Print the matrix in spiral manner

Medium

Four moving boundaries closing inwards

Problem

Given an M * N matrix, print the elements in a clockwise spiral manner. Return an array with the elements in the order of their appearance when printed in a spiral manner.

In simple words

Walk right, down, left, up, shrinking the boundary after each side.

The idea

Hold top, bottom, left and right boundaries and walk one edge at a time, shrinking the relevant boundary after each edge. Re-checking that the boundaries have not crossed before the bottom and left edges is what stops a single remaining row or column being printed twice.

The trick

Order: left-to-right along top, down the right, right-to-left along bottom, up the left.
Check top <= bottom and left <= right again before the last two edges.
O(rows x cols), each cell printed once.

←→stepspaceplay

1/18

Optimal

timeO(rows·cols)spaceO(1)

Peel the matrix ring by ring.

1while (top <= bottom && left <= right) {2  for (let c=left; c<=right; c++) out.push(M[top][c]);    top++;3  for (let r=top; r<=bottom; r++) out.push(M[r][right]);  right--;4  if (top<=bottom) for (let c=right;c>=left;c--) out.push(M[bottom][c]); bottom--;5  if (left<=right) for (let r=bottom;r>=top;r--) out.push(M[r][left]);   left++;6}

Input

grid: 4 × 4

Memory

at: —
cells marked: 0

Output

output: —
done: —

Check yourself

3 quick questions about this walkthrough. A wrong answer costs nothing.

Examples

Example 1

Input:: matrix = [[1,2,3],[4,5,6],[7,8,9]]
Output:: [1, 2, 3, 6, 9, 8, 7, 4, 5]
Explanation:: Peel the outer ring, then spiral inward.

Example 2

Input:: matrix = [[1,2],[3,4]]
Output:: [1, 2, 4, 3]
Explanation:: 1,2,4,3 winds around.

Example 3

Input:: matrix = [[1]]
Output:: [1]
Explanation:: A single cell.

Constraints

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

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