Problem Description

You need to enhance JavaScript/TypeScript arrays with a new method called snail(rowsCount, colsCount) that transforms a 1D array into a 2D array following a specific "snail traversal" pattern.

The snail traversal pattern works as follows:

• Start at the top-left cell (position [0][0])
• Move down through the entire first column from top to bottom
• Move to the next column and traverse it from bottom to top
• Continue alternating the direction (down, up, down, up...) for each subsequent column
• Fill the 2D array with values from the original 1D array in order

Input Validation:

• If rowsCount * colsCount does not equal the length of the input array, return an empty array []

Example: Given array [19, 10, 3, 7, 9, 8, 5, 2, 1, 17, 16, 14, 12, 18, 6, 13, 11, 20, 4, 15] with rowsCount = 5 and colsCount = 4:

The resulting 2D array would be:

[[19, 8, 16, 13],
 [10, 5, 14, 11],
 [3,  2, 12, 20],
 [7,  1, 18, 4],
 [9, 17, 6,  15]]

Following the snail pattern:

• Column 0: 19→10→3→7→9 (downward)
• Column 1: 17→1→2→5→8 (upward)
• Column 2: 16→14→12→18→6 (downward)
• Column 3: 13→11→20→4→15 (upward)

Intuition

The key insight is that we're filling a 2D array column by column, but the direction alternates for each column. When we visualize this pattern, we notice:

1. We always move vertically within a column (never horizontally within a row)
2. For even-numbered columns (0, 2, 4...), we move downward (row index increases)
3. For odd-numbered columns (1, 3, 5...), we move upward (row index decreases)

This suggests we need a direction indicator that flips between moving down (+1) and moving up (-1) each time we complete a column.

The traversal can be tracked with just a few variables:

• i for the current row position
• j for the current column position
• k as the direction multiplier (+1 for down, -1 for up)
• h as the index in the original 1D array

The clever part is detecting when we've hit a boundary. When moving down, we hit the boundary at row rowsCount. When moving up, we hit the boundary at row -1. In both cases:

• We need to undo the last row increment/decrement (hence i -= k)
• Flip the direction (k = -k)
• Move to the next column (++j)

This approach elegantly handles the snaking pattern without needing complex conditional logic or tracking which column we're in. The direction automatically alternates as we progress through columns, creating the desired snail traversal pattern.

Solution Approach

The implementation uses a straightforward iterative approach with intelligent direction control:

1. Input Validation:

if (rowsCount * colsCount !== this.length) {
    return [];
}

First check if the dimensions are valid. If the product of rows and columns doesn't match the array length, return an empty array.

2. Initialize the Result Matrix:

const ans: number[][] = Array.from({ length: rowsCount }, () => Array(colsCount));

Create a 2D array with rowsCount rows and colsCount columns using Array.from().

3. Core Traversal Logic:

for (let h = 0, i = 0, j = 0, k = 1; h < this.length; ++h) {
    ans[i][j] = this[h];
    i += k;
    if (i === rowsCount || i === -1) {
        i -= k;
        k = -k;
        ++j;
    }
}

The algorithm maintains four variables:

• h: Index for traversing the original 1D array (0 to length-1)
• i: Current row position in the 2D array
• j: Current column position in the 2D array
• k: Direction multiplier (+1 for moving down, -1 for moving up)

Step-by-step execution:

1. Place the current element from the 1D array at position [i][j] in the 2D array
2. Move to the next row by adding k to i (either +1 or -1)
3. Check if we've hit a boundary:
   • i === rowsCount: Reached bottom boundary while moving down
   • i === -1: Reached top boundary while moving up
4. When a boundary is hit:
   • Undo the last move: i -= k (step back into valid range)
   • Reverse direction: k = -k (flip between +1 and -1)
   • Move to next column: ++j

Example Walkthrough: For array [1,2,3,4,5,6] with rowsCount=3, colsCount=2:

• Start at [0][0], k=1 (moving down)
• Fill column 0: [0][0]=1, [1][0]=2, [2][0]=3
• Hit bottom (i=3), reverse to i=2, flip k=-1, move to column 1
• Fill column 1: [2][1]=4, [1][1]=5, [0][1]=6
• Result: [[1,6],[2,5],[3,4]]

This elegant solution handles the snail pattern without explicitly tracking even/odd columns or using nested loops.

Example Walkthrough

Let's walk through a small example with array [1,2,3,4,5,6,7,8] where rowsCount=2 and colsCount=4.

