算法多维数组转换成一个一维阵列 [英] Algorithm to convert a multi-dimensional array to a one-dimensional array

问题描述

这是很容易二维数组转换成一维数组，但我怎么能转换成一个多维超过2维数组一维数组？例如，假设我是int [5] [5] [5]×和int [125] y和我想要放置在x值[3] [4] [2] y中的正确的地方？

It's easy enough to convert a 2-dimensional array to a single-dimensional array but how can I convert a multi-dimensional array of more than 2 dimensions to a one-dimensional array? For example, let's assume I have int [5][5][5] x and int [125] y and I want to place the value at x[3][4][2] in its right place in y?

希望是有道理的。

推荐答案

一对夫妇在技术上很好的答案已经在这里，但这里的理解成为一个更直观的方式......

A couple of technically good answers here already, but here's a more visual way of understanding it...

好了，你知道如何从一维的情况下进入2维的情况。

OK, so you know how to go from the 1-dimensional case to the 2-dimensional case.

一维数组看起来是这样的：

A 1-D array looks like this:

int [5] :

+-----+-----+-----+-----+-----+
|  0  |  1  |  2  |  3  |  4  |
|     |     |     |     |     |
+-----+-----+-----+-----+-----+

和一个二维数组是这样的：

And a 2-D array looks like this:

int [5][5] :

+-----+-----+-----+-----+-----+     
| 0,0 | 0,1 | 0,2 | 0,3 | 0,4 |     
|     |     |     |     |     |     
+-----+-----+-----+-----+-----+     
| 1,0 | 1,1 | 1,2 | 1,3 | 1,4 |     
|     |     |     |     |     |     
+-----+-----+-----+-----+-----+     
| 2,0 | 2,1 | 2,2 | 2,3 | 2,4 | 
|     |     |     |     |     |     
+-----+-----+-----+-----+-----+     
| 3,0 | 3,1 | 3,2 | 3,3 | 3,4 |     
|     |     |     |     |     |     
+-----+-----+-----+-----+-----+     
| 4,0 | 4,1 | 4,2 | 4,3 | 4,4 |     
|     |     |     |     |     |     
+-----+-----+-----+-----+-----+     

您的可以的图片转化成这样相应的一维数组：

You could picture the conversion to the corresponding 1-D array like this:

+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+- - -
| 0,0 | 0,1 | 0,2 | 0,3 | 0,4 | 1,0 | 1,1 | 1,2 | 1,3 | 1,4 | etc.
|     |     |     |     |     |     |     |     |     |     |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+- - -
                             vvv
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+- - -
|  0  |  1  |  2  |  3  |  4  |  5  |  6  |  7  |  8  |  9  | etc.
|     |     |     |     |     |     |     |     |     |     |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+- - -

但考虑它的另一种方式是将画面中的原始数组，但重新标记 - 是这样的：

But an alternative way of thinking about it is to picture the original array, but re-labelled - like this:

int [5][5] :

+-----+-----+-----+-----+-----+     +-----+-----+-----+-----+-----+
| 0,0 | 0,1 | 0,2 | 0,3 | 0,4 |     |  0  |  1  |  2  |  3  |  4  |
|     |     |     |     |     |     |     |     |     |     |     |
+-----+-----+-----+-----+-----+     +-----+-----+-----+-----+-----+
| 1,0 | 1,1 | 1,2 | 1,3 | 1,4 |     |  5  |  6  |  7  |  8  |  9  |
|     |     |     |     |     |     |     |     |     |     |     |
+-----+-----+-----+-----+-----+     +-----+-----+-----+-----+-----+
| 2,0 | 2,1 | 2,2 | 2,3 | 2,4 | =>  | 10  | 11  | 12  | 13  | 14  |
|     |     |     |     |     |     |     |     |     |     |     |
+-----+-----+-----+-----+-----+     +-----+-----+-----+-----+-----+
| 3,0 | 3,1 | 3,2 | 3,3 | 3,4 |     | 15  | 16  | 17  | 18  | 19  |
|     |     |     |     |     |     |     |     |     |     |     |
+-----+-----+-----+-----+-----+     +-----+-----+-----+-----+-----+
| 4,0 | 4,1 | 4,2 | 4,3 | 4,4 |     | 20  | 21  | 22  | 23  | 24  |
|     |     |     |     |     |     |     |     |     |     |     |
+-----+-----+-----+-----+-----+     +-----+-----+-----+-----+-----+

2-D array index [i][j]          =>  1-D array index [i*5 + j]

...如果你想想这样，3维的情形只是遵循相同的原则（等更高层面 - 它只是越来越难想象！）：

...and if you think about it this way, the 3-dimensional case just follows the same principle (and so on for higher dimensions - it just gets harder and harder to visualise!):

int [5][5][5] :

+-----+-----+-----+-----+-----+         +-----+-----+-----+-----+-----+
|+-----+-----+-----+-----+-----+        |+-----+-----+-----+-----+-----+
||+-----+-----+-----+-----+-----+       ||+-----+-----+-----+-----+-----+
|||+-----+-----+-----+-----+-----+      |||+-----+-----+-----+-----+-----+
||||1,0,0|1,0,1|1,0,2|1,0,3|1,0,4|      |||| 25  | 26  | 27  | 28  | 29  |
||||   +-----+-----+-----+-----+-----+  ||||   +-----+-----+-----+-----+-----+
|||+---|0,0,0|0,0,1|0,0,2|0,0,3|0,0,4|  |||+---|  0  |  1  |  2  |  3  |  4  |
||||1,1|     |     |     |     |     |  |||| 30|     |     |     |     |     |
||||   +-----+-----+-----+-----+-----+  ||||   +-----+-----+-----+-----+-----+
|||+---|0,1,0|0,1,1|0,1,2|0,1,3|0,1,4|  |||+---|  5  |  6  |  7  |  8  |  9  |
||||1,2|     |     |     |     |     |  |||| 35|     |     |     |     |     |
||||   +-----+-----+-----+-----+-----+  ||||   +-----+-----+-----+-----+-----+
|||+---|0,2,0|0,2,1|0,2,2|0,2,3|0,2,4|=>|||+---| 10  | 11  | 12  | 13  | 14  |
||||1,3|     |     |     |     |     |  |||| 40|     |     |     |     |     |
||||   +-----+-----+-----+-----+-----+  ||||   +-----+-----+-----+-----+-----+
+||+---|0,3,0|0,3,1|0,3,2|0,3,3|0,3,4|  +||+---| 15  | 16  | 17  | 18  | 19  |
 +||1,4|     |     |     |     |     |   +|| 45|     |     |     |     |     |
  +|   +-----+-----+-----+-----+-----+    +|   +-----+-----+-----+-----+-----+
   +---|0,4,0|0,4,1|0,4,2|0,4,3|0,4,4|     +---| 20  | 21  | 22  | 23  | 24  |
       |     |     |     |     |     |         |     |     |     |     |     |
       +-----+-----+-----+-----+-----+         +-----+-----+-----+-----+-----+

3-D array index [i][j][k]             =>  1-D array index [i*5*5 + j*5 + k]

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