#212EasyMatrix· Spiral Traversal with Shrinking Borders

Spiral Seat Numbers

A concert hall has `rows` rows of seats and `cols` seats in every row. Each seat carries a printed number, and the numbers are given as a grid: `grid[r][c]` is the number on the seat in row `r`, column `c`, counted from the top-left corner. At the end of the night an usher collects the programmes in a clockwise spiral. She starts at the top-left seat, walks right along the first row, then down the last column, then left along the last row, then up the first column, and keeps winding inwards until every seat has been visited exactly once. Return the seat numbers in the order the usher visits them.

Input format

`grid`: a non-empty rectangular grid of integers.

Output format

An array with every value of the grid, in clockwise spiral order starting at the top-left cell.

Examples

Input: grid = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

Output: [1, 2, 3, 6, 9, 8, 7, 4, 5]

Right along the top (1, 2, 3), down the right edge (6, 9), left along the bottom (8, 7), up the left edge (4) and finally the single middle seat 5.

Input: grid = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]

Output: [1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7]

The first lap visits 1 2 3 4, 8 12, 11 10 9 and 5. The second lap only has the middle row left: 6 and 7.

Input: grid = [[7], [8], [9]]

Output: [7, 8, 9]

A single column: the usher walks straight down. The border logic must not visit the same seat twice on the way back up.

Constraints

1 <= grid.length, grid[0].length <= 100
All rows have the same length.
-1000 <= grid[r][c] <= 1000

#matrix
#simulation
#traversal
#arrays