There are many ways to do just this, provided you are not concerned about reliance on the original decimal data. The first and perhaps most popular method would be the Largest Remainder Method Which is basically: Rounding everything down Getting the difference in sum and 100 Distributing the difference by adding 1 to items in … Read more
UPDATE: This question was the subject of my blog in January 2013. Thanks for the great question! Getting integer arithmetic correct is hard. As has been demonstrated amply thus far, the moment you try to do a “clever” trick, odds are good that you’ve made a mistake. And when a flaw is found, changing the … Read more
Remember that log(n!) = log(1) + log(2) + … + log(n-1) + log(n) You can get the upper bound by log(1) + log(2) + … + log(n) <= log(n) + log(n) + … + log(n) = n*log(n) And you can get the lower bound by doing a similar thing after throwing away the first half … Read more
Let’s say you want to scale a range [min,max] to [a,b]. You’re looking for a (continuous) function that satisfies f(min) = a f(max) = b In your case, a would be 1 and b would be 30, but let’s start with something simpler and try to map [min,max] into the range [0,1]. Putting min into … Read more
Using Math.floor() is one way of doing this. More information: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/floor
Will result always be the floor of the division? What is the defined behavior? Not quite. It rounds toward 0, rather than flooring. 6.5.5 Multiplicative operators 6 When integers are divided, the result of the / operator is the algebraic quotient with any fractional part discarded.88) If the quotient a/b is representable, the expression (a/b)*b … Read more
If you cannot come up with a formula, you can use a table for such a limited number of outcomes: final int[][] result = new int[][] { { 0, 0, 1, 2 }, { 0, 0, 2, 1 }, { 2, 1, 3, 3 }, { 1, 2, 3, 3 } }; return result[one][two];
All integers that can be represented by floating point numbers have an exact representation. So you can safely use int on the result. Inexact representations occur only if you are trying to represent a rational number with a denominator that is not a power of two. That this works is not trivial at all! It’s … Read more
The following program calculates nCr in an efficient manner (compared to calculating factorials etc.) import operator as op from functools import reduce def ncr(n, r): r = min(r, n-r) numer = reduce(op.mul, range(n, n-r, -1), 1) denom = reduce(op.mul, range(1, r+1), 1) return numer // denom # or / in Python 2 As of Python … Read more
There are quite a few projects that have settled on the Generic Graphics Toolkit for this. The GMTL in there is nice – it’s quite small, very functional, and been used widely enough to be very reliable. OpenSG, VRJuggler, and other projects have all switched to using this instead of their own hand-rolled vertor/matrix math. … Read more