loading

54. Spiral Matrix — Step-by-Step Visualization

mediumLeetCode #54ArrayMatrixSimulation

Given an `m x n` matrix, return all elements of the matrix in spiral order. **Example 1:** Input: `matrix = [[1,2,3],[4,5,6],[7,8,9]]` Output: `[1,2,3,6,9,8,7,4,5]` **Example 2:** Input: `matrix = [[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]`

Algorithm Pattern

Boundary Contraction

Key Idea

Maintain four pointers representing the current boundaries: `top`, `bottom`, `left`, and `right`. Move in four directions (right, down, left, up) sequentially, shrinking the corresponding boundary after each pass. Terminate when boundaries overlap.

Step-by-Step Approach

  1. Initialize `top = 0`, `bottom = m-1`, `left = 0`, `right = n-1`.
  2. While `left <= right` and `top <= bottom`:
  3. 1. Move right: Traverse from `left` to `right` at row `top`. Increment `top`.
  4. 2. Move down: Traverse from `top` to `bottom` at column `right`. Decrement `right`.
  5. 3. Move left (if `top <= bottom`): Traverse from `right` to `left` at row `bottom`. Decrement `bottom`.
  6. 4. Move up (if `left <= right`): Traverse from `bottom` to `top` at column `left`. Increment `left`.
  7. Repeat until all elements are visited.

Common Gotchas

  • Crucial: Check `top <= bottom` and `left <= right` before the 'left' and 'up' moves to prevent double-visiting rows/columns in non-square matrices.

Related Problems

← All problems