Initial Setup:

• Create a 2×4 matrix (2 rows, 4 columns)
• Variables: h=0 (array index), i=0 (row), j=0 (column), k=1 (direction: down)

Column 0 (moving down, k=1):

• h=0: Place 1 at [0][0], move to row i=0+1=1
• h=1: Place 2 at [1][0], move to row i=1+1=2
• Hit bottom boundary (i=2 equals rowsCount)!
  • Step back: i=2-1=1
  • Flip direction: k=-1
  • Next column: j=1

Column 1 (moving up, k=-1):

• h=2: Place 3 at [1][1], move to row i=1-1=0
• h=3: Place 4 at [0][1], move to row i=0-1=-1
• Hit top boundary (i=-1)!
  • Step back: i=-1-(-1)=0
  • Flip direction: k=1
  • Next column: j=2

Column 2 (moving down, k=1):

• h=4: Place 5 at [0][2], move to row i=0+1=1
• h=5: Place 6 at [1][2], move to row i=1+1=2
• Hit bottom boundary again!
  • Step back: i=1
  • Flip direction: k=-1
  • Next column: j=3

Column 3 (moving up, k=-1):

• h=6: Place 7 at [1][3], move to row i=1-1=0
• h=7: Place 8 at [0][3], done!

Final Result:

[[1, 4, 5, 8],
 [2, 3, 6, 7]]

The snail pattern traversal:

• Column 0: 1→2 (down)
• Column 1: 3→4 (up)
• Column 2: 5→6 (down)
• Column 3: 7→8 (up)

Notice how the direction automatically alternates between columns without any explicit even/odd checking - the boundary detection and direction flip mechanism handles it elegantly!

Solution Implementation

Time and Space Complexity

Time Complexity: O(n) where n is the length of the input array.

The algorithm iterates through each element of the input array exactly once in the for loop. The loop runs from h = 0 to h < this.length, processing one element per iteration. Inside the loop, all operations (array assignment, increment/decrement, and conditional checks) are O(1) operations. Therefore, the overall time complexity is linear with respect to the input size.

Space Complexity: O(n) where n is the length of the input array.

The space complexity consists of:

• The output array ans which is a 2D array with dimensions rowsCount × colsCount. Since rowsCount * colsCount must equal this.length (or the function returns early), the total space for ans is O(n).
• A few constant variables (h, i, j, k) which take O(1) space.

The total space complexity is therefore O(n) + O(1) = O(n).

Note that this analysis excludes the input array itself, as is standard practice when analyzing space complexity (only counting auxiliary space).

Common Pitfalls

1. Off-by-One Error in Boundary Checking

The Pitfall: A common mistake is checking the boundary condition after placing the element, or incorrectly handling the boundary reversal logic. Developers might write:

# WRONG: Checking boundary after placement and increment
while array_index < len(arr):
    result_matrix[current_row][current_col] = arr[array_index]
    array_index += 1
    current_row += row_direction
  
    if current_row >= rows_count:  # Wrong comparison operator
        current_row = rows_count - 1  # Wrong adjustment
        row_direction = -row_direction
        current_col += 1

This leads to index out of bounds errors or incorrect placement of elements.

The Solution: Always increment the row position first, then check if it's out of bounds (exactly == rows_count or exactly == -1), and if so, undo the increment before changing direction:

current_row += row_direction
if current_row == rows_count or current_row == -1:
    current_row -= row_direction  # Undo the move
    row_direction = -row_direction
    current_col += 1

2. Incorrect Column Advancement Logic

The Pitfall: Developers might advance the column every iteration or forget to advance it when hitting boundaries:

# WRONG: Advancing column in every iteration
while array_index < len(arr):
    result_matrix[current_row][current_col] = arr[array_index]
    current_row += row_direction
    current_col += 1  # Wrong: shouldn't advance every time

The Solution: Only advance to the next column when you hit a row boundary (top or bottom):

if current_row == rows_count or current_row == -1:
    current_row -= row_direction
    row_direction = -row_direction
    current_col += 1  # Only advance column at boundaries

3. Forgetting to Handle Edge Cases

The Pitfall: Not properly handling special cases like single row or single column matrices:

# This might fail for rows_count=1 or cols_count=1
# because the direction reversal logic assumes multiple rows

The Solution: The provided algorithm naturally handles these edge cases because:

• For a single row (rows_count=1): After placing the first element at [0][0], current_row becomes 1, triggers the boundary condition, gets reset to 0, and moves to the next column
• For a single column (cols_count=1): The algorithm fills down the entire column without ever needing to reverse

4. Inefficient Matrix Initialization

The Pitfall: Using append operations or dynamically growing the matrix:

# INEFFICIENT: Building matrix dynamically
result_matrix = []
for i in range(rows_count):
    result_matrix.append([])

The Solution: Pre-allocate the entire matrix at once:

result_matrix = [[0 for _ in range(cols_count)] for _ in range(rows_count)]

5. Mixing Up Row and Column Indices

The Pitfall: Accidentally swapping row and column indices when accessing the matrix:

# WRONG: Swapped indices
result_matrix[current_col][current_row] = arr[array_index]

The Solution: Always remember that in a 2D array, the first index is the row and the second is the column:

result_matrix[current_row][current_col] = arr[array_index]