some reference about shunting-yard algorithm about calculator

[gaoxinge]

• when there are tokens to be read
  • read a token
  • if the token is a number, add it to the output queue
  • if the token is an operator o1
    • while there is an operator o2 at the top of the operator stack, and safisfies that either o1 is left-associative and its precedence <= o2 or o1 is right-associative and its precedence < o2
      • pop o2 from the operator stack, and add it to the output queue
    • push o1 to the operator stack
  • if the token is a function, push it to the operator stack
  • if the token is a left parenthesis, push it to the operator stack
  • if the token is a comma
    • while the top of the operator stack is not left parenthesis
      • pop the operator from the operator stack, and add it to the output queue
    • if there is no left parenthesis encountered, either the comma was misplaced or the parenthesis were mismatched
  • if the token is a right parenthesis
    • while the top of the operator stack is not left parenthesis
      • pop the operator from the operator stack, and add it to the output queue
    • if there is no left parenthesis encountered, the parenthesis were mismatched
    • pop the left parethesis from the operator stack
    • if the token at the top of the operator stack is a function
      • pop it from the operator stack, and add it to the output queue
• when there are no more tokens to be read
  • when there are operators in the operator stack
    • if the operator at the top of the stack is a left parenthesis, the parenthesis were mismatched
    • pop the operator from the operator stack, and add it to the output queue
• exit

[gaoxinge]

attention1

• transfer infix expression into postfix expression
  • output queue
  • operator stack
• transfer infix expression into value
  • operand stack
  • operator stack

[gaoxinge]

attention2

• transfer infix expression into postfix expression
  • can not check the operand number of an operator
  • can not check the parameter number of a function
• transfer infix expression into value
  • can check the operand numer of an operator
  • can check the paramter number of a function

[gaoxinge]

attention3

• the parenthesis were mismatched
  • there is no corresponding left parenthesis before the comma
  • there is no corresponding left parenthesis befoe the right parenthesis
  • there is no corresponding right parenthesis after the left parenthesis

[gaoxinge]

attention4

• operand is float
• support the function without paramters or non-fixed length paramters