python爬山算法解决八皇后问题_重启爬山法八皇后问题python

问题表述为：在8×8的国际象棋棋盘上摆放8个皇后，使其不能互相攻击，即任意两个皇后都不能处于同一行、同一列或同一斜线上，问有多少种摆法

使用爬山算法解决八皇后问题，思路：

1. 先初始化皇后位置，使得每一行每一列一个有且仅有一个皇后

2. 计算冲突的皇后数量(计做冲突值)，比如同一行、同一列、同一斜线的数量

3. 准备移动皇后，但是往哪移动呢？每一行皇后只能在自己所在行移动，所以只有列会改变

    比如把第一行皇后从（0,1）移动到（0,0），那么整个棋局的冲突值会发生改变（假设冲突值变小了6->5），此时记录为(0,0):5

   然后遍历所有空位，记录移动到此空位时所有皇后的对应冲突值

4. 找到棋盘中所有空位的冲突值最小的位置，随机选择一个冲突值最小空位置，移动所在行皇后此位置，然后重复上一步3的动作，重新计算棋盘上所有皇后冲突值和所有空位冲突值，循环动作3，直到所有皇后的冲突值为0，此时已经找到一组正确的8皇后位置

5.到第四步已经完成了爬山算法，但是爬山算法有个缺点，有可能找到局部最优，而不是全局最优

   以本案为例他只找到了一组最佳位置，但事实上有很多组。此时可以随机生成多个初始位置(也就是爬山起点分散多个地方)，就可以找到不同的最佳答案了

代码如下：

import random, copy, time
 
"""
解决8皇后问题
初始化
随机生成皇后位置,使其不同列、不同行只有一个
"""
 
 
def init():
    # 随机生成皇后位置,使其不同列、不同行只有一个
    status = []
    for r in range(8):
        while len(status) <= 8:
            c = random.randint(0, 7)
            if c not in [mm[1] for mm in status]:
                status.append((r, c))
                break
    return status
 
 
"""
遍历所有皇后
计算有冲突的皇后坐标(同一行，同一列，斜边)
计算整个棋盘冲突的数量
假设初始化传入皇后位置：
[(0, 3), (1, 6), (2, 7), (3, 0), (4, 2), (5, 1), (6, 4), (7, 5)]
"""
 
 
def conflict(status):
    num = 0  # 存储冲突数量
    conflict_chess = []
    for pos in status:
        for other_pos in status:
            if pos == other_pos or pos in conflict_chess:
                continue
            elif pos[0] == other_pos[0] or pos[1] == other_pos[1] or abs(pos[0] - other_pos[0]) == abs(
                    pos[1] - other_pos[1]):
                num += 1
                conflict_chess.append(pos)
 
    return num, conflict_chess
 
 
"""
遍历所有空位
计算当行的皇后移动到此空位时整个棋盘的冲突值
会得出8*8-8 = 56个冲突值
也就是56种移动方法
选择冲突值最小的一种进行移动
"""
 
 
def move_chess(status):
    empty_pos = {}  # 用字典保存所有空位冲突值
 
    for r in range(8):
        for c in range(8):
            if (r, c) not in status:
                new_status = copy.deepcopy(status)
                new_status[r] = (r, c)
                empty_pos[(r, c)] = conflict(new_status)[0]
            else:
                continue
    return empty_pos
 
 
"""
循环获取冲突数量
若数量>1,执行move_chess
指导冲突数量=0，此时寻找到最佳位置
"""
 
 
def climbing(status):
    # 获取当前皇后位置的冲突值
    conflict_num = conflict(status)[0]
    # 设置循环次数，避免一直循环，冲突值一直无法降到最低0时，自动跳出循环
    # 设置移动皇后500次，如果找不到正确位置就重新初始化皇后位置
    loop_cnt = 0
    while conflict_num != 0 and loop_cnt < 500:
        # 获取所有空位冲突值
        empty_pos = move_chess(status)
        min_value = min(empty_pos.values())
        # 获取最小冲突值对应的key 即坐标pos
        min_pos_ls = []
        for k, v in empty_pos.items():
            # print(v, min_value)
            if v == min_value and (k not in min_pos_ls):
                min_pos_ls.append(k)
 
        # print(min_pos_ls, min_value)
        # print(status)
        # 随机取一个空位点，与当前同一行皇后交换位置，然后计算所有空位置的冲突值和当前棋局内皇后自身冲突值
        i = random.randint(0, len(min_pos_ls) - 1)
        status[min_pos_ls[i][0]] = min_pos_ls[i]
        conflict_num = conflict(status)[0]
        loop_cnt += 1
    return status, loop_cnt
 
 
if __name__ == '__main__':
 
    # 这一个随机数会导致一直找不到最高点
    # status = [(0, 0), (1, 2), (2, 4), (3, 3), (4, 1), (5, 5), (6, 7), (7, 6)]
    # climbing(status)
 
    """
    生成随机位置，迭代600次尽可能多的找出八皇后不同位置
    """
    start = time.time()
    all_pos = []
    for i in range(600):
        status = init()
        # 设置loop_cnt防止一直陷入死循环无法找到最佳点
        # 如果一直找不到就跳出来并且重新生成初始位置
        status, loop_cnt = climbing(status)
        # print(loop_cnt)
        if loop_cnt == 500:
            continue
        elif status not in all_pos:
            all_pos.append(status)
    end = time.time()
    print("一共找到{}组八皇后位置,共耗时{}s".format(len(all_pos), end - start))
    for pos in all_pos:
        print(pos)

