, 2020, 4:24 p.m.

                                    <p>FORTH, the passion of my youth! It was about 1998, and there were no real computer to try it out, but I just loved the idea!</p>

                                
                            
                                
                                    carel.anthonissen
 on May 3, 2017, 8:04 a.m.

                                    <p>Very tidy.</p>

<p>Would you consider ever using itertools.permutations to collapse multiple outer loops?</p>

<p>For example:</p>

<pre class='brush: python'>for x,y in permutations(ran,2):
    solid+=abs(x+y*1j+1+1j)&lt;=radius
    total+=abs(x+y*1j)&lt;radius
</pre>

                                
                            
                                
                                    veky
 on May 4, 2017, 6:12 a.m.

                                    <p>Those are not the same. I want occasionally x and y to be the same. permutations will only give me injections.</p>

<p>You mean `product(ran, repeat=2)`. And yes, I would use it if I had multiple places in the same program to use it. For only one time, probably nested loops are easier.</p>

                                
                            
                                
                                    Tinus_Trotyl
 on July 26, 2017, 3:34 a.m.

                                    <p>As neat as from a schoolbook !!!  </p>

                                
                            
                                
                                    veky
 on July 26, 2017, 5:33 a.m.

                                    <p>Do you find that surprising? :-)</p>

                                
                            
                                
                                    Tinus_Trotyl
 on July 26, 2017, 3:23 p.m.

                                    <p>What can I say. . . surprising has gone pretty relative in your case :-)</p>

<p>I see you solved it in four times a quarter circle but how about processing eight 45° sectors simultaneously ? <a href="https://py.checkio.org/mission/counting-tiles/publications/Tinus_Trotyl/python-3/8-times-a-45deg-sector/"> here </a></p>

                                
                            
                                
                                    veky
 on July 26, 2017, 3:48 p.m.

                                    <blockquote>
  <p>What can I say. . . surprising has gone pretty relative in your case :-)</p>
</blockquote>

<p>I'm travelling to the Land of Weird Compliments again... :-D</p>

<blockquote>
  <p>processing eight 45° sectors simultaneously ? here</p>
</blockquote>

<p>As you have seen, 4 quarters is <em>simpler</em> than whole circle processing. 8 eighths seems to me more complicated than that.</p>

                                
                            
                                
                                    hao.daniel
 on Feb. 25, 2020, 5:28 p.m.

                                    <p>Hi,  after reading yours, I've a strong urge to pick my math books again, and study hard.  ;-)
(btw, do you think someone with deep math background has<em>* advantage</em>* on coding/solving problems?  </p>

                                
                            
                                
                                    veky
 on Feb. 26, 2020, 7:04 a.m.

                                    <p>I think those things are correlated, but not necessarily in a cause and effect sort of way. But you're welcome to prove me wrong. [Obligatory XKCD: <a href="https://xkcd.com/552/]">https://xkcd.com/552/]</a> :-)</p>

                                
                            
                                
                                    boris_bondarenko
 on Dec. 12, 2021, 1:58 p.m.

                                    <p>Hello, veky!
Please give me your thoughts about my solution of this mission.</p>

<p>Maybe I will make it better.</p>

<p><a href="https://py.checkio.org/mission/counting-tiles/publications/boris_bondarenko/python-3/my-first-solution/">https://py.checkio.org/mission/counting-tiles/publications/boris_bondarenko/python-3/my-first-solution/</a></p>
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