为具有n个元素并为其比例指定范围的表找到最佳的列和行大小 [英] Finding the optimum column and row size for a table with n elements and a given range for its proportion

问题描述

我正在寻找一种由n个元素创建表格的最佳方法，以使理想情况下没有空单元格，但与此同时，表格尺寸的列/行的比例应尽可能接近1. >

当然，如果n是一个平方数，那么从那以后很容易

cols = rows = sqrt( n );

如果n是素数，则很明显会有空单元格，所以我目前的处理方式是:

rows = floor( sqrt(n) );
cols = ceil( n / rows  );

对于所有其他情况，我的计划是获取n的素因子，然后搜索其组合的比例最接近1的那些可能的排列.

所以我的问题是:是否有更好的方法来做到这一点?还是至少有一种方法不必测试主要因素的每种可能组合?

解决方案

不是进行素数分解n，而是从平方根开始并查找下一个较大的(或较小的-无差异)因数.这对因子将最接近平方根，因此最接近1:1的比例.

I am looking for an optimum way to create a table from n elements so that ideally there are no empty cells, but at the same time the proportion of the table dimensions columns / rows becomes as close to 1 as possible.

Of course if n is a square number it is easy since then

cols = rows = sqrt( n );

If n is a prime number it is also clear that there will be empty cells, so my current way to handle this is:

rows = floor( sqrt(n) );
cols = ceil( n / rows  );

For all other cases my plan is to get the prime factors of n and then search all possible permutations for those whose combination has proportions closest to 1.

So my question is: is there is a better way to do this? Or is there at least a way not having to test every possible combination of the prime factors?

解决方案

Instead of doing a prime factorization of n, start from the square root and find the next larger (or smaller -- makes no difference) factor. That pair of factors will the closest to the square root, and therefore the closest to a proportion of 1:1.

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