python5种算法模拟螺旋、分层填充、递归、迭代、分治实现螺旋矩阵ll【力扣题59】

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

def generateMatrix(n):
    """
    使用模拟螺旋遍历的方法生成螺旋矩阵
    :param n: int, 矩阵的大小
    :return: List[List[int]], 螺旋矩阵
    """
    matrix = [[0] * n for _ in range(n)]
    directions = [(0, 1), (1, 0), (0, -1), (-1, 0)]  # right, down, left, up
    row, col, di = 0, 0, 0
    for i in range(1, n*n + 1):
        matrix[row][col] = i
        dr, dc = directions[di]
        if not (0 <= row + dr < n and 0 <= col + dc < n and matrix[row + dr][col + dc] == 0):
            di = (di + 1) % 4  # Change direction
            dr, dc = directions[di]
        row, col = row + dr, col + dc
    return matrix
# 示例调用
print(generateMatrix(3))  # 输出: [[1, 2, 3], [8, 9, 4], [7, 6, 5]]

def generateMatrix(n):
    """
    使用分层填充法生成螺旋矩阵
    :param n: int, 矩阵的大小
    :return: List[List[int]], 螺旋矩阵
    """
    matrix = [[0] * n for _ in range(n)]
    left, right, top, bottom = 0, n-1, 0, n-1
    num = 1
    while left <= right and top <= bottom:
        for i in range(left, right + 1):
            matrix[top][i] = num
            num += 1
        top += 1
        for i in range(top, bottom + 1):
            matrix[i][right] = num
            num += 1
        right -= 1
        if top <= bottom:
            for i in range(right, left - 1, -1):
                matrix[bottom][i] = num
                num += 1
            bottom -= 1
        if left <= right:
            for i in range(bottom, top - 1, -1):
                matrix[i][left] = num
                num += 1
            left += 1
    return matrix
# 示例调用
print(generateMatrix(3))  # 输出: [[1, 2, 3], [8, 9, 4], [7, 6, 5]]

def generateMatrix(n):
    """
    使用递归方法生成螺旋矩阵
    :param n: int, 矩阵的大小
    :return: List[List[int]], 螺旋矩阵
    """
    matrix = [[0] * n for _ in range(n)]
    fill(matrix, 0, n, 1)
    return matrix
def fill(matrix, start, n, val):
    if n <= 0:
        return
    if n == 1:
        matrix[start][start] = val
        return
    for i in range(n - 1):
        matrix[start][start + i] = val
        val += 1
    for i in range(n - 1):
        matrix[start + i][start + n - 1] = val
        val += 1
    for i in range(n - 1):
        matrix[start + n - 1][start + n - 1 - i] = val
        val += 1
    for i in range(n - 1):
        matrix[start + n - 1 - i][start] = val
        val += 1
    fill(matrix, start + 1, n - 2, val)
# 示例调用
print(generateMatrix(3))  # 输出: [[1, 2, 3], [8, 9, 4], [7, 6, 5]]

def generateMatrix(n):
    """
    使用迭代展开的方法生成螺旋矩阵
    :param n: int, 矩阵的大小
    :return: List[List[int]], 螺旋矩阵
    """
    matrix = [[0] * n for _ in range(n)]
    x, y, dx, dy = 0, 0, 0, 1
    for i in range(1, n*n+1):
        matrix[x][y] = i
        if matrix[(x+dx)%n][(y+dy)%n]:
            dx, dy = dy, -dx
        x, y = x + dx, y + dy
    return matrix
# 示例调用
print(generateMatrix(3))  # 输出: [[1, 2, 3], [8, 9, 4], [7, 6, 5]]

def generateMatrix(n):
    """
    使用分治填充法生成螺旋矩阵
    :param n: int, 矩阵的大小
    :return: List[List[int]], 螺旋矩阵
    """
    matrix = [[0] * n for _ in range(n)]
    fill_layer(matrix, 0, n, 1)
    return matrix
def fill_layer(matrix, start, size, start_val):
    if size <= 0:
        return
    if size == 1:
        matrix[start][start] = start_val
        return
    # Fill the perimeter
    for i in range(size - 1):
        matrix[start][start+i] = start_val
        start_val += 1
    for i in range(size - 1):
        matrix[start+i][start+size-1] = start_val
        start_val += 1
    for i in range(size - 1):
        matrix[start+size-1][start+size-1-i] = start_val
        start_val += 1
    for i in range(size - 1):
        matrix[start+size-1-i][start] = start_val
        start_val += 1
    fill_layer(matrix, start+1, size-2, start_val)
# 示例调用
print(generateMatrix(3))  # 输出: [[1, 2, 3], [8, 9, 4], [7, 6, 5]]