Matrix Traversals

A matrix is a 2D array (grid). Learning how to walk through it in different ways is the foundation of all matrix problems.

Row-Wise Traversal

Visit every cell left to right, top row to bottom row.

const matrix = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9],
];

for (let r = 0; r < matrix.length; r++) {
  for (let c = 0; c < matrix[r].length; c++) {
    console.log(matrix[r][c]);
  }
}
// Output: 1, 2, 3, 4, 5, 6, 7, 8, 9

Time: O(R × C) · Space: O(1)

Column-Wise Traversal

Visit every cell top to bottom, left column to right column.

for (let c = 0; c < matrix[0].length; c++) {
  for (let r = 0; r < matrix.length; r++) {
    console.log(matrix[r][c]);
  }
}
// Output: 1, 4, 7, 2, 5, 8, 3, 6, 9

Diagonal Traversal

Main Diagonal (top-left to bottom-right)

for (let i = 0; i < matrix.length; i++) {
  console.log(matrix[i][i]);
}
// Output: 1, 5, 9

Anti-Diagonal (top-right to bottom-left)

const n = matrix.length;
for (let i = 0; i < n; i++) {
  console.log(matrix[i][n - 1 - i]);
}
// Output: 3, 5, 7

Spiral Traversal

Walk the outer perimeter, then move inward.

flowchart TB
    Top["→ Top row (left → right)"] --> Right["↓ Right column (top → bottom)"]
    Right --> Bottom["← Bottom row (right → left)"]
    Bottom --> Left["↑ Left column (bottom → top)"]
    Left --> Inward["Move boundaries inward"]
    Inward --> Top

    style Top fill:#7c3aed,color:#fff
    style Right fill:#4f46e5,color:#fff
    style Bottom fill:#7c3aed,color:#fff
    style Left fill:#4f46e5,color:#fff
    style Inward fill:#059669,color:#fff

function spiralOrder(matrix) {
  const result = [];
  let top = 0, bottom = matrix.length - 1;
  let left = 0, right = matrix[0].length - 1;

  while (top <= bottom && left <= right) {
    // Top row
    for (let i = left; i <= right; i++) result.push(matrix[top][i]);
    top++;

    // Right column
    for (let i = top; i <= bottom; i++) result.push(matrix[i][right]);
    right--;

    if (top <= bottom) {
      // Bottom row
      for (let i = right; i >= left; i--) result.push(matrix[bottom][i]);
      bottom--;
    }

    if (left <= right) {
      // Left column
      for (let i = bottom; i >= top; i--) result.push(matrix[i][left]);
      left++;
    }
  }
  return result;
}

// Example:
// [[1,2,3],
//  [4,5,6],
//  [7,8,9]]  →  [1,2,3,6,9,8,7,4,5]

Time: O(R × C) · Space: O(1) (excluding output)

Boundaries & Common Edge Cases

Case	What to Watch
Empty matrix	`matrix.length === 0` → return `[]`
Single row	`matrix.length === 1` → just row traversal
Single column	`matrix[0].length === 1` → just column traversal
Jagged arrays	Not all rows same length — use `matrix[r].length` per row

In Simple Words

Row-wise is the default double loop: outer = rows, inner = columns.
Column-wise swaps the loops: outer = columns, inner = rows.
Spiral peels off four boundaries one at a time and shrinks them.
Always check empty / single-row / single-column cases before coding.