sting LS y backwar an . The program gnor spaces and on. 12.12 (infie-to-Postfixe Converter) Stacks are used by compilers to help in the process of evaluating expressions and generating machine language code. In this and the next exercise, we investigate how compilers evaluate arithmetic expressions consisting only of constants, operators and parentheses. Humans generally write expressions like 3 + 4 and 7/9 in which the operator (+ or / here) Iis written between its operands -this is called infix notation. Computers "prefer" postfix notation in which the operator is written to the right of its two operands. The preceding infix expressions would appear in postfix notation as 3 4 + and 7 9 /, respectively To evaluate a complex infix expression, a compiler would first convert the expression to post- fix notation, and then evaluate the postfix version of the expression. Each of these algorithms requires only a single left-to-right pass of the expression. Each algorithm uses a stack in support of its operation, and in each the stack is used for a different purpose. In this exercise, you'll write a version of the infix-to-postfix conversion algorithm. In the next exercise, you'll write a version of the postfix expression evaluation algorithm. Write a program that converts an ordinary infix arithmetic expression (assume a valid expression is entered) with single digit integers such as (6 +2) 5 -814 to a postfix expression. The postfix version of the preceding infix expression is 62 5 84 The program should read the expression into character array infix, and use modified vesions of the stack functions implemented in this chapter to help create the postfix expression in character array postfix. The algorithm for creating a postfix expression is as follows: 1) Push a left parenthesis'C" onto the stack 2) Append a right parenthesis' to the end of infix. 3) While the stack is not empty, read infix from left to right and do the following If the current character in infix is a digit, copy it to the next element of postfix. the current character in infix is a lefi parenthesis, push it onto the stack. If the current characer in infix is an operator, Pop operators Gnthere are any) at the top of the stack while they have equal or higher precedence than the current operator, and insert the popped operators in postfix Push the current character in infix onto the stack If the current character in infix is a right parenthesis Pop operators from the top of the stack and insert them in postfix until a lef parenthesis is at the top of the Pop (and discard) the left parenthesis from the stack taken the stack. The following arithmetie operations are allowed in an expression + addition subtraction