Create 幻方.py

幻方.py

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+# -*- coding:utf-8 -*-
+
+from numpy import *
+
+def oddMagic(n):
+    # 罗伯特法求奇数阶幻方/楼梯法
+    A = zeros([n,n])
+    posX = 0
+    posY = int(n/2)
+    for val in range(1,n**2+1):
+        if int(A[posX,posY]):
+            posX = mod(posX+2,n)
+            posY = mod(posY-1,n)
+        # 赋值并更新位置
+        A[posX,posY] = int(val)
+        posX = mod(posX-1,n)
+        posY = mod(posY+1,n)
+    return A
+
+def magic(n):
+    if mod(n,2):
+        # 奇数阶
+        A = oddMagic(n)
+    elif mod( int(n/2) ,2 ):
+        # 仅能被2整除，可拆分成四个奇数阶幻方
+        a = int(n/2)
+        A = zeros([n,n])
+        A[:a,:a] = oddMagic(a)
+        A[a:,a:] = oddMagic(a) + a**2
+        A[:a,a:] = oddMagic(a) + 2*a**2
+        A[a:,:a] = oddMagic(a) + 3*a**2
+    else:
+        # 仅能被4整除
+        A = mat([i for i in range(1,n**2+1)]).reshape([n,n])
+        J = mod( array([i for i in range(1,n+1)]) ,4 )>1.2
+        for x in range(0,n):
+            for y in range(0,n):
+                if (J[x] == J[y]):
+                    A[x,y] = n**2+1 - A[x,y]
+    print(A)
+
+
+magic(6)
+
+
+-----------------------------------------------------------------------
+
+# -*- coding: utf-8 -*-
+# 奇阶幻方
+def odd_magic_square(n):
+    matrix = [[0 for i in range(n)] for i in range(n)]
+    # x, y 的初始位置以及从1开始赋值
+    num, x, y = 1, 0, int(n / 2)
+    while num != n ** 2 + 1:
+        matrix[x][y] = num
+        # 通过x0,y0检测右上方是否已填入数字
+        x0, y0 = x - 1, y + 1
+        # 超界处理
+        if x0 < 0:
+            x0 += n
+        if y0 == n:
+            y0 = n - y0
+        if matrix[x0][y0] == 0:
+            x, y = x0, y0
+        else:
+            # 若有数字填入之前数字的下方
+            x += 1
+            if x == n:
+                x = x - n
+        num += 1
+    i = 0
+    while i < n:
+        print(matrix[i], )
+        i += 1
+
+
+# 双偶幻方
+def double_even_magic_square(n):
+    num = 1
+    matrix = [[] for i in range(n)]
+    # 从1到n**2依次赋值
+    for i in range(n):
+        for j in range(n):
+            matrix[i].append(num)
+            num += 1
+    # 小正方形的对角线上的数字取其补数
+    for i in range(n):
+        for j in range(n):
+            if i % 4 == 0 and abs(i - j) % 4 == 0:
+                for k in range(4):
+                    matrix[i + k][j + k] = n ** 2 - matrix[i + k][j + k] + 1
+            elif i % 4 == 3 and (i + j) % 4 == 3:
+                for k in range(4):
+                    matrix[i - k][j + k] = n ** 2 - matrix[i - k][j + k] + 1
+    i = 0
+    while i < n:
+        print(matrix[i], )
+        i += 1
+
+
+odd_magic_square(3)
+double_even_magic_square(4)