September 2017 Update
This commit is contained in:
Ingy döt Net
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14570 changed files with 153136 additions and 63871 deletions
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@ -1,51 +1,31 @@
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from math import log as ln
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from math import sqrt, log, exp, sin, cos, tan, pi, e
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from ast import literal_eval
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"""
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>>> # EXAMPLE USAGE
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>>> result = rpn_to_infix('3 4 2 * 1 -5 - ln 2 3 ** ** / +', VERBOSE=True)
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>>> result = rpn_to_infix('3 4 2 * 1 5 - 2 3 ^ ^ / +', VERBOSE=True)
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TOKEN STACK
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3 ['3']
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4 ['3', '4']
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2 ['3', '4', '2']
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* ['3', Node('2','*','4')]
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1 ['3', Node('2','*','4'), '1']
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-5 ['3', Node('2','*','4'), '1', '-5']
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- ['3', Node('2','*','4'), Node('-5','-','1')]
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ln ['3', Node('2','*','4'), Node(Node('-5','-','1'),'ln',None)]
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2 ['3', Node('2','*','4'), Node(Node('-5','-','1'),'ln',None), '2']
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3 ['3', Node('2','*','4'), Node(Node('-5','-','1'),'ln',None), '2', '3']
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** ['3', Node('2','*','4'), Node(Node('-5','-','1'),'ln',None), Node('3','**','2')]
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** ['3', Node('2','*','4'), Node(Node('3','**','2'),'**',Node(Node('-5','-','1'),'ln',None))]
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/ ['3', Node(Node(Node('3','**','2'),'**',Node(Node('-5','-','1'),'ln',None)),'/',Node('2','*','4'))]
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+ [Node(Node(Node(Node('3','**','2'),'**',Node(Node('-5','-','1'),'ln',None)),'/',Node('2','*','4')),'+','3')]
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>>> result
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5 ['3', Node('2','*','4'), '1', '5']
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- ['3', Node('2','*','4'), Node('5','-','1')]
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2 ['3', Node('2','*','4'), Node('5','-','1'), '2']
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3 ['3', Node('2','*','4'), Node('5','-','1'), '2', '3']
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^ ['3', Node('2','*','4'), Node('5','-','1'), Node('3','^','2')]
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^ ['3', Node('2','*','4'), Node(Node('3','^','2'),'^',Node('5','-','1'))]
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/ ['3', Node(Node(Node('3','^','2'),'^',Node('5','-','1')),'/',Node('2','*','4'))]
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+ [Node(Node(Node(Node('3','^','2'),'^',Node('5','-','1')),'/',Node('2','*','4')),'+','3')]
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"""
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prec_dict = {'abs':5, 'sqrt':5, 'exp':5, 'log':5, 'ln':5,
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'sin':5, 'cos':5, 'tan':5,
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'**':4, '*':3, '/':3, '+':2, '-':2}
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assoc_dict = {'abs':0, 'sqrt':0, 'exp':0, 'log':0, 'ln':0,
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'sin':0, 'cos':0, 'tan':0,
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'**':1, '*':0, '/':0, '+':0, '-':0}
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arity_dict = {'abs':1, 'sqrt':1, 'exp':1, 'log':1, 'ln':1,
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'sin':1, 'cos':1, 'tan':1,
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'**':2, '*':2, '/':2, '+':2, '-':2}
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prec_dict = {'^':4, '*':3, '/':3, '+':2, '-':2}
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assoc_dict = {'^':1, '*':0, '/':0, '+':0, '-':0}
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class Node:
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def __init__(self,x,op,y=None):
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self.precedence = prec_dict[op]
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self.assocright = assoc_dict[op]
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self.arity = arity_dict[op]
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self.op = op
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if not self.assocright and self > x and \
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isinstance(x, Node) and self.arity == 2:
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self.x = x.x
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self.y = Node(x.y, x.op, y)
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else:
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self.x,self.y = x,y
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self.x,self.y = x,y
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def __str__(self):
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"""
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@ -53,7 +33,6 @@ class Node:
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Building an infix string that looks pretty and evaluates
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correctly requires more effort.
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"""
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# easy case, Node is unary
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if self.y == None:
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return '%s(%s)'%(self.op,str(self.x))
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@ -65,7 +44,6 @@ class Node:
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(str_y[0] is '-' and self.assocright):
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str_y = '(%s)'%str_y
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# determine right side string and operator
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str_x = str(self.x)
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str_op = self.op
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@ -80,7 +58,6 @@ class Node:
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getattr(self.x, 'op', 1) != getattr(self, 'op', 2)):
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str_x = '(%s)'%str_x
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return ' '.join([str_y, str_op, str_x])
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def __repr__(self):
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@ -100,76 +77,25 @@ class Node:
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return self.precedence > other.precedence
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return self.precedence > prec_dict.get(other,9)
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def __eq__(self, other):
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if isinstance(other, Node):
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return self.precedence == other.precedence
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return self.precedence > prec_dict.get(other,9)
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def rpn_to_infix(s, VERBOSE=False):
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"""
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converts rpn notation to infix notation for string s
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"^" are replaced with "**"
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>>> rpn_to_infix('5 4 +')
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'5 + 4'
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>>> rpn_to_infix('5 -4 +')
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'5 - 4'
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>>> rpn_to_infix('5 -4 -')
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'5 + 4'
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>>> rpn_to_infix('5 -4.2 +')
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'5 - 4.2'
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>>> rpn_to_infix('-4 2 **')
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'(-4) ** 2'
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>>> rpn_to_infix('x y +')
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'x + y'
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>>> rpn_to_infix('x -y +')
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'x - y'
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>>> rpn_to_infix('5 4 3 2 ** ** **')
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'5 ** 4 ** 3 ** 2'
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>>> rpn_to_infix('5 6 ** 7 **')
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'(5 ** 6) ** 7'
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>>> rpn_to_infix('1 2 3 + -')
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'1 - (2 + 3)'
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>>> rpn_to_infix('4 3 2 + +')
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'4 + 3 + 2'
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>>> rpn_to_infix('5 4 3 2 + + +')
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'5 + 4 + 3 + 2'
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>>> rpn_to_infix('5 4 3 2 * * *')
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'5 * 4 * 3 * 2'
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>>> rpn_to_infix('5 4 3 2 + - +')
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'5 + (4 - (3 + 2))'
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>>> rpn_to_infix('3 4 5 * -')
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'3 - 4 * 5'
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>>> rpn_to_infix('3 4 5 - *')
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'(3 - 4) * 5'
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>>> rpn_to_infix('4 2 * 1 5 - +')
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'4 * 2 + (1 - 5)'
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>>> rpn_to_infix('4 2 * 1 5 - 2 ** /')
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'4 * 2 / (1 - 5) ** 2'
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>>> rpn_to_infix('3 4 2 * 1 5 - 2 3 ** ** / +')
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'3 + 4 * 2 / (1 - 5) ** 2 ** 3'
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>>> rpn_to_infix('1 2 + 3 4 + ** 5 6 + **')
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'((1 + 2) ** (3 + 4)) ** (5 + 6)'
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>>> rpn_to_infix('x sin')
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'sin(x)'
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>>> rpn_to_infix('5 4 3 2 + sqrt - +')
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'5 + (4 - sqrt(3 + 2))'
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>>> rpn_to_infix('5 4 3 2 + sqrt ln - +')
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'5 + (4 - ln(sqrt(3 + 2)))'
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>>> rpn_to_infix('5 sin 4 cos *')
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'sin(5) * cos(4)'
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>>> rpn_to_infix('5 4 cos * sin')
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'sin(5 * cos(4))'
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>>> rpn_to_infix('3 4 2 * 1 -5 - ln 2 3 ** ** / +')
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'3 + 4 * 2 / ln(1 + 5) ** 2 ** 3'
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"""
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if VERBOSE : print('TOKEN STACK')
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stack=[]
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for token in s.replace('^','**').split():
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for token in s.replace('^','^').split():
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if token in prec_dict:
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if arity_dict[token] == 1:
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stack.append(Node(stack.pop(),token))
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elif arity_dict[token] == 2:
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stack.append(Node(stack.pop(),token,stack.pop()))
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stack.append(Node(stack.pop(),token,stack.pop()))
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else:
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stack.append(token)
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@ -178,36 +104,14 @@ def rpn_to_infix(s, VERBOSE=False):
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return str(stack[0])
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def rpn_eval(s):
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"""
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computes the value of an rpn string
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>>> rpn_eval('5 4 +') == eval(rpn_to_infix('5 4 +'))
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True
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>>> rpn_eval('-4 2 **') == eval(rpn_to_infix('-4 2 **'))
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True
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>>> round(rpn_eval('3 4 2 * 1 -5 - ln 2 3 ** ** / +'),7) == \
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round(eval(rpn_to_infix('3 4 2 * 1 -5 - ln 2 3 ** ** / +')),7)
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True
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>>> round(rpn_eval('5 4 3 2 + sqrt ln - +'),7) == \
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round(eval(rpn_to_infix('5 4 3 2 + sqrt ln - +')),7)
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True
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"""
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stack=[]
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for token in s.replace('^','**').split():
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if token in prec_dict:
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if arity_dict[token] == 1:
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stack.append(literal_eval('%s(%s)'%(token,stack.pop())))
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elif arity_dict[token] == 2:
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x,y=stack.pop(),stack.pop()
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stack.append(literal_eval('(%s) %s %s'%(y,token,x)))
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else:
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stack.append(token)
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return stack[0]
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strTest = "3 4 2 * 1 -5 - ln 2 3 ** ** / +"
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strResult = rpn_to_infix(strTest)
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strTest = "3 4 2 * 1 5 - 2 3 ^ ^ / +"
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strResult = rpn_to_infix(strTest, VERBOSE=False)
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print ("Input: ",strTest)
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print ("Output:",strResult)
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print()
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strTest = "1 2 + 3 4 + ^ 5 6 + ^"
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strResult = rpn_to_infix(strTest, VERBOSE=False)
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print ("Input: ",strTest)
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print ("Output:",strResult)
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