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Matrix Operations (Rotate & In-place)

01 · Question

Given a square n x n matrix, return a new matrix that results from:

  1. Transposing the matrix: matrix[i][j] becomes matrix[j][i].
  2. Rotating the matrix 90 degrees clockwise.

Example:

  • Input:

    [[1, 2, 3],
 [4, 5, 6],
 [7, 8, 9]]

  • Transpose Output:

    [[1, 4, 7],
 [2, 5, 8],
 [3, 6, 9]]

  • Rotate 90° Output:

    [[7, 4, 1],
 [8, 5, 2],
 [9, 6, 3]]

In-place Rotation (Common Follow-up): To rotate the matrix in-place (without allocating a new n x n matrix), you can perform two steps:

  1. Transpose the matrix (swap matrix[i][j] with matrix[j][i]).
  2. Reverse each row.

02 · Solution

Reference solution

1def transpose(matrix: List[List[int]]) -> List[List[int]]:
2    n = len(matrix)
3    res = [[0] * n for _ in range(n)]
4    for r in range(n):
5        for c in range(n):
6            res[c][r] = matrix[r][c]
7    return res
8

9def rotate(matrix: List[List[int]]) -> List[List[int]]:
10    n = len(matrix)
11    res = [[0] * n for _ in range(n)]
12    for r in range(n):
13        for c in range(n):
14            res[c][n - 1 - r] = matrix[r][c]
15    return res
16

17def rotate_in_place(matrix: List[List[int]]) -> None:
18    n = len(matrix)
19    # 1. Transpose
20    for r in range(n):
21        for c in range(r + 1, n):
22            matrix[r][c], matrix[c][r] = matrix[c][r], matrix[r][c]
23            
24    # 2. Reverse Rows
25    for r in range(n):
26        matrix[r].reverse()
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