python 五种算法转置后翻转、层次旋转、递归分块、一次性旋转、环状替换 实现旋转图像【力扣题48】

输入：matrix = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9]
]
输出：[
  [7, 4, 1],
  [8, 5, 2],
  [9, 6, 3]
]

输入：matrix = [
  [ 5, 1, 9,11],
  [ 2, 4, 8,10],
  [13, 3, 6, 7],
  [15,14,12,16]
]
输出：[
  [15,13, 2, 5],
  [14, 3, 4, 1],
  [12, 6, 8, 9],
  [16, 7,10,11]
]

def rotate(matrix):
    """
    通过转置矩阵后翻转每行来顺时针旋转图像
    :param matrix: List[List[int]], n x n 的二维矩阵
    :return: None
    """
    n = len(matrix)
    # 转置矩阵
    for i in range(n):
        for j in range(i + 1, n):
            matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
    
    # 翻转每行
    for i in range(n):
        matrix[i].reverse()
# 示例调用
matrix_example = [[1,2,3],[4,5,6],[7,8,9]]
rotate(matrix_example)
print(matrix_example)  # 输出: [[7,4,1],[8,5,2],[9,6,3]]

def rotate(matrix):
    """
    使用层次旋转法顺时针旋转图像
    :param matrix: List[List[int]], n x n 的二维矩阵
    :return: None
    """
    n = len(matrix)
    for i in range(n // 2):
        for j in range(i, n - i - 1):
            temp = matrix[i][j]
            matrix[i][j] = matrix[n-j-1][i]
            matrix[n-j-1][i] = matrix[n-i-1][n-j-1]
            matrix[n-i-1][n-j-1] = matrix[j][n-i-1]
            matrix[j][n-i-1] = temp
# 示例调用
matrix_example = [[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]]
rotate(matrix_example)
print(matrix_example)  # 输出: [[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]

def rotate(matrix):
    """
    使用递归分块法顺时针旋转图像
    :param matrix: List[List[int]], n x n 的二维矩阵
    :return: None
    """
    def rotate_submatrix(matrix, row, col, size):
        if size <= 1:
            return
        for i in range(size - 1):
            tmp = matrix[row][col + i]
            matrix[row][col + i] = matrix[row + size - 1 - i][col]
            matrix[row + size - 1 - i][col] = matrix[row + size - 1][col + size - 1 - i]
            matrix[row + size - 1][col + size - 1 - i] = matrix[row + i][col + size - 1]
            matrix[row + i][col + size - 1] = tmp
        rotate_submatrix(matrix, row + 1, col + 1, size - 2)
    rotate_submatrix(matrix, 0, 0, len(matrix))
# 示例调用
matrix_example = [[1,2,3],[4,5,6],[7,8,9]]
rotate(matrix_example)
print(matrix_example)  # 输出: [[7,4,1],[8,5,2],[9,6,3]]

def rotate(matrix):
    """
    使用一次性旋转法顺时针旋转图像，需要额外空间
    :param matrix: List[List[int]], n x n 的二维矩阵
    :return: None
    """
    n = len(matrix)
    new_matrix = [[0] * n for _ in range(n)]
    for i in range(n):
        for j in range(n):
            new_matrix[j][n-i-1] = matrix[i][j]
    for i in range(n):
        for j in range(n):
            matrix[i][j] = new_matrix[i][j]
# 示例调用
matrix_example = [[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]]
rotate(matrix_example)
print(matrix_example)  # 输出: [[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]

def rotate(matrix):
    """
    使用环状替换顺时针旋转图像
    :param matrix: List[List[int]], n x n 的二维矩阵
    :return: None
    """
    n = len(matrix)
    layers = n // 2
    for layer in range(layers):
        first, last = layer, n - layer - 1
        for i in range(first, last):
            offset = i - first
            top = matrix[first][i]
            matrix[first][i] = matrix[last-offset][first]
            matrix[last-offset][first] = matrix[last][last-offset]
            matrix[last][last-offset] = matrix[i][last]
            matrix[i][last] = top
# 示例调用
matrix_example = [[1,2,3],[4,5,6],[7,8,9]]
rotate(matrix_example)
print(matrix_example)  # 输出: [[7,4,1],[8,5,2],[9,6,3]]