数独问题
数独问题
数独(shù dú)是源自18世纪瑞士的一种数学游戏。玩家需要根据9×9盘面上的已知数字,推理出所有剩余空格的数字,并满足每一行、每一列、每一个粗线宫(3*3)内的数字均含1-9,不重复。
数独盘面是个九宫,每一宫又分为九个小格(cell)。在这八十一格中给出一定的已知数字和解题条件,利用逻辑和推理,在其他的空格上填入1-9的数字。使1-9每个数字在每一行、每一列和每一宫中都只出现一次,所以又称“九宫格”。
我采用的是枚举的方式去处理数独问题:
即每个格子用1-9这个数字进行测试,判断是否满足两个规则
数独文件存储在easy50.txt中
在代码中会对其进行读取
import copy
import time
t1=time.time()
import os
import os
def readfile():
a=[]
b=[[0]*9]*9
with open('easy50.txt', 'r') as f:
for line in f.readlines():
line=line.strip()
if '=' not in line:
a.append(line)
if '=' in line:
print(a)
xx=input("是否继续:\n")
while xx is 'y':
a.clear()
print("清空",a)
break
else:
return a
f.close()
li=readfile()
arr=[]
for i in range(9):
for j in range(9):
arr.append(int(li[i][j]))
a1=[]
a2=[]
a3=[]
a4=[]
a5=[]
a6=[]
a7=[]
a8=[]
a9=[]
for i in range(9):
a1.append(arr[i])
for i in range(9,18):
a2.append(arr[i])
for i in range(18,27):
a3.append(arr[i])
for i in range(27,36):
a4.append(arr[i])
for i in range(36,45):
a5.append(arr[i])
for i in range(45,54):
a6.append(arr[i])
for i in range(54,63):
a7.append(arr[i])
for i in range(63,72):
a8.append(arr[i])
for i in range(72,81):
a9.append(arr[i])
origin = [a1, a2,a3,a4,a5,a6,a7,a8,a9]
print("原始origin的值:\n",a1,'\n', a2,'\n',a3,'\n',a4,'\n',a5,'\n',a6,'\n',a7,'\n',a8,'\n',a9)
print("--------------------------------------start---------------------------------------")
class sudoku:
def debug(self): # 调试
for list in origin:
print(list)
print("\n")
def check_repetition(self,list):#判断表中是否有重复值,0除外
flag=0
for i in range(1,10):
if list.count(i)>=2:
return 1
else:
flag=flag+1
if flag==9:
return 0
def check_row(self,row):#检测横向是否有重复值,无则为返回0,有则返回1
list = origin[row] # 横向
r1 = self.check_repetition(list)
if r1 == 0:
return 0
else :
return 1
def check_column(self,column):#检测纵向是否重复值,无则为返回0,有则返回1
list = [] # 纵向
for num in origin:
list.append(num[column])
r2 = self.check_repetition(list)
if r2==0:
return 0
else:
return 1
def check_square(self,x,y):#检测九宫格是否有重复值,无则为返回0,有则返回1
x,y=y,x
if x>=9 or y>=9:
return
square = []#九宫格
for i in range(0+y//3*3, 3+y//3*3):
for j in range(0+x//3*3, 3+x//3*3):
square.append(origin[i][j])
r3 = self.check_repetition(square)
if r3==0:
return 0
else:
return 1
def check(self,x,y):#检测是否有重复值,无则为0,有则不为0
r1 = self.check_row(x)
r2 = self.check_column(y)
r3 = self.check_square(x, y)
result=r1+r2+r3
return result
def get_next(self): # 获得下一个空值,返回row,column值
i = 0
for list in origin:
try: # 当0不在列表中时,跳过
column = list.index(0)
row = origin.index(list)
res = (row, column)
return res
except ValueError:
i = i + 1
if i == 9:
t2=time.time()
print("总用时={}".format(t2 - t1))
exit(0)
def poi(self,row, column): # 位置修正
if row == 0 and column == -1:
return
if row == 8 and column == 9:
return
if column == -1:
column = 8
row = row - 1
if column == 9:
column = 0
row = row - 1
return (row, column)
def get_last(self,row, column):
origin[row].insert(column, 0)
origin[row].pop(column + 1)
column = column - 1 # 获得上一个已填值的行、列位置
row, column = self.poi(row, column)#位置修正
r = origin[row][column] * compare[row][column]
while r != 0:
column = column - 1
row, column = self.poi(row, column)
r = origin[row][column] * compare[row][column]
return (row, column)
def blank(self):
try:
row,column=self.get_next()
except TypeError:#已填完
exit(0)
j=0
flag=0
for i in range(1,10):
origin[row].insert(column,i)
origin[row].pop(column+1)
self.debug()
r = self.check(row, column)
if r==0:#无重复值
return
else:
j = j + 1
if j==9:
flag=1
break
if flag==1:
row, column = self.get_last(row, column)
value=origin[row][column]
self.debug()
while value == 9:
row, column = self.get_last(row, column)
value = origin[row][column]
self.debug()
while value<9:
for k in range(value+1,10):
origin[row].insert(column, k)
origin[row].pop(column + 1)
self.debug()
r=self.check(row,column)
if r!=0:#有重复
if k==9:
row, column = self.get_last(row, column)
value=origin[row][column]
self.debug()
while value==9:
row, column = self.get_last(row, column)
value = origin[row][column]
self.debug()
break
else:
return
if __name__=="__main__":
compare = copy.deepcopy(origin)#深复制 被复制出来对象对复制出来的对象没有任何影响
sudoku = sudoku()#对象的id值
while 1:
sudoku.blank()
读取的数独问题文件:
003020600
900305001
001806400
008102900
700000008
006708200
002609500
800203009
005010300
========
200080300
060070084
030500209
000105408
000000000
402706000
301007040
720040060
004010003
========
000000907
000420180
000705026
100904000
050000040
000507009
920108000
034059000
507000000
========
030050040
008010500
460000012
070502080
000603000
040109030
250000098
001020600
080060020
========
020810740
700003100
090002805
009040087
400208003
160030200
302700060