运行结果如下：

C:\Users\LU\.conda\envs\ai_course\python.exe C:/Users/LU/PycharmProjects/ai_course/eight_queens_2d.py
一共找到92组八皇后位置,共耗时31.383877515792847s
[(0, 5), (1, 3), (2, 1), (3, 7), (4, 4), (5, 6), (6, 0), (7, 2)]
[(0, 1), (1, 4), (2, 6), (3, 0), (4, 2), (5, 7), (6, 5), (7, 3)]
[(0, 5), (1, 2), (2, 0), (3, 6), (4, 4), (5, 7), (6, 1), (7, 3)]
[(0, 6), (1, 3), (2, 1), (3, 7), (4, 5), (5, 0), (6, 2), (7, 4)]
[(0, 4), (1, 2), (2, 0), (3, 5), (4, 7), (5, 1), (6, 3), (7, 6)]
[(0, 4), (1, 2), (2, 0), (3, 6), (4, 1), (5, 7), (6, 5), (7, 3)]
[(0, 3), (1, 7), (2, 0), (3, 4), (4, 6), (5, 1), (6, 5), (7, 2)]
[(0, 3), (1, 6), (2, 0), (3, 7), (4, 4), (5, 1), (6, 5), (7, 2)]
[(0, 4), (1, 6), (2, 0), (3, 2), (4, 7), (5, 5), (6, 3), (7, 1)]
[(0, 5), (1, 1), (2, 6), (3, 0), (4, 3), (5, 7), (6, 4), (7, 2)]
[(0, 3), (1, 1), (2, 7), (3, 5), (4, 0), (5, 2), (6, 4), (7, 6)]
[(0, 5), (1, 7), (2, 1), (3, 3), (4, 0), (5, 6), (6, 4), (7, 2)]
[(0, 2), (1, 5), (2, 1), (3, 6), (4, 0), (5, 3), (6, 7), (7, 4)]
[(0, 3), (1, 6), (2, 4), (3, 2), (4, 0), (5, 5), (6, 7), (7, 1)]
[(0, 4), (1, 1), (2, 3), (3, 5), (4, 7), (5, 2), (6, 0), (7, 6)]
[(0, 1), (1, 3), (2, 5), (3, 7), (4, 2), (5, 0), (6, 6), (7, 4)]
[(0, 4), (1, 2), (2, 7), (3, 3), (4, 6), (5, 0), (6, 5), (7, 1)]
[(0, 3), (1, 5), (2, 7), (3, 1), (4, 6), (5, 0), (6, 2), (7, 4)]
[(0, 4), (1, 1), (2, 7), (3, 0), (4, 3), (5, 6), (6, 2), (7, 5)]
[(0, 5), (1, 2), (2, 6), (3, 1), (4, 3), (5, 7), (6, 0), (7, 4)]
[(0, 0), (1, 6), (2, 3), (3, 5), (4, 7), (5, 1), (6, 4), (7, 2)]
[(0, 5), (1, 3), (2, 0), (3, 4), (4, 7), (5, 1), (6, 6), (7, 2)]
[(0, 2), (1, 5), (2, 1), (3, 4), (4, 7), (5, 0), (6, 6), (7, 3)]
[(0, 2), (1, 5), (2, 7), (3, 1), (4, 3), (5, 0), (6, 6), (7, 4)]
[(0, 4), (1, 6), (2, 1), (3, 3), (4, 7), (5, 0), (6, 2), (7, 5)]
[(0, 3), (1, 0), (2, 4), (3, 7), (4, 1), (5, 6), (6, 2), (7, 5)]
[(0, 6), (1, 1), (2, 5), (3, 2), (4, 0), (5, 3), (6, 7), (7, 4)]
[(0, 6), (1, 1), (2, 3), (3, 0), (4, 7), (5, 4), (6, 2), (7, 5)]
[(0, 2), (1, 7), (2, 3), (3, 6), (4, 0), (5, 5), (6, 1), (7, 4)]
[(0, 3), (1, 5), (2, 7), (3, 2), (4, 0), (5, 6), (6, 4), (7, 1)]
[(0, 2), (1, 4), (2, 6), (3, 0), (4, 3), (5, 1), (6, 7), (7, 5)]
[(0, 2), (1, 4), (2, 1), (3, 7), (4, 0), (5, 6), (6, 3), (7, 5)]
[(0, 4), (1, 1), (2, 5), (3, 0), (4, 6), (5, 3), (6, 7), (7, 2)]
[(0, 6), (1, 0), (2, 2), (3, 7), (4, 5), (5, 3), (6, 1), (7, 4)]
[(0, 2), (1, 5), (2, 7), (3, 0), (4, 4), (5, 6), (6, 1), (7, 3)]
[(0, 4), (1, 7), (2, 3), (3, 0), (4, 2), (5, 5), (6, 1), (7, 6)]
[(0, 2), (1, 0), (2, 6), (3, 4), (4, 7), (5, 1), (6, 3), (7, 5)]
[(0, 5), (1, 2), (2, 6), (3, 3), (4, 0), (5, 7), (6, 1), (7, 4)]
[(0, 4), (1, 7), (2, 3), (3, 0), (4, 6), (5, 1), (6, 5), (7, 2)]
[(0, 5), (1, 3), (2, 6), (3, 0), (4, 7), (5, 1), (6, 4), (7, 2)]
[(0, 3), (1, 1), (2, 4), (3, 7), (4, 5), (5, 0), (6, 2), (7, 6)]
[(0, 5), (1, 2), (2, 6), (3, 1), (4, 7), (5, 4), (6, 0), (7, 3)]
[(0, 5), (1, 3), (2, 6), (3, 0), (4, 2), (5, 4), (6, 1), (7, 7)]
[(0, 3), (1, 6), (2, 4), (3, 1), (4, 5), (5, 0), (6, 2), (7, 7)]
[(0, 2), (1, 5), (2, 1), (3, 6), (4, 4), (5, 0), (6, 7), (7, 3)]
