Rotate In Place

The Idea

A quarter turn clockwise sends row 0 up the right-hand edge. Getting there directly means juggling four cells at once.

Do it in two easy moves instead. Transpose — swap grid[r][c] with grid[c][r] — and rows become columns. Then reverse each row, and those columns end up on the correct side. No second grid, no index gymnastics.

Real-World Example

Photo viewers rotate large images with exactly this pair of passes, because allocating a second full-resolution buffer on a phone is what makes the app stutter. The same trick turns a landscape-only sensor feed upright in place.

The Code

def rotate(g):
    n = len(g)
    for r in range(n):
        for c in range(r + 1, n):      # upper triangle only, or you undo it
            g[r][c], g[c][r] = g[c][r], g[r][c]
    for row in g:
        row.reverse()                  # mirror each row left to right
    return g

print(rotate([[1, 2, 3],
              [4, 5, 6],
              [7, 8, 9]]))             # [[7, 4, 1], [8, 5, 2], [9, 6, 3]]

for r in range(n):
    for c in range(___, n):
        g[r][c], g[c][r] = g[c][r], g[r][c]