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How do you rotate an N×N matrix by 90 degrees in place?

Q: How do you rotate an N×N matrix by 90 degrees in place?

**Intuition.** A clockwise 90° rotation is two simple in-place steps: **transpose** the matrix (swap across the main diagonal), then **reverse each row**. Together they move every element to its rotated position without an extra matrix. original 1 <rect x="60" y="30" width="30" height="30" fill="#3b82f6" fill-o

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Explain in-place matrix rotation.

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Transpose then reverse rows

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def rotate(matrix):
    n = len(matrix)
    for i in range(n):                 # transpose (upper triangle)
        for j in range(i + 1, n):
            matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
    for row in matrix:                 # reverse each row
        row.reverse()
    return matrix


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

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