python经典趣味24点游戏程序设计

时间:2021-05-22

一、游戏玩法介绍:

24点游戏是儿时玩的主要益智类游戏之一,玩法为:从一副扑克中抽取4张牌,对4张牌使用加减乘除中的任何方法,使计算结果为24。例如,2,3,4,6,通过( ( ( 4 + 6 ) - 2 ) * 3 ) = 24,最快算出24者剩。

二、设计思路:

由于设计到了表达式,很自然的想到了是否可以使用表达式树来设计程序。本程序的确使用了表达式树,也是程序最关键的环节。简要概括为:先列出所有表达式的可能性,然后运用表达式树计算表达式的值。程序中大量的运用了递归,各个递归式不是很复杂,大家耐心看看,应该是能看懂的

表达式树:

表达式树的所有叶子节点均为操作数(operand),其他节点为运算符(operator)。由于本例中都是二元运算,所以表达式树是二叉树。下图就是一个表达式树

具体步骤:

1、遍历所有表达式的可能情况

遍历分为两部分,一部分遍历出操作数的所有可能,然后是运算符的所有可能。全排列的计算采用了递归的思想

#返回一个列表的全排列的列表集合def list_result(l): if len(l) == 1: return [l] all_result = [] for index,item in enumerate(l): r = list_result(l[0:index] + l[index+1:]) map(lambda x : x.append(item),r) all_result.extend(r) return all_result

2、根据传入的表达式的值,构造表达式树

由于表达式树的特点,所有操作数均为叶子节点,操作符为非叶子节点,而一个表达式(例如( ( ( 6 + 4 ) - 2 ) * 3 ) = 24) 只有3个运算符,即一颗表达式树只有3个非叶子节点。所以树的形状只有两种可能,就直接写死了

 

#树节点class Node: def __init__(self, val): self.val = val self.left = None self.right = Nonedef one_expression_tree(operators, operands): root_node = Node(operators[0]) operator1 = Node(operators[1]) operator2 = Node(operators[2]) operand0 = Node(operands[0]) operand1 = Node(operands[1]) operand2 = Node(operands[2]) operand3 = Node(operands[3]) root_node.left = operator1 root_node.right =operand0 operator1.left = operator2 operator1.right = operand1 operator2.left = operand2 operator2.right = operand3 return root_nodedef two_expression_tree(operators, operands): root_node = Node(operators[0]) operator1 = Node(operators[1]) operator2 = Node(operators[2]) operand0 = Node(operands[0]) operand1 = Node(operands[1]) operand2 = Node(operands[2]) operand3 = Node(operands[3]) root_node.left = operator1 root_node.right =operator2 operator1.left = operand0 operator1.right = operand1 operator2.left = operand2 operator2.right = operand3 return root_node

3、计算表达式树的值

也运用了递归

#根据两个数和一个符号,计算值def cal(a, b, operator): return operator == '+' and float(a) + float(b) or operator == '-' and float(a) - float(b) or operator == '*' and float(a) * float(b) or operator == '÷' and float(a)/float(b)def cal_tree(node): if node.left is None: return node.val return cal(cal_tree(node.left), cal_tree(node.right), node.val)

4、输出所有可能的表达式

还是运用了递归

def print_expression_tree(root): print_node(root) print ' = 24'def print_node(node): if node is None : return if node.left is None and node.right is None: print node.val, else: print '(', print_node(node.left) print node.val, print_node(node.right) print ')', #print ' ( %s %s %s ) ' % (print_node(node.left), node.val, print_node(node.right)),

5、输出结果

三、所有源码

#coding:utf-8from __future__ import divisionfrom Node import Nodedef calculate(nums): nums_possible = list_result(nums) operators_possible = list_result(['+','-','*','÷']) goods_noods = [] for nums in nums_possible: for op in operators_possible: node = one_expression_tree(op, nums) if cal_tree(node) == 24: goods_noods.append(node) node = two_expression_tree(op, nums) if cal_tree(node) == 24: goods_noods.append(node) map(lambda node: print_expression_tree(node), goods_noods)def cal_tree(node): if node.left is None: return node.val return cal(cal_tree(node.left), cal_tree(node.right), node.val)#根据两个数和一个符号,计算值def cal(a, b, operator): return operator == '+' and float(a) + float(b) or operator == '-' and float(a) - float(b) or operator == '*' and float(a) * float(b) or operator == '÷' and float(a)/float(b)def one_expression_tree(operators, operands): root_node = Node(operators[0]) operator1 = Node(operators[1]) operator2 = Node(operators[2]) operand0 = Node(operands[0]) operand1 = Node(operands[1]) operand2 = Node(operands[2]) operand3 = Node(operands[3]) root_node.left = operator1 root_node.right =operand0 operator1.left = operator2 operator1.right = operand1 operator2.left = operand2 operator2.right = operand3 return root_nodedef two_expression_tree(operators, operands): root_node = Node(operators[0]) operator1 = Node(operators[1]) operator2 = Node(operators[2]) operand0 = Node(operands[0]) operand1 = Node(operands[1]) operand2 = Node(operands[2]) operand3 = Node(operands[3]) root_node.left = operator1 root_node.right =operator2 operator1.left = operand0 operator1.right = operand1 operator2.left = operand2 operator2.right = operand3 return root_node#返回一个列表的全排列的列表集合def list_result(l): if len(l) == 1: return [l] all_result = [] for index,item in enumerate(l): r = list_result(l[0:index] + l[index+1:]) map(lambda x : x.append(item),r) all_result.extend(r) return all_resultdef print_expression_tree(root): print_node(root) print ' = 24'def print_node(node): if node is None : return if node.left is None and node.right is None: print node.val, else: print '(', print_node(node.left) print node.val, print_node(node.right) print ')',if __name__ == '__main__': calculate([2,3,4,6])

以上就是本文的全部内容,希望对大家的学习有所帮助,也希望大家多多支持。

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