从中缀到前缀的转换 [英] conversion from infix to prefix

问题描述

我正准备考试，对于以下表达式，我无法理解中缀表示法到波兰表示法的转换：

I am preparing for an exam where i couldn't understand the convertion of infix notation to polish notation for the below expression:

(a–b)/c*(d + e – f / g)

可以一步一步讲给定的表达式将如何转换为前缀？

Can any one tell step by step how the given expression will be converted to prefix?

推荐答案

Algorithm ConvertInfixtoPrefix

Purpose: Convert an infix expression into a prefix expression. Begin 
// Create operand and operator stacks as empty stacks. 
Create OperandStack
Create OperatorStack

// While input expression still remains, read and process the next token.

while( not an empty input expression ) read next token from the input expression

    // Test if token is an operand or operator 
    if ( token is an operand ) 
    // Push operand onto the operand stack. 
        OperandStack.Push (token)
    endif

    // If it is a left parentheses or operator of higher precedence than the last, or the stack is empty,
    else if ( token is '(' or OperatorStack.IsEmpty() or OperatorHierarchy(token) > OperatorHierarchy(OperatorStack.Top()) )
    // push it to the operator stack
        OperatorStack.Push ( token )
    endif

    else if( token is ')' ) 
    // Continue to pop operator and operand stacks, building 
    // prefix expressions until left parentheses is found. 
    // Each prefix expression is push back onto the operand 
    // stack as either a left or right operand for the next operator. 
        while( OperatorStack.Top() not equal '(' ) 
            OperatorStack.Pop(operator) 
            OperandStack.Pop(RightOperand) 
            OperandStack.Pop(LeftOperand) 
            operand = operator + LeftOperand + RightOperand 
            OperandStack.Push(operand) 
        endwhile

    // Pop the left parthenses from the operator stack. 
    OperatorStack.Pop(operator)
    endif

    else if( operator hierarchy of token is less than or equal to hierarchy of top of the operator stack )
    // Continue to pop operator and operand stack, building prefix 
    // expressions until the stack is empty or until an operator at 
    // the top of the operator stack has a lower hierarchy than that 
    // of the token. 
        while( !OperatorStack.IsEmpty() and OperatorHierarchy(token) lessThen Or Equal to OperatorHierarchy(OperatorStack.Top()) ) 
            OperatorStack.Pop(operator) 
            OperandStack.Pop(RightOperand) 
            OperandStack.Pop(LeftOperand) 
            operand = operator + LeftOperand + RightOperand 
            OperandStack.Push(operand)
        endwhile 
        // Push the lower precedence operator onto the stack 
        OperatorStack.Push(token)
    endif
endwhile 
// If the stack is not empty, continue to pop operator and operand stacks building 
// prefix expressions until the operator stack is empty. 
while( !OperatorStack.IsEmpty() ) OperatorStack.Pop(operator) 
    OperandStack.Pop(RightOperand) 
    OperandStack.Pop(LeftOperand) 
    operand = operator + LeftOperand + RightOperand

    OperandStack.Push(operand) 
endwhile

// Save the prefix expression at the top of the operand stack followed by popping // the operand stack.

print OperandStack.Top()

OperandStack.Pop()

End

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