[(0, 6), (1, 4), (2, 2), (3, 0), (4, 5), (5, 7), (6, 1), (7, 3)]
[(0, 1), (1, 6), (2, 4), (3, 7), (4, 0), (5, 3), (6, 5), (7, 2)]
[(0, 5), (1, 0), (2, 4), (3, 1), (4, 7), (5, 2), (6, 6), (7, 3)]
[(0, 5), (1, 2), (2, 4), (3, 6), (4, 0), (5, 3), (6, 1), (7, 7)]
[(0, 5), (1, 2), (2, 0), (3, 7), (4, 4), (5, 1), (6, 3), (7, 6)]
[(0, 2), (1, 5), (2, 3), (3, 0), (4, 7), (5, 4), (6, 6), (7, 1)]
[(0, 2), (1, 5), (2, 3), (3, 1), (4, 7), (5, 4), (6, 6), (7, 0)]
[(0, 1), (1, 5), (2, 7), (3, 2), (4, 0), (5, 3), (6, 6), (7, 4)]
[(0, 2), (1, 6), (2, 1), (3, 7), (4, 4), (5, 0), (6, 3), (7, 5)]
[(0, 4), (1, 6), (2, 3), (3, 0), (4, 2), (5, 7), (6, 5), (7, 1)]
[(0, 5), (1, 2), (2, 4), (3, 7), (4, 0), (5, 3), (6, 1), (7, 6)]
[(0, 5), (1, 2), (2, 0), (3, 7), (4, 3), (5, 1), (6, 6), (7, 4)]
[(0, 2), (1, 5), (2, 7), (3, 0), (4, 3), (5, 6), (6, 4), (7, 1)]
[(0, 1), (1, 7), (2, 5), (3, 0), (4, 2), (5, 4), (6, 6), (7, 3)]
[(0, 3), (1, 5), (2, 0), (3, 4), (4, 1), (5, 7), (6, 2), (7, 6)]
[(0, 1), (1, 5), (2, 0), (3, 6), (4, 3), (5, 7), (6, 2), (7, 4)]
[(0, 6), (1, 2), (2, 7), (3, 1), (4, 4), (5, 0), (6, 5), (7, 3)]
[(0, 0), (1, 4), (2, 7), (3, 5), (4, 2), (5, 6), (6, 1), (7, 3)]
[(0, 3), (1, 7), (2, 4), (3, 2), (4, 0), (5, 6), (6, 1), (7, 5)]
[(0, 3), (1, 1), (2, 6), (3, 2), (4, 5), (5, 7), (6, 0), (7, 4)]
[(0, 3), (1, 6), (2, 2), (3, 7), (4, 1), (5, 4), (6, 0), (7, 5)]
[(0, 4), (1, 0), (2, 3), (3, 5), (4, 7), (5, 1), (6, 6), (7, 2)]
[(0, 4), (1, 0), (2, 7), (3, 5), (4, 2), (5, 6), (6, 1), (7, 3)]
[(0, 5), (1, 1), (2, 6), (3, 0), (4, 2), (5, 4), (6, 7), (7, 3)]
[(0, 6), (1, 3), (2, 1), (3, 4), (4, 7), (5, 0), (6, 2), (7, 5)]
[(0, 4), (1, 1), (2, 3), (3, 6), (4, 2), (5, 7), (6, 5), (7, 0)]
[(0, 3), (1, 7), (2, 0), (3, 2), (4, 5), (5, 1), (6, 6), (7, 4)]
[(0, 4), (1, 0), (2, 7), (3, 3), (4, 1), (5, 6), (6, 2), (7, 5)]
[(0, 3), (1, 1), (2, 6), (3, 4), (4, 0), (5, 7), (6, 5), (7, 2)]
[(0, 2), (1, 4), (2, 1), (3, 7), (4, 5), (5, 3), (6, 6), (7, 0)]
[(0, 2), (1, 6), (2, 1), (3, 7), (4, 5), (5, 3), (6, 0), (7, 4)]
[(0, 1), (1, 4), (2, 6), (3, 3), (4, 0), (5, 7), (6, 5), (7, 2)]
[(0, 0), (1, 5), (2, 7), (3, 2), (4, 6), (5, 3), (6, 1), (7, 4)]
[(0, 3), (1, 1), (2, 7), (3, 4), (4, 6), (5, 0), (6, 2), (7, 5)]
[(0, 4), (1, 6), (2, 1), (3, 5), (4, 2), (5, 0), (6, 7), (7, 3)]
[(0, 3), (1, 0), (2, 4), (3, 7), (4, 5), (5, 2), (6, 6), (7, 1)]
[(0, 6), (1, 2), (2, 0), (3, 5), (4, 7), (5, 4), (6, 1), (7, 3)]
[(0, 4), (1, 6), (2, 0), (3, 3), (4, 1), (5, 7), (6, 5), (7, 2)]
[(0, 0), (1, 6), (2, 4), (3, 7), (4, 1), (5, 3), (6, 5), (7, 2)]
[(0, 2), (1, 4), (2, 7), (3, 3), (4, 0), (5, 6), (6, 1), (7, 5)]
[(0, 7), (1, 1), (2, 3), (3, 0), (4, 6), (5, 4), (6, 2), (7, 5)]
[(0, 7), (1, 3), (2, 0), (3, 2), (4, 5), (5, 1), (6, 6), (7, 4)]
[(0, 7), (1, 1), (2, 4), (3, 2), (4, 0), (5, 6), (6, 3), (7, 5)]
[(0, 1), (1, 6), (2, 2), (3, 5), (4, 7), (5, 4), (6, 0), (7, 3)]
[(0, 4), (1, 6), (2, 1), (3, 5), (4, 2), (5, 0), (6, 3), (7, 7)]
[(0, 3), (1, 1), (2, 6), (3, 2), (4, 5), (5, 7), (6, 4), (7, 0)]
[(0, 7), (1, 2), (2, 0), (3, 5), (4, 1), (5, 4), (6, 6), (7, 3)]
 
Process finished with exit code 0