44. Rotate a Telemetry Dashboard Matrix

Problem

An ops dashboard lays out N region/model latency tiles in an N x N grid. When the dashboard's orientation changes — say, switching from a wide monitor layout to a narrow one — the whole grid needs to rotate 90 degrees clockwise, without allocating a second full matrix, since the grid can be large and this runs on every orientation change.

The function mutates grid in place (e.g. transpose then reverse each row, or layer-by-layer rotation), using O(1) extra space (aside from the input itself) and O(n²) time. It returns nothing; the caller inspects the mutated grid.

Source: src/44_rotate_telemetry_matrix.py

def rotate_telemetry_grid(grid: list[list[int]]) -> None:

>>> g = [[120, 95, 60], [200, 150, 80], [300, 250, 100]]
>>> rotate_telemetry_grid(g)
>>> g
[[300, 200, 120], [250, 150, 95], [100, 80, 60]]

Step-by-Step Approach

1. Recognize that a 90-degree clockwise rotation decomposes into two simpler, well-known in-place operations: transpose, then reverse each row.
2. Transpose the grid in place by swapping grid[i][j] with grid[j][i] for every pair where j > i (only the upper triangle, to avoid swapping each pair back).
3. After the transpose, each row currently holds what will become that row of the rotated grid, but in reverse column order.
4. Reverse each row in place (row.reverse()) to finish the rotation.
5. Handle the trivial cases (empty grid, 1x1 grid) — they fall out naturally since the loops simply don't execute.

The key insight is that "rotate 90° clockwise" decomposes into "transpose" (reflect across the main diagonal) followed by "reverse each row" (reflect across the vertical axis) — two reflections compose into the rotation, and both are doable in place with only pairwise swaps.

Reference solution

def rotate_telemetry_grid(grid: list[list[int]]) -> None:
    # transpose in place, then reverse each row: O(n^2) time, O(1) extra space
    n = len(grid)
    for i in range(n):
        # upper triangle only (j > i), so each pair swaps exactly once
        for j in range(i + 1, n):
            grid[i][j], grid[j][i] = grid[j][i], grid[i][j]
    for row in grid:
        # flips column order to finish the clockwise rotation
        row.reverse()

Key Functions & Tricks

• a, b = b, a — Python's tuple-swap idiom, no temp variable needed.
• range(i + 1, n) for the inner loop — upper-triangle-only swap so each pair swaps exactly once.
• list.reverse() — reverses a list in place, returns None.
• Transpose + row-reverse — two reflections that compose into a 90° clockwise rotation, O(n²) time, O(1) space.

How to Recognize This Pattern