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20. Spiral Matrix

mediumAsked at Unity

Traverse an m×n matrix in spiral order — the same UV unwrapping traversal Unity uses to pack a grid of texture tiles into a single atlas in a predictable, cache-friendly sequence.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given an m x n matrix, return all elements of the matrix in spiral order (clockwise from the top-left).

Constraints

  • m == matrix.length
  • n == matrix[i].length
  • 1 <= m, n <= 10
  • -100 <= matrix[i][j] <= 100

Examples

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]

Approaches

1. Direction vector cycling

Maintain a direction array [right, down, left, up]. Walk until out-of-bounds or visited; turn clockwise. Use a visited set.

Time
O(m*n)
Space
O(m*n)
function spiralOrder(matrix) {
  const m = matrix.length, n = matrix[0].length;
  const dirs = [[0,1],[1,0],[0,-1],[-1,0]];
  const seen = Array.from({length:m}, () => new Array(n).fill(false));
  const res = [];
  let r = 0, c = 0, d = 0;
  for (let i = 0; i < m * n; i++) {
    res.push(matrix[r][c]);
    seen[r][c] = true;
    const nr = r + dirs[d][0], nc = c + dirs[d][1];
    if (nr < 0 || nr >= m || nc < 0 || nc >= n || seen[nr][nc]) d = (d + 1) % 4;
    r += dirs[d][0];
    c += dirs[d][1];
  }
  return res;
}

Tradeoff:

2. Layer shrinking (four-pointer)

Track top/bottom/left/right boundaries. Peel the outermost layer each iteration, shrinking boundaries inward. O(1) extra space.

Time
O(m*n)
Space
O(1)
function spiralOrder(matrix) {
  const res = [];
  let top = 0, bottom = matrix.length - 1;
  let left = 0, right = matrix[0].length - 1;
  while (top <= bottom && left <= right) {
    for (let c = left; c <= right; c++) res.push(matrix[top][c]);
    top++;
    for (let r = top; r <= bottom; r++) res.push(matrix[r][right]);
    right--;
    if (top <= bottom) {
      for (let c = right; c >= left; c--) res.push(matrix[bottom][c]);
      bottom--;
    }
    if (left <= right) {
      for (let r = bottom; r >= top; r--) res.push(matrix[r][left]);
      left++;
    }
  }
  return res;
}

Tradeoff:

Unity-specific tips

Unity interviewers look for spatial reasoning — describe the four-pointer approach as shrinking the tile region inward after each pass, mirroring how an atlas-packer reserves a border and moves inward. Draw the boundaries on a whiteboard before coding.

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Output

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