螺旋星号矩阵生成器遗漏行列问题求助

问题 #

我写了一段生成星号螺旋图案的Python代码，能生成螺旋结构，但漏掉了最外层右侧列、底部行和左侧列。我用检查两步前方单元格是否填充的逻辑控制转向，但找不到问题根源。

原代码 #

def asterisk_spiral(size):
    matrix = [[' ' for _ in range(size)] for _ in range(size)]

    row, col = 0, 0
    directions = [(0, 1), (1, 0), (0, -1), (-1, 0)]
    direction = 0

    for i in range(1, size * size // 2):
        matrix[row][col] = '*'

        next_row, next_col = row + directions[direction][0], col + directions[direction][1]
        next_next_row, next_next_col = row + 2 * directions[direction][0], col + 2 * directions[direction][1]
        
        if (
            0 <= next_row < size
            and 0 <= next_col < size
            and 0 <= next_next_row < size
            and 0 <= next_next_col < size
            and matrix[next_row][next_col] == ' '
            and matrix[next_next_row][next_next_col] != '*'
        ):
            row, col = next_row, next_col
        else:
            # turn
            direction = (direction + 1) % 4
            row, col = row + directions[direction][0], col + directions[direction][1]

    return matrix

def print_spiral(matrix):
    for row in matrix:
        print(' '.join(row))

size = 9

spiral_matrix = asterisk_spiral(size)
print_spiral(spiral_matrix)

实际输出 #

[['*', '*', '*', '*', '*', '*', '*', '*', ' '],
 [' ', ' ', ' ', ' ', ' ', ' ', ' ', '*', ' '],
 [' ', '*', '*', '*', '*', '*', ' ', '*', ' '],
 [' ', '*', ' ', ' ', ' ', '*', ' ', '*', ' '],
 [' ', '*', ' ', '*', '*', '*', ' ', '*', ' '],
 [' ', '*', ' ', '*', '*', '*', ' ', '*', ' '],
 [' ', '*', ' ', ' ', ' ', ' ', ' ', '*', ' '],
 [' ', '*', '*', '*', '*', '*', '*', '*', ' '],
 [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ']]

期望输出 #

[['*', '*', '*', '*', '*', '*', '*', '*', '*'],
 [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', '*'],
 ['*', '*', '*', '*', '*', '*', '*', ' ', '*'],
 ['*', ' ', ' ', ' ', ' ', ' ', '*', ' ', '*'],
 ['*', ' ', '*', '*', '*', ' ', '*', ' ', '*'],
 ['*', ' ', '*', ' ', ' ', ' ', '*', ' ', '*'],
 ['*', ' ', '*', '*', '*', '*', '*', ' ', '*'],
 ['*', ' ', ' ', ' ', ' ', ' ', ' ', ' ', '*'],
 ['*', '*', '*', '*', '*', '*', '*', '*', '*']]

问题分析与修复 #

核心问题 #

• 循环次数不足：原代码用range(1, size * size // 2)循环，对于奇数size=9，仅循环39次，远少于实际需要填充的星号数量，导致大量位置未被处理。
• 转向条件过于严苛：检查两步前方单元格的逻辑，在靠近边界时会因两步超出矩阵范围而提前转向，无法走完最外层完整路径。

修复后的代码 #

def asterisk_spiral(size):
    matrix = [[' ' for _ in range(size)] for _ in range(size)]

    row, col = 0, 0
    directions = [(0, 1), (1, 0), (0, -1), (-1, 0)]
    direction = 0

    while True:
        # 当前位置已填充则退出循环
        if matrix[row][col] != ' ':
            break
        matrix[row][col] = '*'
        
        # 尝试按当前方向移动
        next_row = row + directions[direction][0]
        next_col = col + directions[direction][1]
        # 下一步合法且未填充，则移动
        if 0 <= next_row < size and 0 <= next_col < size and matrix[next_row][next_col] == ' ':
            row, col = next_row, next_col
        else:
            # 转向后再次检查能否移动
            direction = (direction + 1) % 4
            next_row = row + directions[direction][0]
            next_col = col + directions[direction][1]
            if not (0 <= next_row < size and 0 <= next_col < size and matrix[next_row][next_col] == ' '):
                break
            row, col = next_row, next_col
    return matrix

def print_spiral(matrix):
    for row in matrix:
        print(' '.join(row))

size = 9

spiral_matrix = asterisk_spiral(size)
print_spiral(spiral_matrix)

改动说明 #

• 替换循环逻辑：用while循环替代固定次数循环，直到当前位置已填充或转向后无法移动，确保所有应填充的星号都被处理。
• 简化转向判断：仅检查下一步是否合法且未被填充，避免边界处提前转向，保证路径完整性。
• 增加退出判断：转向后再次验证下一步可行性，防止无限循环或越界。

内容的提问来源于stack exchange，提问作者Michael