Gah! When you're so close to an answer but it is so far away
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I need to permutate for every combination of 2 colors in a palette. More specifically I need to compute the size of this. It would normally be N*N I think where N is the number of colors in the palette Except I need to subtract instances. For example, when I have pair (A,B) and pair (B,A), I should only accept one. This is simple enough to find every pair, but I need the count of how many pairs I need based on N. This should be easy. I can *almost* wrap my head around it and that's - it's something like N*N/2 or maybe N*(N-1) I think. But it's weird to check it. I hate problems like this.
Real programmers use butterflies
You may find this useful: Permutations, Combinations, and Variations using C# Generics[^] I use his code in a couple of projects, and the explanations are pretty good.
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
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You may find this useful: Permutations, Combinations, and Variations using C# Generics[^] I use his code in a couple of projects, and the explanations are pretty good.
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
Ah thanks
Real programmers use butterflies
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Thanks actually. I just had someone on reddit clear it up for me. I'm crap at math/maths :~
Real programmers use butterflies
I can help you with math/maths. math/maths = 1/s
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I wasn't being very clear. I can't use a brute force method of iteration to check it because I actually want to use the resulting formula to check *that* against, if that makes sense.
Real programmers use butterflies
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It's kind of funny how my mind works. I'm great at some things, like I can think in several levels of abstraction at once, which helps immensely with coding. And simple arithmetic like pointer math I'm good at, as well as sets (usually though I still get tripped up sometimes) and (related) lambda calculus. However, go to geometry or anything non-trivial in algebra and you lose me. Plus there are gaping holes in my knowledge due to my lack of schooling. I didn't even know trig was based around triangles until my 20s. :laugh:
Real programmers use butterflies
For me, the trick to making math click was realizing the tools themselves are actually pretty simple. It's just specific examples/problems that make them look complex. Like an integral in its basic form is just the summation of a bunch of rectangular area calculations. So integral_{a}^{b} (2x * 1dx) just means "from a to b, add up all the rectangles with a height of 2x units and a width of 1 unit." The "dx" is just there to let you know what the independent variable is. What you're integrating "with respect to." Line and surface integrals are just taking this same idea, and using geometry to figure out what the "1" should be since we're not doing the integral with respect to the x-axis anymore. Not trying to pressure you into learning more math, I just think schools do a generally poor job at really teaching the basics. I mostly just memorized how to solve problems for a long time because that's what schools teach, but it wasn't until the why of the "how" clicked that I actually started enjoying math.
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For me, the trick to making math click was realizing the tools themselves are actually pretty simple. It's just specific examples/problems that make them look complex. Like an integral in its basic form is just the summation of a bunch of rectangular area calculations. So integral_{a}^{b} (2x * 1dx) just means "from a to b, add up all the rectangles with a height of 2x units and a width of 1 unit." The "dx" is just there to let you know what the independent variable is. What you're integrating "with respect to." Line and surface integrals are just taking this same idea, and using geometry to figure out what the "1" should be since we're not doing the integral with respect to the x-axis anymore. Not trying to pressure you into learning more math, I just think schools do a generally poor job at really teaching the basics. I mostly just memorized how to solve problems for a long time because that's what schools teach, but it wasn't until the why of the "how" clicked that I actually started enjoying math.
I have to learn the "why"s first or I don't retain anything. My associative memory is great, so if I understand how something works I can remember it, but the rest of my memory is pretty terrible. I wish I could learn the other ways too.
Real programmers use butterflies
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I need to permutate for every combination of 2 colors in a palette. More specifically I need to compute the size of this. It would normally be N*N I think where N is the number of colors in the palette Except I need to subtract instances. For example, when I have pair (A,B) and pair (B,A), I should only accept one. This is simple enough to find every pair, but I need the count of how many pairs I need based on N. This should be easy. I can *almost* wrap my head around it and that's - it's something like N*N/2 or maybe N*(N-1) I think. But it's weird to check it. I hate problems like this.
Real programmers use butterflies
These will be the triangular numbers: Triangular number - Wikipedia[^] Gives the formula: count = n(n+1)/2
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Thanks actually. I just had someone on reddit clear it up for me. I'm crap at math/maths :~
Real programmers use butterflies
One of Neil deGrasse Tyson's quotes comes to mind here. You know? The one that ends with "illiterate dolt".. :-D Obviously doesn't apply to ya, but the reminder has left me laughing and the cat looking at me with a "wtf did you wake me up for?" look. Thanks :thumbsup:
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Brute force?! So the argument in favour of
N(N-1)does not convince you? [update] It definitely did not convince Caslen :laugh: :laugh: :laugh: [/update]"In testa che avete, Signor di Ceprano?" -- Rigoletto
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I could be wrong but... shouldn't it be N(N-1)/2 to get the unique combinations? (ie discarding one of AB or BA combinations as required in the OP)
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In fact, you are right and I was wrong :-O It is
C(N,k) = N! / ((N-k)! k! )
with
k=2."In testa che avete, Signor di Ceprano?" -- Rigoletto
