Principle of Computing (Python)學習筆記(7) DFS Search + Tic Tac Toe use MiniMax Stratedy，minimaxstratedy

Principle of Computing (Python)學習筆記(7) DFS Search + Tic Tac Toe use MiniMax Stratedy，minimaxstratedy
1. Trees

Tree is a recursive structure.

1.1 math nodes  

https://class.coursera.org/principlescomputing-001/wiki/view?page=trees

1.2 CODE無parent域的樹     

http://www.codeskulptor.org/#poc_tree.py

class Tree:    """    Recursive definition for trees plus various tree methods    """        def __init__(self, value, children):        """        Create a tree whose root has specific value (a string)        Children is a list of references to the roots of the subtrees.          """                self._value = value        self._children = children                    def __str__(self):        """        Generate a string representation of the tree        Use an pre-order traversal of the tree        """                ans = "["        ans += str(self._value)                           for child in self._children:             ans += ", "             ans += str(child)        return ans + "]"    def get_value(self):        """        Getter for node's value        """        return self._value    def children(self):        """        Generator to return children        """        for child in self._children:            yield child                        def num_nodes(self):        """        Compute number of nodes in the tree        """        ans = 1        for child in self._children:            ans += child.num_nodes()        return ans        def num_leaves(self):        """        Count number of leaves in tree        """        if len(self._children) == 0:            return 1                ans = 0        for child in self._children:            ans += child.num_leaves()        return ans    def height(self):        """        Compute height of a tree rooted by self        """        height = 0        for child in self._children:            height = max(height, child.height() + 1)        return height    def run_examples():    """    Create some trees and apply various methods to these trees    """    tree_a = Tree("a", [])    tree_b = Tree("b", [])    print "Tree consisting of single leaf node labelled 'a'", tree_a    print "Tree consisting of single leaf node labelled 'b'", tree_b        tree_cab = Tree("c", [tree_a, tree_b])    print "Tree consisting of three node", tree_cab        tree_dcabe = Tree("d", [tree_cab, Tree("e", [])])    print "Tree consisting of five nodes", tree_dcabe    print         my_tree = Tree("a", [Tree("b", [Tree("c", []), Tree("d", [])]),                          Tree("e", [Tree("f", [Tree("g", [])]), Tree("h", []), Tree("i", [])])])    print "Tree with nine nodes", my_tree        print "The tree has", my_tree.num_nodes(), "nodes,",     print my_tree.num_leaves(), "leaves and height",    print my_tree.height()    #import poc_draw_tree    #poc_draw_tree.TreeDisplay(my_tree)                 #run_examples()

1.3 CODE有parent域的樹 

 http://www.codeskulptor.org/#user36_3SjNfYqJMV_4.py

import poc_treeclass NavTree(poc_tree.Tree):    """    Recursive definition for navigable trees plus extra tree methods    """        def __init__(self, value, children, parent = None):        """        Create a tree whose root has specific value (a string)        children is a list of references to the roots of the children.          parent (if specified) is a reference to the tree's parent node        """                poc_tree.Tree.__init__(self, value, children)        self._parent = parent        for child in self._children:            child._parent = self                  def set_parent(self, parent):        """        Update parent field        """        self._parent = parent                               def get_root(self):        """        Return the root of the tree        """        if self._parent == None:            return self;        else:            return self._parent.get_root();    def depth(self):        """        Return the depth of the self with respect to the root of the tree        """        pass    def run_examples():    """    Create some trees and apply various methods to these trees    """    tree_a = NavTree("a", [])    tree_b = NavTree("b", [])    tree_cab = NavTree("c", [tree_a, tree_b])     tree_e = NavTree("e", [])    tree_dcabe = NavTree("d", [tree_cab, tree_e])        print "This is the main tree -", tree_dcabe    print "This is tree that contains b -", tree_b.get_root()        import poc_draw_tree    poc_draw_tree.TreeDisplay(tree_dcabe)    print "The node b has depth", tree_b.depth()    print "The node e has depth", tree_e.depth()             run_examples()# Expect output#This is the main tree - [d, [c, [a], [b]], [e]]]#This is tree that contains b - [d, [c, [a], [b]], [e]]#The node b has depth 2#The node e has depth 1

1.4 CODE arithmetic expreesion由樹來表達

Interior nodes in the tree are always arithmetic operators. The leaves of the tree are always numbers.

