分区一个矩形接近正方形给定的区域 [英] Partition a rectangle into near-squares of given areas

问题描述

我有一组的 N 的正数，和尺寸的长方形的 X 和是的，我需要分成的 ñ的小矩形，使得：

I have a set of N positive numbers, and a rectangle of dimensions X and Y that I need to partition into N smaller rectangles such that:

• 每个较小矩形的表面面积成正比对应的号码，在给定的
• 在大矩形的所有空间被占用，还有更小的矩形之间没有多余的空间，
• 在每个小矩形的形状应尽量接近正方形，可行
• 执行时间应该是相当小

我需要在这个方向。你知道这种在网络上描述的算法？你有什么想法（伪code是罚款）？

I need directions on this. Do you know of such an algorithm described on the web? Do you have any ideas (pseudo-code is fine)?

感谢。

推荐答案

你描述像树形的声音是什么：

What you describe sounds like a treemap:

树图显示层次结构（树状结构）的数据为一组嵌套的矩形。树的每个分支都有一个矩形，然后将其与更小的矩形重新presenting支行瓷砖。叶节点的矩形的面积成比例的数据指定维度

Treemaps display hierarchical (tree-structured) data as a set of nested rectangles. Each branch of the tree is given a rectangle, which is then tiled with smaller rectangles representing sub-branches. A leaf node's rectangle has an area proportional to a specified dimension on the data.

这是维基百科页面链接到本·施奈德曼，这给出了一个很好的页面概述和链接的Java实现：

That Wikipedia page links to a page by Ben Shneiderman, which gives a nice overview and links to Java implementations:

然后同时在教师休息室纳闷这一点，我有啊哈！分割屏幕分成矩形交替水平和垂直方向为向下遍历的经验水平。这个递归算法似乎有吸引力，但我花了几天来说服自己，它会一直工作，并写了六线算法。

Then while puzzling about this in the faculty lounge, I had the Aha! experience of splitting the screen into rectangles in alternating horizontal and vertical directions as you traverse down the levels. This recursive algorithm seemed attractive, but it took me a few days to convince myself that it would always work and to write a six line algorithm.

维基百科也正方树图由马克Bruls，基斯Huizing和Jarke J.面包车Wijk （PDF）是presents一种可能的算法：

Wikipedia also to "Squarified Treemaps" by Mark Bruls, Kees Huizing and Jarke J. van Wijk (PDF) that presents one possible algorithm:

我们怎样才能tesselate矩形递归成矩形，使得它们的纵横比（如最大（高/宽，宽/高））的方法1尽可能接近？所有可能tesselations的数量是非常大的。这个问题落在了NP难问题的范畴。然而，对于我们的应用，我们不需要的最优解，良好的解决方案   可在很短的时间来计算是必需的。

How can we tesselate a rectangle recursively into rectangles, such that their aspect-ratios (e.g. max(height/width, width/height)) approach 1 as close as possible? The number of all possible tesselations is very large. This problem falls in the category of NP-hard problems. However, for our application we do not need the optimal solution, a good solution that can be computed in short time is required.

您没有提到的问题的任何递归，所以你的情况可能是树形图的只是一个级别;但由于算法的时间在一个水平上工作，这应该是没有问题的。

You do not mention any recursion in the question, so your situation might be just one level of the treemap; but since the algorithms work on one level at a time, this should be no problem.

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