The Shunting-yard algorithm can be used to convert an infix notation expression into a postfix notation expression, which can then be evaluated using the Postfix algorithm.
To evaluate a Reverse Polish notation expression using this method, the steps are as follows:
- Convert the Reverse Polish notation expression into infix notation using the Reverse Polish notation algorithm.
- Convert the infix notation expression into postfix notation using the Shunting-yard algorithm.
- Evaluate the postfix notation expression using the Postfix algorithm.
For example, suppose we have the following Reverse Polish notation expression:
3 4 + 5 *
- Using the Reverse Polish notation algorithm, we can convert this expression into infix notation as follows:
3 + 4 * 5
- Using the Shunting-yard algorithm, we can convert the infix notation expression into postfix notation as follows:
3 4 5 * +
- Using the Postfix algorithm, we can evaluate the postfix notation expression as follows:
- Push 3 onto the stack.
- Push 4 onto the stack.
- Push 5 onto the stack.
- Pop 5 and 4 from the stack, multiply them together (5 * 4 = 20), and push the result (20) onto the stack.
- Pop 20 and 3 from the stack, add them together (20 + 3 = 23), and push the result (23) onto the stack.
- The final result is the only number left on the stack, which is 23.
