def show(a, n):#輸出結果
for i in range(n):
for j in range(n):
print(a[i][j], end=" ")
print()
print()
import copy
def sudoku(a, n):
def is_ok(b, n):
def answer(r, c):
t = [0] * (n + 1)
for i in range(n):#標記同行同列的已有數字
t[b[r][i]], t[b[i][c]] = 1, 1
s = int(n ** 0.5)#每個宮的尺寸
#確定a[r][c]所在宮的起始行列座標
br, bc = (r // s) * s, (c // s) * s
for i in range(br, br+s):#標記同宮已有數字
for j in range(bc, bc+s):
t[b[i][j]] = 1
k = 0
for i in range(1, n+1):
if t[i] == 0:
num = i
else:
k += 1 #累計已有數字
if k == n - 1: #b[r][c]的值確定為num
return num
else:
return 0
flag = false
while not flag:
flag = true
for r in range(n):
for c in range(n):
if b[r][c] == 0:
b[r][c] = answer(r, c)
if b[r][c] > 0:
flag = false
#判定是否已經有解
for i in range(n):
for j in range(n):
if b[i][j] == 0:
return false
return true
def dfs(r, c):
nonlocal count
b = copy.deepcopy(a)
if is_ok(b, n) or r == n: #所有位置都填好了，輸出解
count += 1
print(f':')
show(b, n)
elif a[r][c] > 0:#該位置的值已確定，直接下一步
if c < n - 1:#確定下乙個位置的座標
tr, tc = r, c + 1
else:
tr, tc = r + 1, 0
dfs(tr, tc)
else:
for i in range(1, n+1):#列舉本位置的可能取值
if check(a, n, r, c, i):#如果可以取數字i，遞迴進入下一層
a[r][c] = i
if c < n - 1:
tr, tc = r, c + 1
else:
tr, tc = r + 1, 0
dfs(tr, tc)
a[r][c] = 0 #所有數字都取過了，恢復原值，回溯
count = 0
dfs(0, 0)
a = [[0,1,0,0],
[0,0,0,0],
[0,0,3,0],
[0,2,0,0]]
n = 4
show(a, n)
sudoku(a, n)
print()
a = [[1,0,8,0,0,4,0,5,0],
[0,0,4,0,3,7,0,0,2],
[0,0,2,0,0,6,4,3,0],
[0,0,1,0,9,0,0,0,4],
[5,7,0,4,8,0,0,6,3],
[4,0,0,0,5,0,8,0,0],
[0,9,5,1,0,0,3,0,0],
[8,0,0,2,6,0,7,0,0],
[0,1,0,3,0,0,9,0,8]]
n = 9
show(a, n)
sudoku(a, n)
print()
a = [[1,3,0,0,0,4,0,5,0],
[0,0,4,0,0,0,0,0,2],
[0,0,2,0,0,6,4,3,0],
[0,2,1,0,9,0,0,0,4],
[5,7,0,0,0,0,0,6,3],
[4,0,0,0,5,0,8,0,0],
[0,0,0,1,0,0,3,0,0],
[8,0,0,0,0,0,7,0,0],
[0,1,5,3,8,0,0,0,6]]
n = 9
show(a, n)
sudoku(a, n)
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