Tree is a recursive structure.

1.1 math nodes  

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

page=trees

1.2 CODE无parent域的树     

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 = http://www.mamicode.com/value"""
        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域的树 

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

import poc_tree

class 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由树来表达

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 definition
import poc_tree

# Use dictionary of lambdas to abstract function definitions

OPERATORS = {"+" : (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 = http://www.mamicode.com/self._children[0].evaluate()"""
    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()

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 = http://www.mamicode.com/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()

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_gui
import poc_ttt_provided as provided

# Set timeout, as mini-max can take a long time
import codeskulptor
codeskulptor.set_timeout(60)

# SCORING VALUES - DO NOT MODIFY
SCORES = {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_board




def 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)

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

假设要用if else的写法。是这种:

    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