P9857 [CCC 2008 J4] From Prefix to Postfix

Prefix notation is a non-conventional notation for writing arithmetic expressions. The standard way of writing arithmetic expressions, also known as infix notation, positions a binary operator between the operands, e.g., $3 + 4$, while in prefix notation the operator is positioned before the operands, e.g., $+$ $3$ $4$. Similarly, the prefix notation for $5$ $-$ $2$ is $-$ $5$ $2$. A nice property of prefix expressions with binary operators is that parentheses are not required since there is no ambiguity about the order of operations. For example, the prefix representation of $5 - (4 - 2)$ is $-5$ $-$ $4$ $2$, while the prefix representation of $(5 - 4) - 2$ is $-$ $-$ $5$ $4$ $2$. The prefix notation is also known as Polish notation, due to Jan Łukasiewicz, a Polish logician, who invented it around $1920$. Similarly, in postfix notation, orreverse Polish notation, the operator is positioned after the operands. For example, postfix representation of the infix expression $(5 - 4) - 2$ is $5$ $4$ $-$ $2$ $-$. Your task is to write a program that translates a prefix arithmetic expression into a postfix arithmetic expression.

Each line contains an arithmetic prefix expression. The operators are $+$ and $-$, and numbers are all single-digit decimal numbers. The operators and numbers are separated by exactly one space with no leading spaces on the line. The end of input is marked by $0$ on a single line. You can assume that each input line contains a valid prefix expression with less than $20$ operators.

Translate each expression into postfix notation and produce it on a separate line. The numbers and operators are separated by at least one space. The final $0$ is not translated.