http://www.codeskulptor.org/#poc_arith_expression.py

# import Tree class definitionimport poc_tree# Use dictionary of lambdas to abstract function definitionsOPERATORS = {"+" : (lambda x, y : x + y),             "-" : (lambda x, y : x - y),            "*" : (lambda x, y : x * y),            "/" : (lambda x, y : x / y),            "//" : (lambda x, y : x // y),            "%" : (lambda x, y : x % y)}class ArithmeticExpression(poc_tree.Tree):    """    Basic operations on arithmetic expressions    """        def __init__(self, value, children, parent = None):        """        Create an arithmetic expression as a tree        """        poc_tree.Tree.__init__(self, value, children)                    def __str__(self):        """        Generate a string representation for an arithmetic expression        """                if len(self._children) == 0:            return str(self._value)        ans = "("        ans += str(self._children[0])        ans += str(self._value)        ans += str(self._children[1])        ans += ")"        return ans                    def evaluate(self):        """        Evaluate the arithmetic expression        """                if len(self._children) == 0:            if "." in self._value:                return float(self._value)            else:                return int(self._value)        else:            function = OPERATORS[self._value]            left_value = self._children[0].evaluate()            right_value = self._children[1].evaluate()            return function(left_value, right_value) def run_example():    """    Create and evaluate some examples of arithmetic expressions    """    one = ArithmeticExpression("1", [])    two = ArithmeticExpression("2", [])    three = ArithmeticExpression("3", [])    print one    print one.evaluate()        one_plus_two = ArithmeticExpression("+", [one, two])    print one_plus_two    print one_plus_two.evaluate()        one_plus_two_times_three = ArithmeticExpression("*", [one_plus_two, three])    print one_plus_two_times_three        import poc_draw_tree    poc_draw_tree.TreeDisplay(one_plus_two_times_three)    print one_plus_two_times_three.evaluate()    run_example()

2 List

In Python, lists are primarily iterative data structures that are processed using loops. However, in other languages such as Lisp and Scheme, lists are treated primarily as recursive data structures and processed recursively.

2.1 a list example 

class NodeList:    """    Basic class definition for non-empty lists using recursion    """        def __init__(self, val):        """        Create a list with one node        """        self._value = val        self._next = None             def append(self, val):        """        Append a node to an existing list of nodes        """#        print "---------called---append()--------\n"        if self._next == None:#            print "A:"+str(isinstance(val,int))+"\n";#            print "B:"+str(isinstance(val,type(self)))+"\n";            new_node = NodeList(val)            self._next = new_node        else:            self._next.append(val)                def __str__(self):        """        Build standard string representation for list        """        if self._next == None:            return "[" + str(self._value) + "]"        else:            rest_str = str(self._next)            rest_str = rest_str[1 :]            return "[" + str(self._value) + ", " + rest_str    def run_example():    """    Create some examples    """    node_list = NodeList(2)    print node_list        sub_list = NodeList(5)#    print "--------"    sub_list.append(6)#    print "--------"        sub_list2 = sub_list    node_list.append(sub_list)    node_list.append(sub_list2)    print node_list    run_example()

3 Minimax

https://class.coursera.org/principlescomputing-001/wiki/minimax
X and O alternate back and forth between min and max.
In X’s term, try to maximize the score.
the O’s term, try to minimize the score.

