整理一下中缀表达式转后缀表达式(逆波兰表达式)的算法-调度场算法(shunting yard algorithm)

由于后缀表达式求值比较容易，一个下推栈即可，所以在编译过程中，中缀表达式会转成后缀表达式，简单算法如下：

中缀表达式转换为后缀表达式（逆波兰表达式），即调度场算法(shunting yard algorithm)
1.建立运算符栈用于运算符的存储，此运算符遵循越往栈顶优先级越高的原则。
2.预处理表达式，正、负号前加0(如果一个加号（减号）出现在最前面或左括号后面，则该加号（减号） 为正负号)。 　　
3.顺序扫描表达式，如果当前字符是数字（优先级为0的符号），则直接输出该数字；如果当前字符为运算符或者括号（优先级不为0的符号），则判断第四点。
4.若当前运算符为'('，直接入栈；
  若为')'，出栈并顺序输出运算符直到遇到第一个'(',遇到的第一个'('出栈但不输出；
  若为其它，比较运算符栈栈顶元素与当前元素的优先级：
      如果栈顶元素是'('，当前元素直接入栈；
      如果栈顶元素优先级>=当前元素优先级，出栈并顺序输出运算符直到栈顶元素优先级<当前元素优先级，然后当前元素入栈；
      如果栈顶元素优先级<当前元素优先级，当前元素直接入栈。
5.重复第三点直到表达式扫描完毕。
6.顺序出栈并输出运算符直到栈元素为空。

下面给出英文版本：

• While there are tokens to be read:

• Read a token.
• If the token is a number, then add it to the output queue.
• If the token is a functiontoken, then push it onto the stack.
• If the token is a function argument separator (e.g., a comma):

• Until the token at the top of the stack is a left parenthesis, pop operators off the stack onto the output queue. If no left parentheses are encountered, either the separator was misplaced or parentheses were mismatched.

• If the token is an operator, o₁, then:

• while there is an operator token, o₂, at the top of the stack, and

either o₁ is left-associative and its precedence is less than or equal to that of o₂,

or o₁ is right-associative and its precedence is less than that of o₂,

pop o₂ off the stack, onto the output queue;

• push o₁ onto the stack.

• If the token is a left parenthesis, then push it onto the stack.
• If the token is a right parenthesis:

• Until the token at the top of the stack is a left parenthesis, pop operators off the stack onto the output queue.
• Pop the left parenthesis from the stack, but not onto the output queue.
• If the token at the top of the stack is a function token, pop it onto the output queue.
• If the stack runs out without finding a left parenthesis, then there are mismatched parentheses.

• When there are no more tokens to read:

• While there are still operator tokens in the stack:

• If the operator token on the top of the stack is a parenthesis, then there are mismatched parentheses.
• Pop the operator onto the output queue.

• Exit.