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Magic_Square.py
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131 lines (117 loc) · 4.47 KB
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# -*- coding：utf-8 -*-
# &Author AnFany
# 引入库
import numpy as np
# 奇数阶
def OddMagic(jieshu):
# 存储幻方结构
huanfang = np.zeros((jieshu, jieshu))
# 需要填写的数字列表
listnum = list(range(1, jieshu ** 2 + 1))
# 第一行中间填1
i = 0
j = int(jieshu / 2)
# 记录填写的个数
count = 0
while count < jieshu ** 2:
huanfang[i][j] = listnum[count]
# 记录i,j
cc = i
dd = j
# 超出了第一行，则填到最底下一行
if i - 1 < 0:
i = jieshu - 1
else:
i -= 1
# 超出了最右边一列，则填到最左边一列
if j + 1 == jieshu:
j = 0
else:
j += 1
# 遇到下一个格子里已经有数字的，就填到当前格子的下方
if huanfang[i][j] != 0:
i = cc + 1
j = dd
# 次序加1
count += 1
return huanfang
# 双偶阶幻方：阶数=2*偶数
def DoubleEvenMagic(jieshu):
##存储幻方结构
huanfang = np.zeros((jieshu, jieshu))
# 需要填写的数字列表
listnum = list(range(1, jieshu ** 2 + 1))
# 第一轮填充,从第一行第一列开始,从左到右,从上到下,从1到jieshu平方,依次填充
# 每四乘四的正方形,画主副对角线。规则是只填充没对角线的,画了对角线格子不写
# 记录个数
count = 0
for hang in range(len(huanfang)):
for lie in range(len(huanfang)):
if (hang % 4 in [0, 3] and lie % 4 in [1, 2]) or \
(hang % 4 in [1, 2] and lie % 4 in [0, 3]): # 判断对角线
huanfang[hang][lie] = listnum[count]
# 第二轮填充,从最后一行最后一列开始,从右到左,从下到上,从1到jieshu平方依次填充。
# 规则是只填充画了对角线的，没画对角线的不填
else:
huanfang[hang][lie] = listnum[::-1][count]
count += 1
return huanfang
# 单偶阶幻方：阶数=2*奇数
def SingleEvenMagic(jieshu):
# 幻方结构
huanfang = np.zeros((jieshu, jieshu))
# 子幻方阶数
son = int(jieshu / 2)
# A象限幻方
SAhf = OddMagic(son)
huanfang[:, 0:son][0:son] = SAhf
# 依次填充DBC象限
huanfang[:, son:][son:] = huanfang[:, 0:son][0:son] + son ** 2
huanfang[:, son:][0:son] = huanfang[:, son:][son:] + son ** 2
huanfang[:, 0:son][son:] = huanfang[:, son:][0:son] + son ** 2
# 计算K值
k = int((jieshu - 2) / 4)
# AC象限互换
# 从A象限的中间行中间列开始为第一格,往右标出K格；标出A象限其他行的左边K列
# 先换AC象限所有行的左边K列
middle = huanfang[:, 0:k][0:son].copy()
huanfang[:, 0:k][0:son] = huanfang[:, 0:k][son:]
huanfang[:, 0:k][son:] = middle
# 再换中间行的前2K列
middle = huanfang[:, 0:2 * k][int(son / 2):(int(son / 2) + 1)].copy()
huanfang[:, 0:2 * k][int(son / 2):(int(son / 2) + 1)] = huanfang[:, 0:2 * k][
int(son / 2) + son:(int(son / 2) + 1 + son)]
huanfang[:, 0:2 * k][int(son / 2) + son:(int(son / 2) + 1 + son)] = middle
# BD象限互换
if k - 1 != 0:
# 从B象限的中间列所有格子开始,向左标出K-1列,与D象限对换
middle = huanfang[:, son:son + k - 1][0:son].copy()
huanfang[:, son:son + k - 1][0:son] = huanfang[:, son:son + k - 1][son:]
huanfang[:, son:son + k - 1][son:] = middle
return huanfang
# 最终构建幻方的函数
def Magic(jieshu):
if jieshu < 3:
return '阶数不应小于3'
elif jieshu % 2 == 1:
huanfang = OddMagic(jieshu)
elif jieshu % 4 != 0:
huanfang = SingleEvenMagic(jieshu)
else:
huanfang = DoubleEvenMagic(jieshu)
return huanfang
# 验证幻方的函数
def Test(jieshu):
cc = Magic(jieshu)
sumlist = list(cc.sum(axis=1)) + list(cc.sum(axis=0)) + [cc.trace()] # 所有行、列以及主对角线数字和
vicediag = 0
for iv in range(jieshu):
vicediag += cc[iv][jieshu - iv - 1]
sumlist += [vicediag] # 加上副对角线数字和
if len(set(sumlist)) == 1: # 判断和相等
print(cc)
return '结果正确'
else:
print('%s阶程序有bug' % jieshu)
return False
print(Test(7))