基于 Python 的八数码问题的深度、广度搜索 与启发式算法分析代码

八数码问题是一个经典的人工智能问题，可以使用深度搜索、广度搜索和启发式算法等多种方法进行求解。下面给出基于 Python 的八数码问题的深度、广度搜索和启发式算法的代码实现。

首先定义一个表示八数码问题状态的类 `State`，其中 `board` 表示当前状态的棋盘布局，`parent` 表示当前状态的父状态，`action` 表示当前状态到达该状态的操作，`depth` 表示当前状态的深度。

class State:
    def __init__(self, board, parent, action, depth):
        self.board = board
        self.parent = parent
        self.action = action
        self.depth = depth

接下来定义一个函数 `get_blank_pos`，用于获取空格（0）的位置。

def get_blank_pos(board):
    for i in range(3):
        for j in range(3):
            if board[i][j] == 0:
                return i, j

定义一个函数 `get_successors`，用于获取当前状态的所有合法后继状态。

def get_successors(state):
    successors = []
    blank_i, blank_j = get_blank_pos(state.board)
    for action, (di, dj) in ACTIONS.items():
        new_i, new_j = blank_i + di, blank_j + dj
        if 0 <= new_i < 3 and 0 <= new_j < 3:
            new_board = [row[:] for row in state.board]
            new_board[blank_i][blank_j], new_board[new_i][new_j] = new_board[new_i][new_j], new_board[blank_i][blank_j]
            successors.append(State(new_board, state, action, state.depth + 1))
    return successors

定义一个函数 `is_goal`，用于判断当前状态是否为目标状态。

def is_goal(state):
    return state.board == GOAL_STATE

接下来实现深度搜索算法，定义一个函数 `depth_first_search`，使用栈（Stack）作为数据结构。

def depth_first_search(initial_state):
    stack = [initial_state]
    visited = set()
    while stack:
        state = stack.pop()
        if is_goal(state):
            return state
        visited.add(tuple(map(tuple, state.board)))
        successors = get_successors(state)
        for successor in reversed(successors):
            if tuple(map(tuple, successor.board)) not in visited:
                stack.append(successor)
    return None

实现广度搜索算法，定义一个函数 `breadth_first_search`，使用队列（Queue）作为数据结构。

def breadth_first_search(initial_state):
    queue = collections.deque([initial_state])
    visited = set()
    while queue:
        state = queue.popleft()
        if is_goal(state):
            return state
        visited.add(tuple(map(tuple, state.board)))
        successors = get_successors(state)
        for successor in successors:
            if tuple(map(tuple, successor.board)) not in visited:
                queue.append(successor)
    return None

接下来实现启发式搜索算法，使用曼哈顿距离作为启发函数，定义一个函数 `manhattan_distance`，用于计算当前状态到目标状态的曼哈顿距离。

def manhattan_distance(board):
    distance = 0
    for i in range(3):
        for j in range(3):
            if board[i][j] != 0:
                row, col = divmod(board[i][j] - 1, 3)
                distance += abs(row - i) + abs(col - j)
    return distance

定义一个函数 `a_star_search`，使用优先队列（Priority Queue）作为数据结构。

def a_star_search(initial_state):
    queue = [(manhattan_distance(initial_state.board), initial_state)]
    visited = set()
    while queue:
        _, state = heappop(queue)
        if is_goal(state):
            return state
        visited.add(tuple(map(tuple, state.board)))
        successors = get_successors(state)
        for successor in successors:
            if tuple(map(tuple, successor.board)) not in visited:
                heappush(queue, (manhattan_distance(successor.board) + successor.depth, successor))
    return None

最后定义一些常量和操作字典。

import collections
from heapq import heappush, heappop

INITIAL_STATE = [
    [2, 8, 3],
    [1, 6, 4],
    [7, 0, 5]
]

GOAL_STATE = [
    [1, 2, 3],
    [8, 0, 4],
    [7, 6, 5]
]

ACTIONS = {
    'Up': (-1, 0),
    'Down': (1, 0),
    'Left': (0, -1),
    'Right': (0, 1)
}

可以使用以下代码测试以上算法：

initial_state = State(INITIAL_STATE, None, None, 0)

print('Depth First Search:')
result = depth_first_search(initial_state)
if result is not None:
    print('Solution found in', result.depth, 'steps')
    while result.parent is not None:
        print(result.action)
        result = result.parent
else:
    print('No solution found')

print('Breadth First Search:')
result = breadth_first_search(initial_state)
if result is not None:
    print('Solution found in', result.depth, 'steps')
    while result.parent is not None:
        print(result.action)
        result = result.parent
else:
    print('No solution found')

print('A* Search:')
result = a_star_search(initial_state)
if result is not None:
    print('Solution found in', result.depth, 'steps')
    while result.parent is not None:
        print(result.action)
        result = result.parent
else:
    print('No solution found')