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Understand n dimension array with real life examples


You are/were struggling with one of these terms: nested array, high dimension, n dimension array, ... Probably you have tried to visualize an n dimension array and got stuck at 3 dimension or even 2.

The simple way to understand

You don't need to visualize it. You just need to know that an n dimension array is a group of groups ... (many "of groups").

Let start with 1D array. 1D array is a group of values [1, 2, 3]. 2D array is a group of 1D groups [[1, 2, 3], [1, 2, 3]]. 3D array is a group of 2D groups [[[1, 2, 3], [1, 2, 3]], [[1, 2, 3], [1, 2, 3]]].

An n dimension array is also just a 1D array whose values are organized into groups. This is 1D array [1, 2, 3, 4, 5, 6]. Now we will group 123, and 456. By doing that, it becomes 2D array [[1, 2, 3], [4, 5, 6]]. Now we put each value into a group. As a result, 3D array is made [[[1], [2], [3]], [[4], [5], [6]]].

Every array has a very important attribute called shape. A shape is a set of the number of groups/values in each dimension (ordered from the highest dimension to the lowest one). Let visit the previous example. 1D array has 6 values or shape (6). 2D array has 2 groups, each group has 3 values. In other word, its shape is (2, 3). That 3D array has shape (2, 3, 1).

Real life example 1: A book

A book is a 5D array of letters whose shape is (c, p, s, w, l). A book has C chapters. Each chapter has P paragraphs. Each paragraph has S sentences. Each sentence has W words. Each word has L letters.

Real life example 2: A library

A library is a 7D array of letters. A library has G genres. Each genre has B books. And so on.

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