Hello, Go programmer! Are you ready to embark on an intriguing coding journey? In this lesson, we're going to explore special traversals of matrices in Go. Matrices are rectangular 2D arrays, where each inner array maintains the same size. We'll navigate a matrix by zigzagging through columns, climbing up and down. Sound exciting? Buckle up, then, and get ready!

Here's the task: You've been given a 2D slice consisting of individual cells, each holding a unique integer value. Your goal is to create a function that will traverse this matrix, starting at the bottom-right cell. From there, you'll travel up to the top of the same column, then move left to the next column, and continue downward from the top of this new column. After reaching the bottom of the column, you'll again move left and start moving upward. This unique traversal pattern will be performed until all the cells have been visited.

Consider this small 3x4 matrix as an example:

Go
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1matrix := [][]int{
2    {1, 2, 3, 4},
3    {5, 6, 7, 8},
4    {9, 10, 11, 12},
5}

With the described traversal pattern, your function should return this list: [12, 8, 4, 3, 7, 11, 10, 6, 2, 1, 5, 9].

The first step toward a solution is understanding the dimensions of the matrix with which we're working. We can do this using Go's built-in functions to determine the length of slices. Let's set up our function and identify the matrix size:

Go
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1package main
2
3import "fmt"
4
5func ColumnTraverse(matrix [][]int) []int {
6    rows := len(matrix)
7    cols := len(matrix[0])
8    return nil
9}

Now that we're aware of the matrix dimensions, we should establish the starting point (bottom-right) and the direction of travel (upward initially). Additionally, we'll need a slice to keep track of the cells we've visited in order.

Go
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1package main
2
3import "fmt"
4
5func ColumnTraverse(matrix [][]int) []int {
6    rows := len(matrix)
7    cols := len(matrix[0])
8    direction := "up"
9    row := rows - 1
10    col := cols - 1
11    output := make([]int, 0, rows*cols)
12    index := 0
13
14    return output
15}

It's time to go exploring! We'll now implement a for loop to traverse the matrix. This loop will continue until we have covered all the cells in the matrix. As we "visit" each cell, we'll add the value in the cell to our slice.

Go
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1package main
2
3import "fmt"
4
5func ColumnTraverse(matrix [][]int) []int {
6    rows := len(matrix)
7    cols := len(matrix[0])
8    direction := "up"
9    row := rows - 1
10    col := cols - 1
11    output := make([]int, 0, rows*cols)
12    index := 0
13
14    for index < rows*cols {
15        output = append(output, matrix[row][col])
16        index++
17
18        if direction == "up" {
19            if row-1 < 0 {
20                direction = "down"
21                col--
22            } else {
23                row--
24            }
25        } else {
26            if row+1 == rows {
27                direction = "up"
28                col--
29            } else {
30                row++
31            }
32        }
33    }
34
35    return output
36}
37
38func main() {
39    matrix := [][]int{
40        {1, 2, 3, 4},
41        {5, 6, 7, 8},
42        {9, 10, 11, 12},
43    }
44
45    result := ColumnTraverse(matrix)
46    for _, num := range result {
47        fmt.Print(num, " ")
48    }
49}

Let's explore one more way of traversal. We can leverage Go's for loop to traverse a 2D slice in reverse order. This capability can also create a sequence that decrements.

Consider our familiar 3x4 matrix:

Go
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1matrix := [][]int{
2    {1, 2, 3, 4},
3    {5, 6, 7, 8},
4    {9, 10, 11, 12},
5}

Using decrementing loops, the reverse traverse pattern would produce this list: {12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}.

Here's how we can implement this reverse traversal:

Go
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1package main
2
3import "fmt"
4
5func ReverseTraverse(matrix [][]int) []int {
6    rows := len(matrix)
7    cols := len(matrix[0])
8    output := make([]int, 0, rows*cols)
9    index := 0
10
11    for row := rows - 1; row >= 0; row-- {
12        for col := cols - 1; col >= 0; col-- {
13            output = append(output, matrix[row][col])
14            index++
15        }
16    }
17
18    return output
19}
20
21func main() {
22    matrix := [][]int{
23        {1, 2, 3, 4},
24        {5, 6, 7, 8},
25        {9, 10, 11, 12},
26    }
27
28    result := ReverseTraverse(matrix)
29    for _, num := range result {
30        fmt.Print(num, " ")
31    }
32}

In this function, we start the loop for row from rows - 1 and run it to 0, decrementing it at each step. Similarly, our nested loop for col starts from cols - 1 and goes to 0. This allows us to start from the bottom-right corner and traverse leftward, then upward, covering the entire matrix in reverse order.

Congratulations! You have successfully navigated your way through complex matrix traversal patterns in Go. The functions you've designed test your Go coding skills and your ability to visualize spatial patterns.

It's time to put your new knowledge to the test! The next step is to tackle similar challenges on your own. I encourage you to use this lesson as your guide, and don't forget to experiment with different matrix sizes and cell values. With plenty of practice, you'll soon master these traversal patterns in Go!