数独箱指数起始位置 [英] Sudoku box indices start position

问题描述

我使用的是回溯实现一个数独解算器。它的形式读取数独板：

I'm implementing a sudoku solver using backtracking. It reads a sudoku board in the form:

<$c$c>027800061000030008910005420500016030000970200070000096700000080006027000030480007

我知道我该怎么做计算在列的元素索引％9 （然后做比9简单的等差数列），以及在一个元素通过使用行指数/ 9 （然后通过添加一个，直到我让他们每个人），其中index是一个数字的范围为[0,80]。

I know how I can figure the elements on a column by doing index % 9 (and then doing a simple arithmetic progression of ratio 9) as well the elements on a line by using index/9 (and then by adding one until I get every one of them), where index is a number in the range [0,80].

我无法弄清楚什么是如何得到一箱的起始索引，如果我有那个盒子元素的索引。

What I cannot figure out is how to get the starting index of a box if I have an element's index in that box.

所以，我用Google搜索，我得到：的 http://jakevdp.github.io/blog/2013/04/15/$c$c-golf-in-python-sudoku/

So I googled and I got: http://jakevdp.github.io/blog/2013/04/15/code-golf-in-python-sudoku/

这家伙越来越起始索引在一个盒子里是这样的：

This guy is getting the starting index in a box like this:

开始= 27 * INT（I / 27）+ 3 * INT（（I％9）/ 3） 其中，我是该指数在我的元素列表。

start = 27 * int(i / 27) + 3 * int((i % 9) / 3) Where i is the index in my list of elements.

我不明白他是怎么想通了，公式，我怎么能演绎出它自己，所以请解释给我。

I cannot understand how he figured out that formula and how can I deduce it myself, so please explain that to me.

据我所知，名单COM prehension自带这个公式后，这一切才有意义只是没有这个公式。

I understand the list comprehension that comes after this formula, it all makes sense just not this formula.

PS： 我写这篇文章的学习哈斯克尔，但它其实并不重要，因为现在我想要得到这个公式的要点。

PS: I write this to learn Haskell, but it really doesn't matter, since now I want to get the gist of that formula.

推荐答案

首页表示索引列表中。 blockRow ， blockCol 和 blockIndex 指行/列/该块开始索引。所有的部门是整数除法（四舍五入到下一个整数）。

index means index into your list. blockRow, blockCol and blockIndex refer to row/column/index of the block start. All divisions are integer divisions (rounding down to next integer).

index = row*9 + col

row = index / 9
col = index % 9

blockRow = (row / 3) * 3
blockCol = (col / 3) * 3

blockRow = (index / 9 / 3) * 3 = (index / 27) * 3
blockCol = (index % 9 / 3) * 3

blockIndex = (blockRow*9) + blockCol = ((index / 27) * 3 * 9) + (index % 9 / 3) * 3  = 
(index / 27) * 27 + 3 * (index % 9 / 3)

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