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Does this equation have a name?by gamow99
Tags: equation 
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#1
Sep314, 06:07 PM

P: 4

I'm trying to figure out how many times my computer will have to loop through an array. I'm building a logic calculator so it's checking contradictions. If there are four sentences, a b c d, then one has to check the following combinations to see if there is a contradiction
ab ac ad bc bd cd The equation seems to be, let n = the number of sentences: (n  1) + (n  2) + (n  3) But that's not a good equation because it does not inform us how many things to add together. If there are six sentences then the equation would be (n  1) + (n  2) + (n  3) + (n  4) + (n  5) There has to be a better way to write that equation. 


#2
Sep314, 06:28 PM

P: 45

In probability, it looks like it would be written as 4 choose 2, meaning that you have 4 sentences and choose 2 of them. The equation gives the number of unique results (ab is the same as ba). Google "Combination".



#3
Sep614, 01:36 PM

P: 9

Hey, computer scientist here. Cool project you're working on. I stumbled across this pattern while messing around with tabular Kmap simplification (boolean logic):
You have 4 variables (but this can be generalized to n variables) and are trying to find the total number of associative expressions such that AB = BA. (Looping through for A AND B as well as B AND A would be inefficient) This problem is analogous to finding the number of lines between a given number of points (see below). The formula is $$ \frac{n^2n}{2} $$ Send me a PM: I'd like to take a closer look at your logic calculator. *plus sign changed to minus sign as per jz92's post 


#4
Sep614, 03:46 PM

P: 45

Does this equation have a name?
The general equation for evaluating the number of unique combinations when you select k items from a set of n items is:
$$ \frac{n!}{(nk)!*k!} $$ n choose 2 is $$ \frac{n!}{(n2)!*2!} $$ Simplified, it is: $$ \frac{n^2n}{2} $$ Comparing each combination of 2, where there are 4 sentences, comes out to a total of (164)/2, or 6 comparisons. This, of course, requires that the loops are set up in a way that you never test the same combination twice. 


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