One-scan infix expression evaluation using stacks | Infix-notation

Infix notation is a widely used method of writing arithmetic expressions, but evaluating them can be a complex task. One way to simplify this process is by using stacks, which allow for quick and efficient evaluation of these expressions.

When evaluating an infix expression using stacks, the process involves scanning the expression from left to right, one character at a time. Numbers are pushed onto the stack, and when an operator is encountered, the top two numbers are popped off the stack, the operation is performed, and the result is pushed back onto the stack.

One advantage of this method is that it only requires a single scan of the expression, making it more efficient than other methods that may require multiple scans. Additionally, the use of stacks allows for easy handling of parentheses, as they can simply be pushed onto the stack and popped off as needed.

To implement this method, it is necessary to create two stacks, one for numbers and one for operators. As the expression is scanned, numbers are pushed onto the number stack, and operators are pushed onto the operator stack. When an operator with a higher precedence is encountered, it is pushed onto the operator stack, and when an operator with a lower precedence is encountered, the top two numbers are popped off the number stack, the operation is performed, and the result is pushed back onto the number stack.

In conclusion, using stacks for one-scan infix expression evaluation can greatly simplify the process and improve efficiency. By scanning the expression left to right and using two stacks for numbers and operators, complex arithmetic expressions can be evaluated quickly and accurately, making this method a valuable tool for programmers.