python实现数独游戏-创新互联

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一、数独问题的基本规则
规则一：同一行数字不同
规则二：同一列数字不同
规则三：同一宫数字不同

二、解决数独的策略
1，简单方法
第一步，在每个格子中按照基本规则MT4写入可能的结果
第二步，判断每个格子中结果的个数，如果结果唯一，则写入该数字。
第三步，返回步骤一，循环
停止的标志：填满所有格子，或格子中可能的结果最小数大于1。

2，中级方法
第一步，使用简单方法
第二步，在每一宫中，某个数字出现的次数只有一次，直接填入该数字
第三步，返回步骤一，循环
停止的标志：不在有数字填入

3，终极方法
第一步，使用中级方法
第二步，对每个位置的每个可能的答案进行假设，并推导矛盾，排除。
（1）在第一个位置上，填入第一个可能的答案
（2）使用中级方法，推导填入数字
（3）如果矛盾A出现，假设不成立，返回该位置，填入第二个答案。
如果矛盾B出现，假设暂时成立，进入下一位置，填入答案。
循环结束标志：填满数字并符合基本规则

三 代码如下

import pandas as pd
import numpy as np
shudu_data=pd.read_csv('data/shudu.csv')
data=shudu_data.copy()
def block(i,data):
ru3_1=data.iloc[0:3,0:3]
ru3_2=data.iloc[0:3,3:6]
ru3_3=data.iloc[0:3,6:]
ru3_4=data.iloc[3:6,0:3]
ru3_5=data.iloc[3:6,3:6]
ru3_6=data.iloc[3:6,6:]
ru3_7=data.iloc[6:,0:3]
ru3_8=data.iloc[6:,3:6]
ru3_9=data.iloc[6:,6:]

ru3_list=[ru3_1,ru3_2,ru3_3,ru3_4,ru3_5,ru3_6,ru3_7,ru3_8,ru3_9]
ru3=ru3_list[i]
ru3=ru3.values.tolist()
lis=[]
for l in ru3:
   lis+=l
ru3=set(lis)-{0}
return ru3

def Block_dataframe(i,data):
ru3_1=pd.DataFrame(data=data.iloc[0:3,0:3],index=[0,1,2],columns=['0','1','2'])
ru3_2=pd.DataFrame(data=data.iloc[0:3,3:6],index=[0,1,2],columns=['3','4','5'])
ru3_3=pd.DataFrame(data=data.iloc[0:3,6:],index=[0,1,2],columns=['6','7','8'])
ru3_4=pd.DataFrame(data=data.iloc[3:6,0:3],index=[3,4,5],columns=['0','1','2'])
ru3_5=pd.DataFrame(data=data.iloc[3:6,3:6],index=[3,4,5],columns=['3','4','5'])
ru3_6=pd.DataFrame(data=data.iloc[3:6,6:],index=[3,4,5],columns=['6','7','8'])
ru3_7=pd.DataFrame(data=data.iloc[6:,0:3],index=[6,7,8],columns=['0','1','2'])
ru3_8=pd.DataFrame(data=data.iloc[6:,3:6],index=[6,7,8],columns=['3','4','5'])
ru3_9=pd.DataFrame(data=data.iloc[6:,6:],index=[6,7,8],columns=['6','7','8'])

ru3_list=[ru3_1,ru3_2,ru3_3,ru3_4,ru3_5,ru3_6,ru3_7,ru3_8,ru3_9]

return ru3_list[i]

def jianyan(data):

flag=True
for ind in range(9):
   li_1=list(data.iloc[ind].values)
   li_=[]
   for li in li_1:
     if li!=0:
       li_.append(li)
   flag=(len(set(li_))==len(li_))
   if flag==False:
     return flag

for col in ['0','1','2','3','4','5','6','7','8']:
   li_2=list(data.iloc[:][col].values)
   li_=[]
   for li in li_2:
     if li!=0:
       li_.append(li)
   #print(set(li_))
   #print(li_)
   flag=(len(set(li_))==len(li_))
   if flag==False:
     return flag

for i in range(9):
   block_dataframe=Block_dataframe(i,data)
   li_3=block_dataframe.values.tolist()
   li_q=[]
   for li_ in li_3:
     li_q=li_q+li_  
   li_=[]
   for li in li_q:
     if li!=0:
       li_.append(li) 

   flag=(len(set(li_))==len(li_))
   if flag==False:
     return flag
return flag
def full(data):
for i in range(9):
for j in ['0','1','2','3','4','5','6','7','8']:
if data[j][i]==0:
return False
return True
def Block_num(index,colums,data):
if index in [0,1,2]:
if colums in ['0','1','2']:
block_num=0
elif colums in ['3','4','5']:
block_num=1
else:
block_num=2
if index in [3,4,5]:
if colums in ['0','1','2']:
block_num=3
elif colums in ['3','4','5']:
block_num=4
else:
block_num=5
if index in [6,7,8]:
if colums in ['0','1','2']:
block_num=6
elif colums in ['3','4','5']:
block_num=7
else:
block_num=8
return block_num
def len_re(index,colums,data):
result={1,2,3,4,5,6,7,8,9}
ru1=set(data.iloc[index])
ru2=set(data[colums])
if index in [0,1,2]:
if colums in ['0','1','2']:
ru3=block(0,data)
elif colums in ['3','4','5']:
ru3=block(1,data)
else:
ru3=block(2,data)
if index in [3,4,5]:
if colums in ['0','1','2']:
ru3=block(3,data)
elif colums in ['3','4','5']:
ru3=block(4,data)
else:
ru3=block(5,data)
if index in [6,7,8]:
if colums in ['0','1','2']:
ru3=block(6,data)
elif colums in ['3','4','5']:
ru3=block(7,data)
else:
ru3=block(8,data)
re=result-ru1-ru2-ru3-{0}
return re

class result():
def result(self,data):

   #计算每个位置上可能的结果，返回pos，ans
   index=[0,1,2,3,4,5,6,7,8]
   colums=['0','1','2','3','4','5','6','7','8']
   pos=[]
   ans=[]
   for ind in index:
     for col in colums:
       if data[col][ind] ==0:
         re=len_re(ind,col,data)
         ans.append(list(re))
         pos.append((ind,col)) 
   return zip(pos,ans)

    def result_min_len(data):
R=result()
c=R.result(data)
reslut_len=[]
reslut_list=[]
try:
for pos,ans in c:
reslut_list.append(ans)
reslut_len.append(len(ans))
return min(reslut_len)
except:return False

class paichu():
def result(self,data):
   data_copy=data.copy()
   #如果一个位置出现多个结果，循序试错,排除错误答案：
   i=0
   j=0
   if result_min_len(data_copy)==0:
     print('传入数据错误，计算中止')
   else:
     result_=result()
     result_1=result_.result(data_copy)
     pos_=[]
     ans_1_b=[]
     for pos,ans_list in result_1:
       ind=pos[0]
       col=pos[1]
       ans_1_a=[]
       for ans in ans_list:
         j+=1
         data_copy[col][ind]=ans
         f=result_min_len(data_copy)
         if f:
           i+=1
           ans_1_a.append(ans)
         data_copy[col][ind]=0
       ans_1_b.append(ans_1_a)
       pos_.append((ind,col))
     print('已经排除{}个数'.format(j-i))
     return zip(pos_,ans_1_b)

class rule_1():

class rule_1():
def result(self,data):
   #如果ind=0，按行，ind=1，按列排除
   ind=0
   result_000=result()
   answer_zip=result_000.result(data)

   #rule1 如果n个相同的list在同一行/列，且元素数量等于list的个数，则该行其他待定cell可以排除list中所有元素
   index_0=[]
   index_1=[]
   index_2=[]
   index_3=[]
   index_4=[]
   index_5=[]
   index_6=[]
   index_7=[]
   index_8=[] 

   ans_0=[]
   ans_1=[]
   ans_2=[]
   ans_3=[]
   ans_4=[]
   ans_5=[]
   ans_6=[]
   ans_7=[]
   ans_8=[]

   for pos,ans in answer_zip:
     if pos[ind]==0:
       index_0.append(pos)
       ans_0.append(ans)
     elif pos[ind]==1:
       index_1.append(pos)
       ans_1.append(ans)
     elif pos[ind]==2:
       index_2.append(pos)
       ans_2.append(ans)
     elif pos[ind]==3:
       index_3.append(pos)
       ans_3.append(ans)
     elif pos[ind]==4:
       index_4.append(pos)
       ans_4.append(ans)
     elif pos[ind]==5:
       index_5.append(pos)
       ans_5.append(ans)
     elif pos[ind]==6:
       index_6.append(pos)
       ans_6.append(ans)
     elif pos[ind]==7:
       index_7.append(pos)
       ans_7.append(ans)
     elif pos[ind]==8:
       index_8.append(pos)
       ans_8.append(ans)

   index=[index_0,index_1,index_2,index_3,index_4,index_5,index_6,index_7,index_8]
   ans=[ans_0,ans_1,ans_2,ans_3,ans_4,ans_5,ans_6,ans_7,ans_8]

   ans_=[]
   for ans_array in ans:
     l2=[]
     for i in ans_array:
       l2.append(set(i))

     for i in np.unique(l2):
       if l2.count(i)==len(i):
         for k,j in enumerate(l2):
           if i!=j:
             j=j-i
             l2[k]=j

     ans_.append(list(l2))

   pos_=[]
   for i in index:
     pos_=pos_+i

   ans_list=[]
   for i in ans_:
     ans_list=ans_list+i
   ans_listn=[]
   for i in ans_list:
     ans_listn.append(list(i))
   return zip(pos_,ans_listn)

class rule_2():

def result(self,data):
   #如果ind=0，按行，ind=1，按列排除
   ind=1
   result_000=result()
   answer_zip=result_000.result(data)

   #rule1 如果n个相同的list在同一行/列，且元素数量等于list的个数，则该行其他待定cell可以排除list中所有元素
   index_0=[]
   index_1=[]
   index_2=[]
   index_3=[]
   index_4=[]
   index_5=[]
   index_6=[]
   index_7=[]
   index_8=[] 

   ans_0=[]
   ans_1=[]
   ans_2=[]
   ans_3=[]
   ans_4=[]
   ans_5=[]
   ans_6=[]
   ans_7=[]
   ans_8=[]

   for pos,ans in answer_zip:
     if pos[ind]=='0':
       index_0.append(pos)
       ans_0.append(ans)
     elif pos[ind]=='1':
       index_1.append(pos)
       ans_1.append(ans)
     elif pos[ind]=='2':
       index_2.append(pos)
       ans_2.append(ans)
     elif pos[ind]=='3':
       index_3.append(pos)
       ans_3.append(ans)
     elif pos[ind]=='4':
       index_4.append(pos)
       ans_4.append(ans)
     elif pos[ind]=='5':
       index_5.append(pos)
       ans_5.append(ans)
     elif pos[ind]=='6':
       index_6.append(pos)
       ans_6.append(ans)
     elif pos[ind]=='7':
       index_7.append(pos)
       ans_7.append(ans)
     elif pos[ind]=='8':
       index_8.append(pos)
       ans_8.append(ans)

   index=[index_0,index_1,index_2,index_3,index_4,index_5,index_6,index_7,index_8]
   ans=[ans_0,ans_1,ans_2,ans_3,ans_4,ans_5,ans_6,ans_7,ans_8]

   ans_=[]
   for ans_array in ans:
     l2=[]
     for i in ans_array:
       l2.append(set(i))

     for i in np.unique(l2):
       if l2.count(i)==len(i):
         for k,j in enumerate(l2):
           if i!=j:
             j=j-i
             l2[k]=j
     ans_.append(list(l2))

   pos_=[]
   for i in index:
     pos_=pos_+i

   ans_list=[]
   for i in ans_:
     ans_list=ans_list+i
   ans_listn=[]
   for i in ans_list:
     ans_listn.append(list(i))
   return zip(pos_,ans_listn)

class rule_3():

def result(self,data):

   result_000=result()
   answer_zip=result_000.result(data)

   #rule3 如果n个相同的list在同一9宫格，且元素数量等于list的个数，则该行其他待定cell可以排除list中所有元素
   block_0=[]
   block_1=[]
   block_2=[]
   block_3=[]
   block_4=[]
   block_5=[]
   block_6=[]
   block_7=[]
   block_8=[] 

   index_0=[]
   index_1=[]
   index_2=[]
   index_3=[]
   index_4=[]
   index_5=[]
   index_6=[]
   index_7=[]
   index_8=[] 

   for pos,ans in answer_zip:
     index=pos[0]
     colums=pos[1]

     if index in [0,1,2]:
       if colums in ['0','1','2']:
         block_0.append(ans)
         index_0.append(pos)
       elif colums in ['3','4','5']:
         block_1.append(ans)
         index_1.append(pos)
       else:
         block_2.append(ans)
         index_2.append(pos)
     if index in [3,4,5]:
       if colums in ['0','1','2']:
         block_3.append(ans)
         index_3.append(pos)
       elif colums in ['3','4','5']:
         block_4.append(ans)
         index_4.append(pos)
       else:
         block_5.append(ans)
         index_5.append(pos)
     if index in [6,7,8]:
       if colums in ['0','1','2']:
         block_6.append(ans)
         index_6.append(pos)
       elif colums in ['3','4','5']:
         block_7.append(ans)
         index_7.append(pos)
       else:
         block_8.append(ans)
         index_8.append(pos)

   index=[index_0,index_1,index_2,index_3,index_4,index_5,index_6,index_7,index_8]    
   block=[block_0,block_1,block_2,block_3,block_4,block_5,block_6,block_7,block_8]

   ans_=[]  
   for index_array in block:
     l2=[]
     for i in index_array:
       l2.append(set(i))

     for i in np.unique(l2):
       if l2.count(i)==len(i):
         for k,j in enumerate(l2):
           if i!=j:
             j=j-i
             l2[k]=j   
     ans_.append(list(l2))

   pos_=[]
   for i in index:
     pos_=pos_+i

   ans_list=[]
   for i in ans_:
     ans_list=ans_list+i
   ans_listn=[]
   for i in ans_list:
     ans_listn.append(list(i))
   return zip(pos_,ans_listn)

class rule_():

def result(self,data):
   Rule_1=rule_1()
   Rule_2=rule_2()
   Rule_3=rule_3()

   result_dict_1={}
   for pos,ans in Rule_1.result(data):
     result_dict_1[pos]=set(ans)
   result_dict_2={}
   for pos,ans in Rule_2.result(data):
     result_dict_2[pos]=set(ans)  
   result_dict_3={}
   for pos,ans in Rule_3.result(data):
     result_dict_3[pos]=set(ans)

   #三本字典根据key值 取交集融合为最终结果
   key_list=result_dict_1.keys()
   result_dict={}
   for key in key_list:
     result_dict[key]=(result_dict_1[key])&(result_dict_2[key])&(result_dict_3[key])

   ans=[]
   pos=[]
   for key,value in result_dict.items():
     k=list(value)
     k.sort()
     ans.append(k)
     pos.append(key)

   return zip(pos,ans)

def fill_pinlv(result_zip,data):
#输入数据类型为zip
result_zip=result_zip
result_list=list(result_zip)
#print(result_zip)

block_num_list=[]
for tup in result_list:
   pos=tup[0]
   ans=tup[1]
   block_num=Block_num(pos[0],pos[1],data)
   block_num_list.append(block_num)
#print(block_num_list)

ind_list_0=[]
ind_list_1=[]
ind_list_2=[]
ind_list_3=[]
ind_list_4=[]
ind_list_5=[]
ind_list_6=[]
ind_list_7=[]
ind_list_8=[]
ind_block_array=[]
for ind,num in enumerate(block_num_list):

   if num==0:
     ind_list_0.append(ind)
   if num==1:
     ind_list_1.append(ind)       
   if num==2:
     ind_list_2.append(ind)       
   if num==3:
     ind_list_3.append(ind)
   if num==4:
     ind_list_4.append(ind)       
   if num==5:
     ind_list_5.append(ind)   
   if num==6:
     ind_list_6.append(ind)
   if num==7:
     ind_list_7.append(ind)       
   if num==8:
     ind_list_8.append(ind)   
ind_block_array=[ind_list_0,ind_list_1,ind_list_2,ind_list_3,ind_list_4,ind_list_5,ind_list_6,ind_list_7,ind_list_8]
#print(ind_block_array)

result_block_array=[]
for ind_list in ind_block_array:
   result_block_list=[]
   for ind in ind_list:
     result_block_list.append(result_list[ind])
   result_block_array.append(result_block_list)  
#print(result_block_array)

#生成block_counter_array
block_counter_array=[]
for block_list in result_block_array:
   counter_list=[]
   for i in range(1,10):
     counter=0
     for pos,ans in block_list:
       if i in ans:
         counter+=1
     counter_list.append(counter)
   block_counter_array.append(counter_list) 
#print(block_counter_array)

#更新数据data
jishuqi=0
for block_index,block in enumerate(block_counter_array):
   processing_num=0
   processing_num_pos=False
   for num,count in enumerate(block):
     if count==1:
       processing_num=num+1
       for tup in result_list:
         pos=tup[0]
         ans=tup[1]

         if block_index==Block_num(pos[0],pos[1],data):
           #print(block_index)
           if processing_num in ans:
             #print(pos)
             processing_num_pos=pos
             jishuqi+=1
             data[processing_num_pos[1]][processing_num_pos[0]]=processing_num
             if jianyan(data)==False:
               data[processing_num_pos[1]][processing_num_pos[0]]=0
               return jishuqi

return jishuqi 

def fill_jilian(data):
jishuqi=0
for i in range(1,10):
index_list=[]
col_list=[]
block_dataframe=pd.DataFrame()
for block_num in range(9):
#print(block_num)
block_dataframe=Block_dataframe(block_num,data)
index_list=list(block_dataframe.index)
col_list=list(block_dataframe.columns)
if i not in block_dataframe.values:
#排除行 index
for ind in index_list:
for col in range(9):
if i==data.iloc[ind][col]:
index_list.remove(ind)
#排除列 col
for col in col_list:
for ind in range(9):
if i ==data[col][ind]:
col_list.remove(col) 
 #排除有数的cell
     pos_list=[]
     for ind in index_list:
       for col in col_list:
         pos=(ind,col)
         pos_list.append(pos)
     for pos in pos_list:
       if data[pos[1]][pos[0]]!=0:
         pos_list.remove(pos)
     #print(pos_list)
     #填入数字
     if len(pos_list)==1:
       pos=pos_list[0]
       data[pos[1]][pos[0]]=i  
       jishuqi+=1
#print('已经填入{}个数字'.format(jishuqi))
return jishuqi

def fill(data,classname):
#print('执行中。。。')
data=data
if classname =='result':
cla=result()
elif classname=='paichu':
cla=paichu()
elif classname=='rule':
cla=rule()
#如果位置上只有一种可能，就直接填入data
i=0
m=0
flag_1=True
while(flag_1):

   if result_min_len(data)==0:
     #print('上一轮输入的数据有误')
     flag_1=False  
   m=i
   for pos,ans in cla.result(data):
     #print(len(ans))
     if len(ans)==1:
       i+=1
       ind=pos[0]
       col=pos[1]
       data[col][ind]=ans[0]
       if jianyan(data)==False:
         #print('填入数据出错，已停止填写')
         flag_1=False
         break      
   if m == i:
     break       

#如果位置上只有多种可能，就使用fill_jilian（）填入data
j=0
m=0
flag_2=True
while(flag_2):

   if result_min_len(data)==0:
     #print('上一轮输入的数据有误')
     flag_2=False
   if jianyan(data)==False:
     #print('填入数据出错，已停止填写')
     flag_2=False
   m=j
   j=j+fill_pinlv(cla.result(data),data)
   if m == j:
     break

def labelinit(data):
R=rule()
label_list=[]
for pos,ans in R.result(data):
label_list.append([pos,ans,[None]*len(ans)])
return label_list
def label_change_B(pos,ans,label_list):
#label_list_copy=label_list.copy()
for l in label_list:
if l[0]==pos:
for a in range(len(l[2])):
l[2][a]=False
if ans == l[1][a]:
l[2][a]=True
return
def label_change_A(pos,ans,label_list):
#label_list_copy=label_list.copy()
for l in label_list:
if l[0]==pos:
for a in range(len(l[2])):
l[2][a]=False
if ans == l[1][a]:
l[2][a]=False
return
def label_rechange(data,label_list):
try:
#更新label_list
for ind,l in enumerate(label_list):
if (None not in l[2]) and (True not in l[2]):
#清空最后一行
process_1=[None]*len(l[1])
#上一行True后移一个单位
process_2=label_list[ind-1][2]
index=process_2.index(True)+1
process_2.pop()
process_2.insert(0,False)
label_list[ind][2]=process_1
label_list[ind-1][2]=process_2
return True
except:
print('label_rechange 出错')
print('请确认输入数据正确！！！')
return False
def data_change(data,label_list):
#根据label_list更新数据data
try:
for l in label_list:
if True in l[2]:
pos=l[0]
ans=l[1]
marker=l[2]
data[pos[1]][pos[0]]=ans[marker.index(True)]
else:
print('data 按照label假设完成')
break
except:
print('data_change 出错')
def AB_test(data_copy):

flag=None
#AB判断（3种方向，1成功，2返回，3继续，）
flag_1=jianyan(data_copy)
flag_2=full(data_copy)
flag_3=result_min_len(data)
if flag_1==True:
   if flag_2==True:
     #1成功
     print('C:成功找到结果')
     print(data_copy)
     flag='C'
   if flag_2==False:
     if flag_3==0:
       #2返回
       print('A:遍历下一个ans')
       flag='A'
       #label_change(pos,ans,result_label_list)
     if flag_3>0:
       #3继续
       print('B:进入下一位置')
       flag='B'
       #label_change(pos,ans,result_label_list) 
if flag_1==False:
   #2返回
   print('A:遍历下一个ans')
   flag='A'
   #label_change(pos,ans,result_label_list)
return flag

def jiashe(data,label_list_array,lunci):
data_copy=data.copy()
R=result()
ans_list=label_list_array[lunci][1]
pos=label_list_array[lunci][0]

for ans in ans_list:
   #假设
   data_copy[pos[1]][pos[0]]=ans 
   #推导
   fill(data_copy,'result')
   fill(data_copy,'rule_')
   fill(data_copy,'rule_')
   label=AB_test(data_copy)

   if label=='B':
     #假设下一位置 重启假设函数
     label_change_B(pos,ans,label_list_array)
     return 'B'
   elif label=='A':
     #假设下一ans 遍历下一个ans
     label_change_A(pos,ans,label_list_array) 
   elif label=='C':
     #print('success')
     return data_copy

def jie(data,label_list_array):
ind=0
for i in range(10): 
 f_1=jiashe(data,label_list_array,ind)
   if type(f_1)==pd.core.frame.DataFrame:
     return f_1

   f_2=label_rechange(data,label_list_array)
   data_change(data,label_list_array)
   ind+=1
   if f_2:
     ind-=1
     print('B：返回上一位置')
   if f_2==False:
     return False
   #print(label_list_array[0:5]) 
def main(data):
datacopy=data.copy()
fill(data,'result')
fill(data,'rule')
label_list_array=label_init(data)
shudu_jie=jie(data,label_list_array)
print('原始数据')
print(data_copy)
print('结果是')
print(shudu_jie)
main(data)

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