【Dison夏令营 Day 17】使用 Python Turtle 的 24 游戏求解器

24 点是一个数学谜题，用基本算术运算符（+、-、×、÷）将 4 个数字运算成 24。例如，给定 4 个数字 1,5,5,5，我们可以得到表达式 (5-(1÷5))×5，等于 24。

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我们可以用 Python 程序暴力解决这个问题。最多有 24×5×4×4×4 = 7,680 个不同的表达式可以用 4 个数字组成。这对我们来说似乎很难，但对计算机程序来说应该很容易解决。下面是这个项目的源代码：

import turtle
screen = turtle.Screen()
screen.setup(500,500)
screen.title("24 Game Solver - PythonTurtle.Academy")
turtle.hideturtle()
turtle.speed(0)
turtle.up()def permutation(a):if len(a) == 1: return [[a[0]]]res = permutation(a[1:])r = []for x in res:# need to insert n into x: into all possible positionfor i in range(len(x)+1):y = x.copy()y.insert(i,a[0])if y not in r:r.append(y)return rop = ['+', '−', '×', '÷']
def evaluate(a):v = []for x in a:if type(x) is int:v.append(x)else:num2 = v.pop()num1 = v.pop()if x=='+': v.append(num1+num2)elif x=='−': v.append(num1-num2)elif x=='×': v.append(num1*num2)else:if num2 != 0: v.append(num1/num2)else: return 0return v[0]class tree_node:def __init__(self,value,left,right):self.value = valueself.left = leftself.right = rightdef inorder(root):if type(root.value) is int: return str(root.value)if type(root.left.value) is not int: left = '('+inorder(root.left)+')'else: left = inorder(root.left)if type(root.right.value) is not int: right = '('+inorder(root.right)+')'else: right = inorder(root.right)    return left + root.value + rightdef convert_to_infix(a):# convert to infix# convert to tree firstv = list()for x in a:if type(x) is int:v.append(tree_node(x,None,None))else:t2 = v.pop()t1 = v.pop()v.append(tree_node(x,t1,t2))return inorder(v[0])def twentyfour(a):# postfix# try n,n,n,n, p,p,pfor i in range(4):for j in range(4):for k in range(4):b = a.copy()b.append(op[i])b.append(op[j])b.append(op[k])v = evaluate(b)if v==24.0:return(convert_to_infix(b))# try n,n,n,p,p,n,pfor i in range(4):for j in range(4):for k in range(4):b = a[:3]b.append(op[i])b.append(op[j])b.append(a[3])b.append(op[k])v = evaluate(b)if v==24.0:return(convert_to_infix(b))# try n,n,n,p,n,p,pfor i in range(4):for j in range(4):for k in range(4):b = a[:3]b.append(op[i])b.append(a[3])b.append(op[j])b.append(op[k])v = evaluate(b)if v==24.0:return(convert_to_infix(b))# try n,n,p,n,p,n,pfor i in range(4):for j in range(4):for k in range(4):b = a[:2]b.append(op[i])b.append(a[2])b.append(op[j])b.append(a[3])b.append(op[k])v = evaluate(b)if v==24.0:return(convert_to_infix(b))# try n,n,p,n,n,p,pfor i in range(4):for j in range(4):for k in range(4):b = a[:2]b.append(op[i])b.append(a[2])b.append(a[3])b.append(op[j])b.append(op[k])v = evaluate(b)if v==24.0:return(convert_to_infix(b))return ''            while True:fournumbers = []while len(fournumbers) != 4:numbers = screen.textinput("24 Game Solver", "Enter four numbers separated by spaces: ")fournumbers = list(map(int,numbers.split()))p = permutation(fournumbers)foundsolution = Falseturtle.clear()for a in p:r = twentyfour(a)if len(r)>0:turtle.goto(0,0)turtle.color('royal blue')turtle.write(r,font=('Courier', 45, 'bold'), align='center')foundsolution = Truebreakif not foundsolution:turtle.color('red')turtle.write("No solution",font=('Courier', 45, 'bold'), align='center')