最接近一定的价值公约数逼近？ [英] Approximation of a common divisor closest to some value?

问题描述

假设我们有两个数（不一定是整数） X1 和 X2 。这样说来，用户输入一个数是。我想找到，是一个数 Y'靠近是让 X1％ Y'和 X2％Y 非常小（小于 0.02 ，例如小，但让拨打此号码限制）。换句话说，我并不需要一个最佳的算法，但是一个很好的近似。

Say we have two numbers (not necessarily integers) x1 and x2. Say, the user inputs a number y. What I want to find, is a number y' close to y so that x1 % y' and x2 % y' are very small (smaller than 0.02, for example, but lets call this number LIMIT). In other words, I don't need an optimal algorithm, but a good approximation.

我感谢大家的时间和精力，这真有种！

I thank you all for your time and effort, that's really kind!

让我解释一下这个问题是在我的应用程序是什么的：说了，屏幕大小，给出的宽度屏幕宽度和高度对 screenHeight （像素）。我填充屏幕的长度 Y'的平方。再说了，用户希望平方大小为是。如果是不是屏幕宽度和/或 screenHeight ，将有在屏幕，没有足够大，以适应正方形的侧面的未使用的空间。如果未使用的空间很小（例如一行像素），它不是那么糟糕，但如果它不是，也不会好看。我怎样才能找到共同的除数屏幕宽度和 screenHeight ？

Let me explain what the problem is in my application : say, a screen size is given, with a width of screenWidth and a height of screenHeight (in pixels). I fill the screen with squares of a length y'. Say, the user wants the square size to be y. If y is not a divisor of screenWidth and/or screenHeight, there will be non-used space at the sides of the screen, not big enough to fit squares. If that non-used space is small (e.g. one row of pixels), it's not that bad, but if it's not, it won't look good. How can I find common divisors of screenWidth and screenHeight?

推荐答案

我看不出你如何能确保X1％Y'和x2％Y'均低于一定的价值 - 如果X1是素数，没有任何事情以低于你的限制（如限制为小于1），除了X1（或非常接近）和1。

I don't see how you can ensure that x1%y' and x2%y' are both below some value - if x1 is prime, nothing is going to be below your limit (if the limit is below 1) except x1 (or very close) and 1.

所以永远奏效的唯一答案是微不足道的Y'= 1。

So the only answer that always works is the trivial y'=1.

如果您允许非整数的除数，然后随便挑Y'= 1 /（X1 * X2），因为其余始终为0。

If you are permitting non-integer divisors, then just pick y'=1/(x1*x2), since the remainder is always 0.

在不限制公约数为整数，它可以是任何东西，而整个最大公约数的概念就走出了窗外。

Without restricting the common divisor to integers, it can be anything, and the whole 'greatest common divisor' concept goes out the window.

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