Magic Spiral [javascript, rust]

For a given number: generate an array with numeric values, those values should be stored in an ascendant mode following an spiral figure.

Examples:

n = 3

7	8	9
6	1	2
5	4	3

n = 2

1	2
4	3

n = 1

|1|

n = 4

7	8	9	10
6	1	2	11
5	4	3	12
16	15	14	13

Usage

Node [javascript]

node ./src/js/index.js [number]

Passing 2 as argument

node ./src/js/index.js 2

Rust

Compiling the code

rust src/rust/rust.rs

Passing 2 as argument

./src/rust/rust 2

Execute with bash/batch scripts:

// windows:
./src/rust/compile_run.bat 2

// Linux:
./src/rust/compile_run.sh 2

Generated

1	2
4	3

Problem Solving

Basically, the easy way to solve the prolem is to realize that a magic spiral contains only "L figures". Exists two kinds of "L" Figures: Upper and Lower.

Every L figure is composed by a Column and a Row. The Only Difference between Upper L and Lower L, it's the order of the numeric values.

Upper L figures

The numbers in the column are in descendant mode:

[7]
[6]
[5]

The numbers in the row are in ascendant mode.

[ 7][ 8][ 9]

The final array looks like this:

 [ 7][ 8][ 9]
 [ 6][  ][  ]
 [ 5][  ][  ]

Lower L figures Columns are generated in Ascending order, and are push to the end of the array.

 [10]
 [11]
 [12]
 [13]

Rows are generated in descending mode and ar push to the end of the array.

 [16][15][14][13]

The final array looks like this:

 [  ][  ][  ][10] 
 [  ][  ][  ][11]
 [  ][  ][  ][12]
 [16][15][14][13]

Merging ecach L figure of the Matrix

The problem is solved using an iterative approach.

The spiral is divided in sub spirals. if n=3, then we have to generate spiral for 1, spiral for 2 and spiral for 3. And then merge the generated matrix. Every subspiral is named "L" Figure:

For every subspiral (L figure) we need to create a new array and merge it with the previous generated array.

Remember: exists two kinds of L Figures: UP and DOWN!

Upside L: Iterates over the size of matrix to be merged Takes the base array, and add 1 to x and y axis in the base array to reallocate the merged array values.

Downside L: Iterates over the size of matrix to be merged. Takes the base array and maps exactly x and y with the array to be merged.

Example:

n=2

1	2
4	3

Generate Column

	2
	3

Generate Row


4

Merge Columnd and Row and generate a new matrix

	2
4	3

Merge previous Matrix

Previous matrix:

| 1 |

Current Matrix (it's a downside matrix):

	2
4	3

previous matrix size: 1

for (let ty = 0; ty < size - 1; ty++) {
    for (let tx = 0; tx < size - 1; tx++) {
        if (direction == "UP") {
            base[ty + 1][tx + 1] = arr[ty][tx];
        } else if (direction == "DOWN") {
            base[ty][tx] = arr[ty][tx];
        }
    }
}

Merged Matrix: