python实现数独游戏
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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 Truedef 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_numdef 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_listdef 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
returndef 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
returndef 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 Falsedef 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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