4 Mini Project Tic Tac Toe with Minimax

"""Mini-max Tic-Tac-Toe Player"""import poc_ttt_guiimport poc_ttt_provided as provided# Set timeout, as mini-max can take a long timeimport codeskulptorcodeskulptor.set_timeout(60)# SCORING VALUES - DO NOT MODIFYSCORES = {provided.PLAYERX: 1,          provided.DRAW: 0,          provided.PLAYERO: -1}def minimax(board, player):    """    Make a move through minimax method.    """    check_res = board.check_win()    if check_res != None:        return SCORES[check_res] , (-1,-1)    else:        empty_list = board.get_empty_squares()        com_score = -2        max_score = -2        max_each = (-1,-1)        changed_player = provided.switch_player(player)        for each in empty_list:            cur_board = board.clone()            cur_board.move(each[0], each[1], player)            cur_score_tuple = minimax(cur_board, changed_player)            cur_score = cur_score_tuple[0]            if cur_score * SCORES[player] > com_score:                com_score = cur_score * SCORES[player] # used for compare                max_score = cur_score  # used for return a value                max_each = each            if com_score == 1:                return max_score, max_each                    return max_score, max_each       def mm_move(board, player):    """    Make a move on the board.        Returns a tuple with two elements.  The first element is the score    of the given board and the second element is the desired move as a    tuple, (row, col).    """#    print "-----------------new_move--------------"#    print "B1:"+" player="+str(player)+"\n" #    print board#    print "----------------"    score_and_board = minimax(board, player)#    print "C1"#    print score_and_board#    print "-----------------new_move--------------"    return score_and_boarddef move_wrapper(board, player, trials):    """    Wrapper to allow the use of the same infrastructure that was used    for Monte Carlo Tic-Tac-Toe.    """    move = mm_move(board, player)    assert move[1] != (-1, -1), "returned illegal move (-1, -1)"    return move[1]# Test game with the console or the GUI.# Uncomment whichever you prefer.# Both should be commented out when you submit for# testing to save time.#test1#mm_move(provided.TTTBoard(3, False, [[provided.PLAYERX, provided.EMPTY, provided.EMPTY], [provided.PLAYERO, provided.PLAYERO, provided.PLAYERX], [provided.PLAYERO, provided.PLAYERX, provided.EMPTY]]), provided.PLAYERX) #mm_move(provided.TTTBoard(3, False, [[provided.PLAYERX, provided.PLAYERO, provided.EMPTY], [provided.PLAYERO, provided.PLAYERO, provided.PLAYERX], [provided.PLAYERO, provided.PLAYERX, provided.PLAYERX]]), provided.PLAYERX) #mm_move(provided.TTTBoard(3, False, [[provided.PLAYERX, provided.EMPTY, provided.PLAYERX], [provided.PLAYERO, provided.PLAYERO, provided.PLAYERX], [provided.PLAYERO, provided.PLAYERX, provided.EMPTY]]), provided.PLAYERO) #mm_move(provided.TTTBoard(3, False, [[provided.PLAYERX, provided.EMPTY, provided.EMPTY], [provided.PLAYERO, provided.PLAYERO, provided.PLAYERX], [provided.PLAYERO, provided.PLAYERX, provided.PLAYERX]]), provided.PLAYERO) #mm_move(provided.TTTBoard(3, False, [[provided.PLAYERX, provided.EMPTY, provided.EMPTY], [provided.PLAYERO, provided.PLAYERO, provided.PLAYERX], [provided.PLAYERO, provided.PLAYERX, provided.EMPTY]]), provided.PLAYERX) #mm_move(provided.TTTBoard(3, False, [[provided.PLAYERX, provided.EMPTY, provided.EMPTY], [provided.PLAYERO, provided.PLAYERO, provided.EMPTY], [provided.EMPTY, provided.PLAYERX, provided.EMPTY]]), provided.PLAYERX) #mm_move(provided.TTTBoard(2, False, [[provided.EMPTY, provided.EMPTY], [provided.EMPTY, provided.EMPTY]]), provided.PLAYERX)#test1#provided.play_game(move_wrapper, 1, False)        #poc_ttt_gui.run_gui(3, provided.PLAYERO, move_wrapper, 1, False)

注意上面的minimax()方法進行了一些簡化處理:

In Minimax, you need to alternate between maximizing and minimizing. Given the SCORES that we have provided you with, player X is always the maximizing player and play O is always the minimizing player. You can use an if-else statement to decide when to maximize and when to minimize. But, you can also be more clever by noticing that if you multiply the score by SCORES[player] then you can always maximize

如果要用if else的寫法，是這樣的:

    check_res = board.check_win()    if check_res != None:        return SCORES[check_res] , (-1,-1)    else:        empty_list = board.get_empty_squares()        if player == provided.PLAYERX:            max_score = -2;            max_each = (-1,-1)            changed_player = provided.switch_player(player)            for each in empty_list:                cur_board= board.clone()                cur_board.move(each[0], each[1], player)                cur_score_tuple = minimax(cur_board, changed_player)                cur_score = cur_score_tuple[0]                if cur_score > max_score:                    max_score = cur_score                    max_each = each                if max_score == SCORES[provided.PLAYERX]:                    return max_score, max_each            return max_score, max_each            elif player == provided.PLAYERO:            min_score = 2;            min_each = (-1,-1)            changed_player = provided.switch_player(player)            for each in empty_list:                cur_board= board.clone()                cur_board.move(each[0], each[1], player)                             cur_score_tuple = minimax(cur_board, changed_player)                cur_score = cur_score_tuple[0]                if cur_score < min_score:                    min_score = cur_score                    min_each = each                if min_score == SCORES[provided.PLAYERO]:                    return min_score, min_each            return min_score, min_each