Rotate a Matrix 90 Degrees Clockwise

📌 Definition:

📖 Detailed Explanation:

The clean trick is two steps: transpose the matrix (swap across the main diagonal), then reverse each row. This yields a clockwise rotation using O(1) extra space. O(n^2) time.

💻 Solutions:

• Java
• JavaScript
• Python

public static void rotate(int[][] m) {
    int n = m.length;
    for (int i = 0; i < n; i++)
        for (int j = i + 1; j < n; j++) {
            int t = m[i][j]; m[i][j] = m[j][i]; m[j][i] = t;
        }
    for (int[] row : m)
        for (int l = 0, r = n - 1; l < r; l++, r--) {
            int t = row[l]; row[l] = row[r]; row[r] = t;
        }
}

function rotate(m) {
  const n = m.length;
  for (let i = 0; i < n; i++)
    for (let j = i + 1; j < n; j++)
      [m[i][j], m[j][i]] = [m[j][i], m[i][j]];
  for (const row of m) row.reverse();
  return m;
}

def rotate(m):
    n = len(m)
    for i in range(n):
        for j in range(i + 1, n):
            m[i][j], m[j][i] = m[j][i], m[i][j]
    for row in m:
        row.reverse()
    return m

🔑 Key Points:

• Transpose, then reverse each row = clockwise
• Reverse each column instead for counter-clockwise
• In place, O(1) extra space
• O(n^2) time

🌍 Real-World Example: