A*算法解决八数码问题

Posted 2021-01-10 ahappybird

from utils import (  PriorityQueue)
import copy
 
infinity = float(‘inf‘)
 
def best_first_graph_search(problem, f):
    #定义初始节点
    node = Node(problem.initial)
    node.fvalue=f(node)
    #如果是最终结果，返回节点
    if problem.goal_test(node):
        return node
    #frotier是一个顺序队列，从小到大排列，排列比较通过f函数
    #如果order是min，最小的先出队
    frontier = PriorityQueue(min, f)
    #加入节点
    frontier.append(node)
    #print(node.fvalue)
    #展开的节点
    explored = set()
    #当栈不为空
    while frontier:
        #节点出队
        node = frontier.pop()
        #print("pop")
        #node.state.display()
        #print(node.fvalue)
        # 如果是最终结果，返回节点
        if problem.goal_test(node):
            return node
        #加入展开的节点
        explored.add(node)
        #对于出栈的子节点
        for child in node.expand(problem):
            #如果节点没有展开，并且子节点没在队中
            if child not in explored and child not in frontier:
                #子节点入队
                frontier.append(child)
                #print(child.fvalue)
                #如果子节点在队中
            elif child in frontier:
                incumbent = frontier[child]
                #如果子节点的f值小于队中节点的f值
                if f(child) < f(incumbent):
                    #删除栈中的节点，子节点入队
                    del frontier[incumbent]
                    frontier.append(child)
                    #print("change fvalue",child.state.display(),child.fvalue)
    return None
#a*算法 f=g+h
def astar_search(problem, h=None):
    h =  problem.h
    return best_first_graph_search(problem, lambda n:h(n) + n.path_cost)
 
class Problem(object):
    def __init__(self, initial, goal=None):
        self.initial = initial
        self.goal = goal
 
    def actions(self, state):
        raise NotImplementedError
 
    def result(self, state, action):
        raise NotImplementedError
 
    def goal_test(self, node):
        return (node.state.board==self.goal.board)
 
    def path_cost(self, c, state1, action, state2):
        return c + 1
 
    def value(self, state):
        raise NotImplementedError
 
class PuzzleProblem(Problem):
    def __init__(self, initial=None, goal=None):
        Problem.__init__(self, initial, goal)
        self.state=initial
        self.goal=goal
 
    def actions(self, state):
        x,y=state.location(0)
        #空格在边缘时减少活动
        action=[(0,1),(0,-1),(1,0),(-1,0)]
        if (x == 0):
            action.remove((-1,0))
        if (x == 2):
            action.remove((1, 0))
        if (y == 0):
            action.remove((0, -1))
        if (y == 2):
            action.remove((0, 1))
        return list(action)
 
    def result(self, state, action):
        #返回移动空格后的棋盘
        x,y=state.location(0)
        a,b=action
        n= state.board[x+a][y+b]
        s=copy.deepcopy(state)
        s.board[x+a][y+b]=0
        s.board[x][y]=n
        return s
 
    def path_cost( self,node):
        #展开子节点cost+1
        return node.path_cost+1
 
    def h(self, now):
        #当前棋盘每个格到目标棋盘的距离的平方和
        if now.state or self.goal:
            return now.state.distance(self.goal)
        else:
            return infinity
 
class Node:
    def __init__(self, state, parent=None, action=None, path_cost=0):
        self.state = state
        self.parent = parent
        self.action = action
        self.path_cost = path_cost
        self.fvalue=0
        self.depth = 0
        if parent:
            self.depth = parent.depth + 1
 
    def __repr__(self):
        return "<Node {}>".format(self.state.board)
 
    def __lt__(self, node):
        #<运算符 队列排序使用
        return self.fvalue < node.fvalue
 
    def expand(self, problem):
        #展开子节点
        l = []
        for action in problem.actions(self.state):
            n=self.child_node(problem, action)
            l.append(n)
        return l
 
    def child_node(self, problem, action):
        next = problem.result(self.state, action)
        return Node(next, self, action,problem.path_cost(self))
 
    def solution(self):
        return self.path()
 
    def printsolution(self):
        l=self.path()
        print("selution：")
        for x in range(len(l)- 1, -1, -1):
          print(" ↓")
          l[x].state.display()
 
    def path(self):
        #返回父节点路径list
        node, path_back = self, []
        while node:
            path_back.append(node)
            node = node.parent
        return path_back
 
    def __eq__(self, other):
        #==运算符
        return isinstance(other, Node) and self.state.board==other.state.board
 
    def __hash__(self):
        #not in 使用 比较对象Node
        board=self.state.board
        sum=0
        for x in range(0, 3):
            for y in range(0, 3):
                number = board[x][y]
                sum=sum*10+number
        return sum
 
class GameState:
    def __init__(self,board=None,action=None):
        self.board=board
        self.action=action
 
    def display(state):
        board = state.board
        if board:
            for x in range(0, 3):
                for y in range(0, 3):
                    print(board[x][y], end=‘ ‘)
                print()
 
    def location(state, number):
        #数字对应坐标
        for x in range(0, 3):
            for y in range(0, 3):
                if state.board[x][y] == number:
                    return (x, y)
        return (0, 0)
 
    def distance(statea, stateb):
        #棋盘的距离
        board = statea.board
        s = 0
        for x in range(0, 3):
            for y in range(0, 3):
                number = board[x][y]
                a, b = stateb.location(number)
                d = (x - a) ** 2 + (y - b) ** 2
                s = s + d
        return s
 
 
 
 
"""Provides some utilities widely used by other modules"""
 
import bisect
 
class Queue:
 
    """Queue is an abstract class/interface. There are three types:
        Stack(): A Last In First Out Queue.
        FIFOQueue(): A First In First Out Queue.
        PriorityQueue(order, f): Queue in sorted order (default min-first).
    Each type supports the following methods and functions:
        q.append(item)  -- add an item to the queue
        q.extend(items) -- equivalent to: for item in items: q.append(item)
        q.pop()         -- return the top item from the queue
        len(q)          -- number of items in q (also q.__len())
        item in q       -- does q contain item?
    Note that isinstance(Stack(), Queue) is false, because we implement stacks
    as lists.  If Python ever gets interfaces, Queue will be an interface."""
 
    def __init__(self):
        raise NotImplementedError
 
    def extend(self, items):
        for item in items:
            self.append(item)
class PriorityQueue(Queue):
 
    """A queue in which the minimum (or maximum) element (as determined by f and
    order) is returned first. If order is min, the item with minimum f(x) is
    returned first; if order is max, then it is the item with maximum f(x).
    Also supports dict-like lookup.
    如果是order=MIN,最小f(x)值的item将出队"""
 
 
    def __init__(self, order=min, f=lambda x: x):
        self.A = []
        self.order = order
        self.f = f
 
    #按顺序插入,按f（x）从小到大
    def append(self, item):
        item.fvalue=self.f(item)
        bisect.insort(self.A,  item)
        #print("push")
        #item.state.display()
 
    def __len__(self):
        return len(self.A)
 
    #order=min输出最小 否则输出最大
    def pop(self):
        if self.order == min:
            return self.A.pop(0)
        else:
            return self.A.pop()
 
    def __contains__(self, item):
        return any(item.state.board == pair.state.board for pair in self.A)
 
    def __getitem__(self, key):
        for item in self.A:
            if item == key:
                return item
 
    def __delitem__(self, key):
        for item in enumerate(self.A):
            if item == key:
                self.A.pop(item)
 
 
from eightpuzzle import *
 
goal = GameState( [[7,1,6],
                   [5,3,2],
                   [0,8,4]] )
start = GameState([[2,0,3,],
                   [1,8,4,],
                   [7,6,5]] )
goal.action=PuzzleProblem().actions(goal)
start.action=PuzzleProblem().actions(start)
p=PuzzleProblem(start,goal)
result=astar_search(p)
result.printsolution()