八数码问题

八数码

Note：实现代码之前可以先写出伪代码，可以节省很多时间。编程语言只是一种实现工具。

def judge_position(init_m,target_m):#返回当前位置正确的数字的个数，以及0所在位置
    current_right_nums=0 #store numbers of right position currently.
    zero_r=0
    zero_c=0
    count=0  #当前状态中，各数字移动到正确位置的步数
    for row in range(3):
        for col in range(3):
            if init_m[row][col]==0:
                zero_r=row
                zero_c=col
            if init_m[row][col]==target_m[row][col]:
                current_right_nums+=1
            else:
                for j in range(3):
                    for k in range(3): 
                        if init_m[row][col]==target_m[j][k] and init_m[row][col]!=0:
                            count+=abs(row-j)+abs(col-k)
    return (current_right_nums,zero_r,zero_c,count)
    
#----------------------------

def change_position(init_m,zero_r,zero_c):
    #判断当前状态是否等于结束状态
    current_right_nums,zero_r,zero_c,count=judge_position(init_m,target_matrix)
    print("----------")
    m1=[[i for i in row] for row in init_m]
    m2=[[i for i in row] for row in init_m]
    m3=[[i for i in row] for row in init_m]
    m4=[[i for i in row] for row in init_m]
    next_matrixes=[]
    #交换位置：(zero_r+1,zero_c+1)(zero_r,zero_c-1)(zero_r,zero_c+1)(zero_r-1,zero_c)
    if  zero_r+1<3:
        temp=m1[zero_r+1][zero_c]
        m1[zero_r+1][zero_c]=m1[zero_r][zero_c]
        m1[zero_r][zero_c]=temp
        next_matrixes.append(m1)
    
    if zero_c-1>-1:   #zero_r,zero_c-1
        temp=m2[zero_r][zero_c-1]
        m2[zero_r][zero_c-1]=m2[zero_r][zero_c]
        m2[zero_r][zero_c]=temp
        next_matrixes.append(m2)
    
    if zero_c+1<3:    #(zero_r,zero_c+1)
        temp=m3[zero_r][zero_c+1]
        m3[zero_r][zero_c+1]=m3[zero_r][zero_c]
        m3[zero_r][zero_c]=temp
        next_matrixes.append(m3)
    
    if zero_r-1>-1: #(zero_r-1,zero_c)
        temp=m4[zero_r-1][zero_c]
        m4[zero_r-1][zero_c]=m4[zero_r][zero_c]
        m4[zero_r][zero_c]=temp
        next_matrixes.append(m4)
    #判断每一状态中，各数字移动到正确位置的补步数，选取最小的
    matrixes_info=[]
    for martrix in next_matrixes:
        matrixes_info.append(list(judge_position(martrix,target_matrix)))
    to_target_counts=[i[3] for i in matrixes_info]
    best_matrix=next_matrixes[to_target_counts.index(min(to_target_counts))]
    if matrixes_info[next_matrixes.index(best_matrix)][3]==0:
        print("\nSuccess!Next step is target matrix:")
        for row in best_matrix:
            print(row)
        return
    print("next_step:")
    for row in best_matrix:
            print(row)
    print("Current_right_numbers:",matrixes_info[next_matrixes.index(best_matrix)][0])
    print("To target need steps:",matrixes_info[next_matrixes.index(best_matrix)][3])
    zero_r=matrixes_info[next_matrixes.index(best_matrix)][1]
    zero_c=matrixes_info[next_matrixes.index(best_matrix)][2]
    change_position(best_matrix,zero_r,zero_c)
    
def regular_matrix(init_m,target_m):
    current_right_nums,zero_r,zero_c,count=judge_position(init_matrix,target_matrix)
    change_position(init_m,zero_r,zero_c)
    
if __name__ == "__main__":
    
    init_matrix=[[2,8,3],[1,0,4],[7,6,5]]
    target_matrix=[[1,2,3],[8,0,4],[7,6,5]]
    current_right_nums,zero_r,zero_c,count=judge_position(init_matrix,target_matrix)    
    regular_matrix(init_matrix,target_matrix)