逆波兰表达式运算符优先级（用Python举例实现逆波兰表达式）

逆波兰表达式是编译原理中的一种基本表达式    
    
    
    
，利用Python语言也可以实现逆波兰表达式的输出


     


     


     


，这里举例实践说明：

什么是逆波兰表达式？

逆波兰表达式又叫做后缀表达式    
    
    
    
。在通常的表达式中
 




 




 




 ，二元运算符总是置于与之相关的两个运算对象之间   

   

   

   
，所以 

     

     

     

，这种表示法也称为中缀表示


     


     


     


。波兰逻辑学家J.Lukasiewicz于1929年提出了另一种表示表达式的方法
 




 




 




 。按此方法

  




  




  




 ，每一运算符都置于其运算对象之后  


  


  


  
，故称为后缀表示   

   

   

   
。

举例实现：

#-*-coding:utf-8-*- symbol_priority={} symbol_priority[0]=[#] symbol_priority[1]=[(] symbol_priority[2]=[+,-] symbol_priority[3]=[*,/] symbol_priority[4]=[)] defcomparePriority(symbol,RPN_stack,symbol_stack): Compareprioritybetweentwosymbols globalsymbol_priority iflen(symbol_stack)>0: symbol_pop=symbol_stack.pop() else: return forlistinsymbol_priority.values(): if(symbolinlist)and(symbol_popinlist): samepriority symbol_stack.append(symbol_pop) symbol_stack.append(symbol) return elifsymbolinlist: symbolissmaller RPN_stack.append(symbol_pop) #recusioncall comparePriority(symbol,RPN_stack,symbol_stack) return elifsymbol_popinlist: symbolisbigger symbol_stack.append(symbol_pop) symbol_stack.append(symbol) return else: continue symbol_stack.append(symbol_pop) return defscanEveryone(input_string,RPN_stack,symbol_stack): forchininput_string: ifch.isdigit(): RPN_stack.append(ch) else: iflen(symbol_stack)>0: ifch==(: symbol_stack.append(ch) elifch==): whileTrue: symbol_pop=symbol_stack.pop() ifsymbol_pop==(: break else: RPN_stack.append(symbol_pop) else: comparePriority(ch,RPN_stack,symbol_stack) else: symbol_stack.append(ch) defscanInput(RPN_stack,symbol_stack): input_string=raw_input() input_string+=# scanEveryone(input_string,RPN_stack,symbol_stack) defcalRPN(RPN_stack): value_stack=[] RPN_stack.append(#) forvalueinRPN_stack: ifvalue==#: returnvalue_stack.pop() break ifvalue.isdigit(): value_stack.append(value) else: right_value=value_stack.pop() left_value=value_stack.pop() cal_string=left_value+value+right_value value_stack.append(str(eval(cal_string))) defmain(): RPN_stack=[] symbol_stack=[] scanInput(RPN_stack,symbol_stack) printcalRPN(RPN_stack) if__name__==__main__: main() #-*-coding:utf-8-*- symbol_priority={} symbol_priority[0]=[#] symbol_priority[1]=[(] symbol_priority[2]=[+,-] symbol_priority[3]=[*,/] symbol_priority[4]=[)] defcomparePriority(symbol,RPN_stack,symbol_stack): Compareprioritybetweentwosymbols globalsymbol_priority iflen(symbol_stack)>0: symbol_pop=symbol_stack.pop() else: return forlistinsymbol_priority.values(): if(symbolinlist)and(symbol_popinlist): samepriority symbol_stack.append(symbol_pop) symbol_stack.append(symbol) return elifsymbolinlist: symbolissmaller RPN_stack.append(symbol_pop) #recusioncall comparePriority(symbol,RPN_stack,symbol_stack) return elifsymbol_popinlist: symbolisbigger symbol_stack.append(symbol_pop) symbol_stack.append(symbol) return else: continue symbol_stack.append(symbol_pop) return defscanEveryone(input_string,RPN_stack,symbol_stack): forchininput_string: ifch.isdigit(): RPN_stack.append(ch) else: iflen(symbol_stack)>0: ifch==(: symbol_stack.append(ch) elifch==): whileTrue: symbol_pop=symbol_stack.pop() ifsymbol_pop==(: break else: RPN_stack.append(symbol_pop) else: comparePriority(ch,RPN_stack,symbol_stack) else: symbol_stack.append(ch) defscanInput(RPN_stack,symbol_stack): input_string=raw_input() input_string+=# scanEveryone(input_string,RPN_stack,symbol_stack) defcalRPN(RPN_stack): value_stack=[] RPN_stack.append(#) forvalueinRPN_stack: ifvalue==#: returnvalue_stack.pop() break ifvalue.isdigit(): value_stack.append(value) else: right_value=value_stack.pop() left_value=value_stack.pop() cal_string=left_value+value+right_value value_stack.append(str(eval(cal_string))) defmain(): RPN_stack=[] symbol_stack=[] scanInput(RPN_stack,symbol_stack) printcalRPN(RPN_stack) if__name__==__main__: main()