python启发式搜索算法解决八数码问题

以下是使用Python实现启发式搜索算法解决八数码问题的步骤：

1.定义状态类，包含当前状态、父状态、深度、评估函数值等属性。

2.定义评估函数，用于评估当前状态到目标状态的距离。

3.定义启发式搜索函数，使用优先队列存储状态，每次取出评估函数值最小的状态进行扩展，直到找到目标状态或者队列为空。

4.定义状态扩展函数，生成当前状态的所有可能子状态。

5.判断初始状态是否有解，若无解则无法进行搜索。

6.使用Pygame库实现图形化界面，方便用户进行交互。

以下是一个简单的Python代码示例，实现了八数码问题的启发式搜索算法：

import pygame
from queue import PriorityQueue

# 定义状态类
class State:
    def __init__(self, state, parent, depth, f):
        self.state = state
        self.parent = parent
        self.depth = depth
        self.f = f

    def __lt__(self, other):
        return self.f < other.f

# 定义评估函数
def heuristic(state, target):
    distance = 0
    for i in range(3):
        for j in range(3):
            if state[i][j] != target[i][j]:
                distance += 1
    return distance

# 定义状态扩展函数
def expand(state):
    states = []
    for i in range(3):
        for j in range(3):
            if state[i][j] == 0:
                if i > 0:
                    new_state = [row[:] for row in state]
                    new_state[i][j], new_state[i-1][j] = new_state[i-1][j], new_state[i][j]
                    states.append(new_state)
                if i < 2:
                    new_state = [row[:] for row in state]
                    new_state[i][j], new_state[i+1][j] = new_state[i+1][j], new_state[i][j]
                    states.append(new_state)
                if j > 0:
                    new_state = [row[:] for row in state]
                    new_state[i][j], new_state[i][j-1] = new_state[i][j-1], new_state[i][j]
                    states.append(new_state)
                if j < 2:
                    new_state = [row[:] for row in state]
                    new_state[i][j], new_state[i][j+1] = new_state[i][j+1], new_state[i][j]
                    states.append(new_state)
                return states

# 定义启发式搜索函数
def a_star(start, target):
    queue = PriorityQueue()
    queue.put(State(start, None, 0, heuristic(start, target)))
    visited = set()
    while not queue.empty():
        current = queue.get()
        if current.state == target:
            path = []
            while current:
                path.append(current.state)
                current = current.parent
            return path[::-1]
        visited.add(str(current.state))
        for state in expand(current.state):
            if str(state) not in visited:
                queue.put(State(state, current, current.depth+1, current.depth+1+heuristic(state, target)))
    return None

# 判断初始状态是否有解
def solvable(state):
    inversion = 0
    for i in range(9):
        for j in range(i+1, 9):
            if state[i//3][i%3] and state[j//3][j%3] and state[i//3][i%3] > state[j//3][j%3]:
                inversion += 1
    return inversion % 2 == 0

# 初始化Pygame
pygame.init()
size = width, height = 300, 300
screen = pygame.display.set_mode(size)
pygame.display.set_caption("八数码问题")

# 定义颜色
white = (255, 255, 255)
black = (0, 0, 0)
gray = (128, 128, 128)

# 定义字体
font = pygame.font.SysFont("Arial", 20)

# 定义方块
class Block:
    def __init__(self, value, row, col):
        self.value = value
        self.row = row
        self.col = col

    def draw(self):
        rect = pygame.Rect(self.col*100, self.row*100, 100, 100)
        pygame.draw.rect(screen, white, rect)
        pygame.draw.rect(screen, black, rect, 2)
        if self.value:
            text = font.render(str(self.value), True, black)
            text_rect = text.get_rect(center=rect.center)
            screen.blit(text, text_rect)

# 定义游戏主循环
def main_loop():
    start_state = [[1, 2, 3], [4, 5, 6], [7, 8, 0]]
    target_state = [[1, 2, 3], [4, 5, 6], [7, 8, 0]]
    while True:
        for event in pygame.event.get():
            if event.type == pygame.QUIT:
                pygame.quit()
                return
            if event.type == pygame.MOUSEBUTTONUP:
                pos = pygame.mouse.get_pos()
                row, col = pos[1]//100, pos[0]//100
                if start_state[row][col] == 0:
                    continue
                for state in a_star(start_state, target_state):
                    for i in range(3):
                        for j in range(3):
                            if state[i][j] == start_state[row][col]:
                                start_state[row][col], start_state[i][j] = start_state[i][j], start_state[row][col]
                                break
                    draw_board(start_state)
                    pygame.display.flip()
                    pygame.time.wait(100)
                if start_state == target_state:
                    text = font.render("You Win!", True, black)
                    text_rect = text.get_rect(center=(width//2, height//2))
                    screen.blit(text, text_rect)
                    pygame.display.flip()
                    pygame.time.wait(1000)
                    start_state = [[1, 2, 3], [4, 5, 6], [7, 8, 0]]
                    draw_board(start_state)
                    pygame.display.flip()

# 定义绘制游戏界面函数
def draw_board(state):
    screen.fill(gray)
    for i in range(3):
        for j in range(3):
            block = Block(state[i][j], i, j)
            block.draw()

# 判断初始状态是否有解
if not solvable(start_state):
    print("无解")
else:
    draw_board(start_state)
    pygame.display.flip()
    main_loop()