Problem

Write a client program that uses the Stack abstract data type to compile a simple arithmetic expression without parentheses. For example, the expression

a + b * c - d

should be compiled according to the following table

The table shows the order in which the operations are performed (*, +, -) and operands for each operator. The result column gives the name of an identifier (working backward from z) chosen to hold each result. Assume that the operands are the letters a through m and the operators are (+, -, *, /). Your program should read each character and process it as follows: If the character is blank, ignore it. If the character is neither blank nor an operand nor an operator, display an error message and terminate the program. If it is an operand, push it onto the operand stack. If it is an operator, compare its precedence to that of the operator on top of the operator stack. If the current operator has higher precedence than the one currently on top of the stack (or if the stack is empty), it should be pushed onto the operator stack. If the current operator has the same or lower precedence, the operator on top of the operator stack must be evaluated next. This is done by popping that operator off the operator stack along with a pair of operands from the operand stack and writing a new line in the output table. The character selected to hold the result should then be pushed onto the operand stack. Next, the current operator should be compared to the new top of the operator stack. Continue to generate output lines until the top of the operator stack has lower precedence than the current operator or until it is empty. At this point, push the current operator onto the top of the stack and examine the next character in the data string. When the end of the string is reached, pop any remaining operator along with its operand pair just described. Remember to push the result character onto the operand stack after each table line is generated.