Read a Matrix in a Spiral | Practice

You are given matrix, a grid of integers with m rows and n columns.

Return all of its values in spiral order: start at the top-left corner, go right along the top row, down the right column, left along the bottom row and up the left column, then carry on the same way round the part not yet read, until every value is listed exactly once.

Example 1

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

Read in spiral order, this grid counts from 1 to 12.

Example 2

Input: matrix = [[1, 2], [3, 4], [5, 6]]
Output: [1, 2, 4, 6, 5, 3]

Constraints

1 ≤ m, n ≤ 20
−1000 ≤ matrix[r][c] ≤ 1000

Show the pattern

Math and matrices

It is index arithmetic on a 2D layout: walk round the outer ring with four bounds (top, bottom, left, right), pull each bound in once its side is read, and repeat on the ring inside.

Show the approach

Keep four bounds around the part of the grid not read yet: top, bottom, left and right. While they still enclose something, read one ring:

the top row, from left to right, then move top down one;
the right column, from top to bottom, then move right in one;
if a row is still left, the bottom row from right back to left, then move bottom up one;
if a column is still left, the left column from bottom back up to top, then move left in one.

The two checks matter when the last part is a single row or a single column: without them, it would be read twice.

Time: O(m × n) · Space: O(1) beyond the answer