python 8皇后

## 初始化棋盘矩阵和用来表示约束条件的矩阵
def initial(p,limit):
    for i in range(0,8):
        p[i] = list(range(8))
        limit[i] = list(range(8))

    for x in range(8):
        for y in range(8):
            p[x][y] = 0
            limit[x][y] = 1
    return p,limit
def getPL():
    p = list(range(8))
    limit = list(range(8))
    initial(p,limit)
    return p,limit

# 增加约束条件
def addLimit(limit,x,y):
    limit[x][y] = 0
    for i in range(8):
        limit[x][i] = 0
    for i in range(8):
        limit[i][y] = 0
    tx,ty = x+1,y+1
    while tx <8 and ty <8:
        limit[tx][ty] = 0
        tx += 1
        ty += 1
    tx,ty = x-1,y-1
    while tx >=0 and ty >=0 :
        limit[tx][ty] = 0
        tx -= 1
        ty -= 1
    tx,ty = x+1,y-1
    while tx in range(8) and ty in range(8):
        limit[tx][ty] = 0
        tx += 1
        ty -= 1
    tx,ty = x-1,y+1
    while tx in range(8) and ty in range(8):
        limit[tx][ty] = 0
        tx -= 1
        ty += 1

## 获得可以放入的位置
def get_potential_position_list(limit):
    re = []
    for x in range(8):
        for y in range(8):
            if limit[x][y] :
                re.append((x,y))
    return re
    # no potential positon

## 复制
def copy(p,l):
    p_,l_ = getPL()
    for  i in range(len(p)):
        for j in range(len(l)):
            p_[i][j] = p[i][j]
            l_[i][j] = l[i][j]
    return p_,l_

## 放入queen 返回新的棋盘 和 表示约束的矩阵
def insert_no_sf(p,x,y,limit):
    pc,lc= copy(p,limit)
    insert(pc,x,y,lc)
    return pc,lc

## 放入queen
def insert(p,x,y,limit):
    p[x][y] = 1
    addLimit(limit,x,y)

## 深度优先搜索
def search_wrapper(p,l):
    p_in = p
    l_in = l
    ##用来判断 base case
    done = False
    def search(p,l):
        nonlocal done
        nonlocal p_in
        if done:
            return 
        c = count(p)

        if c == 8 :
            done = True
            p_in = p
            return
        else:
            ## 递归访问树
            pot = get_potential_position_list(l)
            ## 出现冲突则停止递归
            if len(pot)+c <8 :return
            for x,y in pot:
                p_,l_ = insert_no_sf(p,x,y,l)
                search(p_,l_)
    search(p_in,l_in)

    return p_in
# queens count
def count(p):
    count__ = 0
    for x in p:
        for y in x:
            if y:
                count__ += 1
    return count__







p,l = getPL()