How would I use a stack to convert infix to postfix and evaluate and to check for errors?

Convert infix arithmetic expressions into postfix arithmetic expressions and evaluate them (whenever possible) For the sake of this exercise, an arithmetic expression is a sequence of space-separated strings. Each string can represent an operand, an operator, or parentheses. Operands: can be either a numerical value or a variable. A variable name only consists of alphanumerical letters and the underscore letter "_". A variable name starts with a English letter. Numerical operands can be either integer or floating point values. Examples of operands: "34", "5", "5.3", "a", "ab", "b1", and "a_1" Operators: one of the characters "+", "-", "*", or "/". As usual, "/" and "*" are regarded as having higher precedence than "+" or "-". Note that all supported operators are binary, that is, they require two operands. Parentheses: "(" or ")" An Infix arithmetic expression is the most common form of arithmetic expression used. Examples: ( 5 + 3 ) * 12 - 7 is an infix arithmetic expression that evaluates to 89 5 + 3 * 12 7 is an infix arithmetic expression that evaluates to 34 For the sake of comparison, postfix arithmetic expressions (also known as reverse Polish notation) equivalent to the above examples are: 5 3 + 12 * 7 5 3 12 * + 7 Two characteristics of the Postfix notation are (1) any operator, such as "+" or "/" is applied to the two prior operand values, and (2) it does not require the use of parenthesis. More examples: a + b1 * c + ( dd * e + f ) * G in Infix notation becomes a b1 c * + dd e * f + G * + in Postfix notation To implement infix to postfix conversion with a stack, one parses the expression as sequence of space-separated strings. When an operand is read in the input, it is immediately output. Operators (i.e., "-", "*") may have to be saved by placement in an operator stack. We also stack left parentheses. Start with an initially empty operator stack. Follow these 4 rules for processing operators/parentheses: If input symbol is "(", push it into stack. If input operator is "+", "-", "*", or "/", repeatedly print the top of the stack to the output and pop the stack until the stack is either (i) empty ; (ii) a "(" is at the top of the stack; or (iii) a lower-precedence operator is at the top of the stack. Then push the input operator into the stack. If input operator is ")" and the last input processed was an operator, report an error. Otherwise, repeatedly print the top of the stack to the output and pop the stack until a "(" is at the top of the stack. Then pop the stack discarding the parenthesis. If the stack is emptied without a "(" being found, report error. If end of input is reached and the last input processed was an operator or "(", report an error. Otherwise print the top of the stack to the output and pop the stack until the stack is empty. If an "(" is found in the stack during this process, report error. For more details on how the conversion works, look up the lecture notes and Section 3.6 of the textbook. Evaluating postfix arithmetic expressions After converting a given expression in infix notation to postfix notation, you will evaluate the resulting arithmetic expression IF all the operands are numeric (int, float, etc.) values. Otherwise, if the resulting postfix expression contains characters, your output should be the same as the input (the postfix expression). Example inputs: 5 3 + 12 * 7 5 3 12 * + 7 3 5 * c 10 / Example outputs: 89 34 3 5 * c 10 / To achieve this, you will have an operand stack, initially empty. Assume that the expression contains only numeric operands (no variable names). Operands are pushed into the stack as they are ready from the input. When an operator is read from the input, remove the two values on the top of the stack, apply the operator to them, and push the result onto the stack. If an operator is read and the stack has fewer than two elements in it, report an error. If end of input is reached and the stack has more than one operand left in it, report an error. If end of input is reached and the stack has exactly one operand in it, print that as the final result, or 0 if the stack is empty. For more information on the evaluation of postfix notation arithmetic expressions, look up the lecture notes and Section 3.6 of the textbook. Summarizing task 2. Your program should expect as input from (possibly re-directed) stdin a series of space-separated strings. If you read a1 (no space) this is the name of the variable a1 and not "a" followed by "1". Similarly, if you read "bb 12", this is a variable "bb" followed by the number "12" and not "b" ,"b", "12" or "bb", "1" ,"2". The resulting postfix expression should be printed to stdout. Your program should evaluate the computed postfix expressions that contain only numeric operands, using the above algorithm, and print the results to stdout. Restrictions The infix to postfix conversion MUST be able to convert expressions containing both numbers and variable names. Your program MUST be able to produce floating number evaluation (i.e., deal with floats correctly). Your program MUST NOT attempt to evaluate postfix expressions containing variable names. It should print the postfix-converted result to stdout and MAY NOT throw an exception nor reach a runtime error in that case. Your program MUST check for mismatched parentheses (this should be taken care of if you infix to postifx expression conversion is performed properly. Your program MUST check invalid infix expressions and report errors. We consider the following types of infix expressions as invalid expressions: 1) an operator does not have the corresponding operands, 2) an operand does not have the corresponding operator; or ) mismatched parentheses. Note that some checks can be performed in the expression conversion or postfix evaluation. Your program MUST re-prompt the user for the next infix expression. Your program must be able to process several inputs before terminating