Decimal numbers can be represented exactly, if you have enough space – just not by floating binary point numbers. If you use a floating decimal point type (e.g. System.Decimal in .NET) then plenty of values which can’t be represented exactly in binary floating point can be exactly represented. Let’s look at it another way – … Read more
Some of the suggested methods will fail in the case of a non-convex polygon, such as a crescent. Here’s a simple one that will work with non-convex polygons (it’ll even work with a self-intersecting polygon like a figure-eight, telling you whether it’s mostly clockwise). Sum over the edges, (x2 − x1)(y2 + y1). If the … Read more
I assume entropy was mentioned in the context of building decision trees. To illustrate, imagine the task of learning to classify first-names into male/female groups. That is given a list of names each labeled with either m or f, we want to learn a model that fits the data and can be used to predict … Read more
Calculate the distance between two coordinates by latitude and longitude, including a Javascript implementation. West and South locations are negative. Remember minutes and seconds are out of 60 so S31 30′ is -31.50 degrees. Don’t forget to convert degrees to radians. Many languages have this function. Or its a simple calculation: radians = degrees * … Read more
Just a clarification Although the previous answers are right whenever you try to spot the randomness of a pseudo-random variable or its multiplication, you should be aware that while Random() is usually uniformly distributed, Random() * Random() is not. Example This is a uniform random distribution sample simulated through a pseudo-random variable: BarChart[BinCounts[RandomReal[{0, 1}, 50000], … Read more
You didn’t say what kind of language they expected… Here’s a static solution (Haskell). It’s basically messing with the 2 most significant bits: f :: Int -> Int f x | (testBit x 30 /= testBit x 31) = negate $ complementBit x 30 | otherwise = complementBit x 30 It’s much easier in a … Read more
Binary floating point math is like this. In most programming languages, it is based on the IEEE 754 standard. The crux of the problem is that numbers are represented in this format as a whole number times a power of two; rational numbers (such as 0.1, which is 1/10) whose denominator is not a power … Read more