正六邊形序列定義如下。
- 最高的六邊形是 1。
- 下一個六邊形在前一個六邊形的順時針方向上。
- 如果下一個六邊形已經有數字，那么內部最高的六邊形被賦予數字。
- 該序列是通過從左上角到右下角讀取所有六邊形來生成的。例如，當n=1時，當n=2時為1，當n=3時為1-6-2-7-5-3-4，1-12-2-11-13-3-18-14- 10-19-4-17-15-9-16-5-8-6-7
如何生成n的正六邊形序列？
uj5u.com熱心網友回復：
我使用了一些觀察結果：
- 請注意，所需的行數是 4 * n - 3
- 請注意，要表示一行，我們需要 2 個向量：
- 如果我們在一個六邊形的右邊，我們追加在那個陣列的前面
- 如果我們在一個六邊形的左邊，我們追加到那個陣列的右邊
- 請注意，如果我們在六邊形的右側，我們需要向下跳一排，如果我們在左側，我們需要向上跳一排
- 請注意，如果我們在六邊形的垂直邊緣（左或右），我們需要跳 2 行：左垂直我們向上跳 2 行，右垂直我們向下跳 2 行
from collections import deque
def hexagon_pattern(n):
if n == 1:
return [1]
# Denotes how many rows we need
n_rows = 4 * n - 3
# Create a row as a tuple of left half and right half
# This is done as if we are in the right half of the
# hexagon, we append to the left, otherwise we append to
# the right
rows = [(deque([]), deque([])) for i in range(n_rows)]
# Denotes the dimension of a line (how many numbers)
# we push to a line
# Obs: this starts from n - 1 and continues to 0
# If this is 0, it means we have to fill in only the number
# in the center of the hexagon
line_dim = n - 1
# Denotes the number that needed to be introduced in the pattern
crt_num = 1
# Start row to the current hexagon
# Obs: the start row of next hexagon is at a distance of 2
# from the previous start row of the previous hexagon
start_row = 0
# We have n hexagon patterns to fill in
while n:
# Every hexagon pattern start at a different row
crt_row = start_row
# Indicator that we are at the middle number
if line_dim == 0:
rows[crt_row][0].append(crt_num)
break
# For every level we have a hexagon
for line_no in range(6):
# We have to fill in the hexagon edge
for _ in range(line_dim):
if crt_row >= n_rows:
continue
if line_no < 3:
# We are on the right part of a hexagon (first 3 edges)
rows[crt_row][1].appendleft(crt_num)
else:
# We are on the left part of a hexagon (last 3 edges)
rows[crt_row][0].append(crt_num)
# Increment the number to be added in pattern
crt_num = 1
# If we are on the right vertical line of the hexagon, then we jump 2 lines down
if line_no == 1:
crt_row = 2
# If we are on the left vertical line of the hexagon, then we jump 2 lines up
elif line_no == 4:
crt_row -= 2
# If we are on the right side of the hexagon we jump one line down
elif line_no < 3:
crt_row = 1
# If we are on the left side of the hexagon we jump one line up
else:
crt_row -= 1
n -= 1
line_dim -= 1
start_row = 2
# We concatenate the two halves of every row
# After that, we concatanate all the sublists in a single list
result = sum(list(filter(lambda l: l, map(lambda t: list(t[0] t[1]), rows))), [])
return result
if __name__ == '__main__':
print(hexagon_pattern(1))
print(hexagon_pattern(2))
print(hexagon_pattern(3))
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