Python之任意阶幻方的构造

向右看齐 2022-06-06 03:30 284阅读 0赞

本文在用Python构造任意阶幻方的时候，参考的资料如下：　  
\- 维基百科：[https://en.wikipedia.org/wiki/Magic\_square][https_en.wikipedia.org_wiki_Magic_square]  
\- 幻方：[http://blog.csdn.net/dxx\_111/article/details/50158355][http_blog.csdn.net_dxx_111_article_details_50158355]  
\- 论文：由矩阵构造奇数阶幻方的方法，高建国，河南大学学报

Python代码如下：（具体的构造方法可参看以上资料）

# -*- coding: utf-8 -*-
    #利用numpy模块构造幻方
    import numpy as np
    
    #列表循环向左移offset位
    def shift_left(lst, offset):
        return [lst[(i+offset)%len(lst)] for i in range(len(lst))]
    
    #列表循环向右移offset位
    def shift_right(lst, offset):
        return [lst[i-offset] for i in range(len(lst))]
    
    #构造奇数阶幻方函数
    def magic_of_odd_order(n):
        p = (int)((n-1)/2)
    
        #创建矩阵1
        initial_lst1 = list(range(p+1,n))+list(range(p+1))
        initial_mat1 = []
        for i in range(n):
            initial_mat1.append(shift_left(initial_lst1, i))
        mat1 = np.array(initial_mat1)
    
        #创建矩阵2
        initial_lst2 = list(range(p,-1,-1))+list(range(2*p,p,-1))
        initial_mat2 = []
        for i in range(n):
            initial_mat2.append(shift_right(initial_lst2, i))
        mat2 = np.array(initial_mat2)
    
        #创建矩阵3,即元素全为1的矩阵
        mat3= np.ones((n,n),dtype=np.int)
    
        #构造幻方
        magic = n*mat2+mat1+mat3
        return magic
    
    #构造4n阶幻方函数
    def magic_of_4n_order(n):
        mat = np.array(range(1,n*n+1)).reshape(n,n)
        for i in range((int)(n/4)):
            for j in range((int)(n/4)):
                for k in range(4): #将每个4*4小方块的对角线换成互补元素
                    mat[k+4*j][k+4*i] = n*n+1-mat[k+4*j][k+4*i]
                    mat[k+4*j][3-k+4*i] = n*n+1-mat[k+4*j][3-k+4*i]
    
        return mat
    
    #构造4n+2阶幻方函数
    def magic_of_4n2_order(n):
        p = (int)(n/2)
        matA = magic_of_odd_order(p)
        matD = matA+p**2
        matB = matD+p**2
        matC = matB+p**2
    
        #交换矩阵块A与矩阵块C中特定元素的位置
        row = (int)((p-1)/2)
        for i in range(p):
            if i != row:
                for k in range((int)((n-2)/4)):
                    matA[i][k],matC[i][k] = matC[i][k],matA[i][k]
            else:
                for k in range((int)((n-2)/4)):
                    matA[i][row+k],matC[i][row+k] = matC[i][row+k],matA[i][row+k]
    
        #交换矩阵块B与矩阵块D中特定元素的位置
        col = (int)((p-1)/2)
        for j in range(col+2-(int)((n-2)/4),col+1):
            for i in range(p):
                matB[i][j],matD[i][j] = matD[i][j],matB[i][j]
    
        #合并矩阵块A,B,C,D组成幻方
        magic = np.row_stack((np.column_stack((matA,matB)),np.column_stack((matC,matD))))
        return magic
    
    def main():
        order = eval(input('Enter the order of magic square(>=3): '))
    
        if order%2 ==1:
            magic = magic_of_odd_order(order)
        elif order%4 == 0:
            magic = magic_of_4n_order(order)
        else:
            magic = magic_of_4n2_order(order)
        print('Generating magic square of %d order......'%order)
    
        for row in magic:
            for col in row:
                print(col, end='\t')
            print()
    
        #验证生成的magic是否为幻方 
        val = input(("Do you want to validate?[Y|N]"))
        if val == 'Y' or val == 'y':
            print('每行的和:', np.sum(magic, axis=0))
            print('每列的和:', np.sum(magic, axis=1))
            print('主对角线的和:', sum([magic[i][i] for i in range(order)]))
            print('副对角线的和:', sum([magic[i][order-1-i] for i in range(order)]))
        print('It\'s Done!')
    
    main()

运行结果如下：  
![这里写图片描述][SouthEast]  
![这里写图片描述][SouthEast 1]  
![这里写图片描述][SouthEast 2]

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本次分享到此结束，欢迎大家批评与交流~~

[https_en.wikipedia.org_wiki_Magic_square]: https://en.wikipedia.org/wiki/Magic_square
[http_blog.csdn.net_dxx_111_article_details_50158355]: http://blog.csdn.net/dxx_111/article/details/50158355
[SouthEast]: /images/20220606/5a8bb9cf0a7e4a27a643b3227262fcdc.png
[SouthEast 1]: /images/20220606/32b1e79099af4bef872521d0bc34e08a.png
[SouthEast 2]: /images/20220606/c8cbed908fa445e4bab7f996b9b146cb.png