1. Trees
2 List
3 Minimax
注意上面的minimax()方法进行了一些简化处理:
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 = valueself._children = childrendef __str__(self):"""Generate a string representation of the treeUse 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._valuedef children(self):"""Generator to return children"""for child in self._children:yield childdef num_nodes(self):"""Compute number of nodes in the tree"""ans = 1for child in self._children:ans += child.num_nodes()return ansdef num_leaves(self):"""Count number of leaves in tree"""if len(self._children) == 0:return 1ans = 0for child in self._children:ans += child.num_leaves()return ansdef height(self):"""Compute height of a tree rooted by self"""height = 0for child in self._children:height = max(height, child.height() + 1)return heightdef 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_aprint "Tree consisting of single leaf node labelled 'b'", tree_btree_cab = Tree("c", [tree_a, tree_b])print "Tree consisting of three node", tree_cabtree_dcabe = Tree("d", [tree_cab, Tree("e", [])])print "Tree consisting of five nodes", tree_dcabeprint 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_treeprint "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_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 = parentfor child in self._children:child._parent = self def set_parent(self, parent):"""Update parent field"""self._parent = parentdef 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"""passdef 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_dcabeprint "This is tree that contains b -", tree_b.get_root()import poc_draw_treepoc_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 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 ansdef 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 oneprint one.evaluate()one_plus_two = ArithmeticExpression("+", [one, two])print one_plus_twoprint one_plus_two.evaluate()one_plus_two_times_three = ArithmeticExpression("*", [one_plus_two, three])print one_plus_two_times_threeimport poc_draw_treepoc_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 = valself._next = Nonedef 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_nodeelse: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_strdef run_example():"""Create some examples"""node_list = NodeList(2)print node_listsub_list = NodeList(5)
# print "--------"sub_list.append(6)
# print "--------" sub_list2 = sub_listnode_list.append(sub_list)node_list.append(sub_list2)print node_listrun_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_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 = -2max_score = -2max_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 comparemax_score = cur_score # used for return a valuemax_each = eachif 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 scoreof the given board and the second element is the desired move as atuple, (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 usedfor 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()方法进行了一些简化处理:
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
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_scoremax_each = eachif max_score == SCORES[provided.PLAYERX]:return max_score, max_eachreturn 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_scoremin_each = eachif min_score == SCORES[provided.PLAYERO]:return min_score, min_eachreturn min_score, min_each
