用代码实现用博弈树搜索算法解决八数码问题,且输出每一步棋盘状态
时间: 2024-04-03 09:37:08 浏览: 75
好的,以下是用 Python 实现的八数码问题博弈树搜索算法,并且输出每一步棋盘状态的代码:
```python
import copy
class Node:
def __init__(self, puzzle, parent=None, move=None):
self.puzzle = puzzle
self.parent = parent
self.move = move
self.depth = 0
if parent is not None:
self.depth = parent.depth + 1
def __lt__(self, other):
return self.heuristic() < other.heuristic()
def heuristic(self):
h = 0
for i in range(3):
for j in range(3):
if self.puzzle[i][j] != 0:
h += abs(i - (self.puzzle[i][j]-1)//3) \
+ abs(j - (self.puzzle[i][j]-1)%3)
return h + self.depth
def get_moves(self):
i, j = next((i, j) for i in range(3) for j in range(3) if self.puzzle[i][j] == 0)
moves = []
if i > 0:
puzzle = copy.deepcopy(self.puzzle)
puzzle[i][j], puzzle[i-1][j] = puzzle[i-1][j], puzzle[i][j]
moves.append(Node(puzzle, self, 'D'))
if i < 2:
puzzle = copy.deepcopy(self.puzzle)
puzzle[i][j], puzzle[i+1][j] = puzzle[i+1][j], puzzle[i][j]
moves.append(Node(puzzle, self, 'U'))
if j > 0:
puzzle = copy.deepcopy(self.puzzle)
puzzle[i][j], puzzle[i][j-1] = puzzle[i][j-1], puzzle[i][j]
moves.append(Node(puzzle, self, 'R'))
if j < 2:
puzzle = copy.deepcopy(self.puzzle)
puzzle[i][j], puzzle[i][j+1] = puzzle[i][j+1], puzzle[i][j]
moves.append(Node(puzzle, self, 'L'))
return moves
def solve(puzzle):
start_node = Node(puzzle)
if start_node.heuristic() == 0:
return start_node.puzzle
queue = [start_node]
visited = set()
visited.add(tuple(map(tuple, start_node.puzzle)))
while queue:
node = queue.pop(0)
for move in node.get_moves():
if tuple(map(tuple, move.puzzle)) not in visited:
if move.heuristic() == 0:
path = []
while move.parent is not None:
path.append(move)
move = move.parent
path.reverse()
for i in path:
print(i.move)
for j in i.puzzle:
print(j)
return move.puzzle
visited.add(tuple(map(tuple, move.puzzle)))
queue.append(move)
# 测试代码
puzzle = [[1, 2, 3], [4, 5, 6], [7, 0, 8]]
solve(puzzle)
```
在上面的代码中,我们定义了 `Node` 类表示一个节点,其中 `puzzle` 属性表示当前状态,`parent` 属性表示父节点,`move` 属性表示当前节点到父节点的移动方式,`depth` 属性表示当前节点的深度。
`__lt__` 方法用于比较两个节点的启发式函数值,`heuristic` 方法表示当前状态到目标状态的估价函数值,使用曼哈顿距离作为启发式函数。
`get_moves` 方法用于获取当前状态所有可能的移动方式生成子节点。
`solve` 方法表示求解八数码问题的算法,其中 `queue` 表示 BFS 中的队列,`visited` 表示已经访问过的状态集合。
在 `solve` 方法中,我们使用 BFS 算法搜索所有可能的状态,直到找到目标状态或者所有状态都已经搜索完成。
当找到目标状态时,我们通过 `path` 反向遍历所有父节点,并输出每一步的移动方式和棋盘状态。