005600008
076051090
========
100920000
524010000
000000070
050008102
000000000
402700090
060000000
000030945
000071006
========
043080250
600000000
000001094
900004070
000608000
010200003
820500000
000000005
034090710
========
480006902
002008001
900370060
840010200
003704100
001060049
020085007
700900600
609200018
========
000900002
050123400
030000160
908000000
070000090
000000205
091000050
007439020
400007000
========
001900003
900700160
030005007
050000009
004302600
200000070
600100030
042007006
500006800
========
000125400
008400000
420800000
030000095
060902010
510000060
000003049
000007200
001298000
========
062340750
100005600
570000040
000094800
400000006
005830000
030000091
006400007
059083260
========
300000000
005009000
200504000
020000700
160000058
704310600
000890100
000067080
000005437
========
630000000
000500008
005674000
000020000
003401020
000000345
000007004
080300902
947100080
========
000020040
008035000
000070602
031046970
200000000
000501203
049000730
000000010
800004000
========
361025900
080960010
400000057
008000471
000603000
259000800
740000005
020018060
005470329
========
050807020
600010090
702540006
070020301
504000908
103080070
900076205
060090003
080103040
========
080005000
000003457
000070809
060400903
007010500
408007020
901020000
842300000
000100080
========
003502900
000040000
106000305
900251008
070408030
800763001
308000104
000020000
005104800
========
000000000
009805100
051907420
290401065
000000000
140508093
026709580
005103600
000000000
========
020030090
000907000
900208005
004806500
607000208
003102900
800605007
000309000
030020050
========
005000006
070009020
000500107
804150000
000803000
000092805
907006000
030400010
200000600
========
040000050
001943600
009000300
600050002
103000506
800020007
005000200
002436700
030000040
========
004000000
000030002
390700080
400009001
209801307
600200008
010008053
900040000
000000800
========
360020089
000361000
000000000
803000602
400603007
607000108
000000000
000418000
970030014
========
500400060
009000800
640020000
000001008
208000501
700500000
000090084
003000600
060003002
========
007256400
400000005
010030060
000508000
008060200
000107000
030070090
200000004
006312700
========
000000000
079050180
800000007
007306800
450708096
003502700
700000005
016030420
000000000
========
030000080
009000500
007509200
700105008
020090030
900402001
004207100
002000800
070000090
========
200170603
050000100
000006079
000040700
000801000
009050000
310400000
005000060
906037002
========
000000080
800701040
040020030
374000900
000030000
005000321
010060050
050802006
080000000
========
000000085
000210009
960080100
500800016
000000000
890006007
009070052
300054000
480000000
========
608070502
050608070
002000300
500090006
040302050
800050003
005000200
010704090
409060701
========
050010040
107000602
000905000
208030501
040070020
901080406
000401000
304000709
020060010
========
053000790
009753400
100000002
090080010
000907000
080030070
500000003
007641200
061000940
========
006080300
049070250
000405000
600317004
007000800
100826009
000702000
075040190
003090600
========
005080700
700204005
320000084
060105040
008000500
070803010
450000091
600508007
003010600
========
000900800
128006400
070800060
800430007
500000009
600079008
090004010
003600284
001007000
========
000080000
270000054
095000810
009806400
020403060
006905100
017000620
460000038
000090000
========
000602000
400050001
085010620
038206710
000000000
019407350
026040530
900020007
000809000
========
000900002
050123400
030000160
908000000
070000090
000000205
091000050
007439020
400007000
========
380000000
000400785
009020300
060090000
800302009
000040070
001070500
495006000
000000092
========
000158000
002060800
030000040
027030510
000000000
046080790
050000080
004070100
000325000
========
010500200
900001000
002008030
500030007
008000500
600080004
040100700
000700006
003004050
========
080000040
000469000
400000007
005904600
070608030
008502100
900000005
000781000
060000010
========
904200007
010000000
000706500
000800090
020904060
040002000
001607000
000000030
300005702
========
000700800
006000031
040002000
024070000
010030080
000060290
000800070
860000500
002006000
========
001007090
590080001
030000080
000005800
050060020
004100000
080000030
100020079
020700400
========
000003017
015009008
060000000
100007000
009000200
000500004
000000020
500600340
340200000
========
300200000
000107000
706030500
070009080
900020004
010800050
009040301
000702000
000008006
大家还可以尝试另外一种方式去解决问题:
1.将每个空格的可能放置一个集合中,利用规则一消去行重复的
2.规则二消除列重复,前面两个规则重复进行
3.进行枚举,一个一个的试