matrix · high

Rotate a Matrix 90 deg

Rotating a square matrix 90 degrees clockwise in place is a classic (LeetCode 48): transpose the matrix, then reverse each row. Transpose maps (i,j) to (j,i) and the row reversal maps column j to n-1-j, so composed they send (i,j) to (j, n-1-i) — exactly a clockwise rotation. It runs in O(n^2) time with O(1) extra space. Counter-clockwise is transpose then reverse each column, and 180 degrees is reversing the row order then reversing each row.

The code

// Rotate a square matrix 90 degrees CLOCKWISE, in place.
// Trick: transpose, then reverse each row.
for (int i = 0; i < n; ++i)
  for (int j = i + 1; j < n; ++j)
    std::swap(a[i][j], a[j][i]);        // 1) transpose
for (int i = 0; i < n; ++i)
  std::reverse(a[i].begin(), a[i].end()); // 2) reverse each row

What this lesson walks through

1. 01Rotate 90° CW — top row → right column
2. 02Pass 1 — transpose (swap across diagonal)
3. 03Pass 2 — reverse each row → rotated

Rotating a square matrix 90° clockwise sends the top row to the rightmost column: [1,2,3] ends up as the right column read top-to-bottom. The elegant trick avoids index gymnastics — do it in two simple passes.