Javascript RPN Scientific Calculator
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Reverse Polish Notation Calculator, RPN Calculator, Polish Notation Calculator
RPN(Reverse Polish Notation) Calculator
An RPN (Reverse Polish Notation) calculator is a type of calculator that uses a different method of inputting and evaluating mathematical expressions compared to the more common algebraic notation.
In RPN, the operators come after the operands, rather than between them as in algebraic notation. Here is an example:
Algebraic notation: 3 + 4 * 5 - 6
RPN notation: 3 4 5 * + 6 -
In RPN notation, the expression is evaluated by placing the operands onto a stack, and then performing operations on the top two items in the stack. This continues until all the operands have been used and only one value remains on the stack, which is the result of the expression.
A simple RPN calculator can be built using a stack data structure and the following steps:
Read the input expression token by token.
If the token is an operand (a number), push it onto the stack.
Also, If the token is an operator, pop the top two items from the stack, perform the operation, and push the result back onto the stack.
Continue reading tokens and performing operations until the end of the expression is reached.
The final result is the last value remaining on the stack.
Here is an example of using an RPN calculator to evaluate the expression 3 4 5 * + 6 - :
Start with an empty stack.
Read the first token, which is 3. Push it onto the stack.
The second token, which is 4. Push it onto the stack.
Read the third token, which is 5. Push it onto the stack.
The fourth token, which is *. Pop 5 and 4 from the stack, multiply them, and push the result (20) back onto the stack.
Read the fifth token, which is +. Pop 20 and 3 from the stack, add them, and push the result (23) back onto the stack.
The sixth token, which is 6. Push it onto the stack.
Read the seventh token, which is -. Pop 6 and 23 from the stack, subtract them, and push the result (-17) back onto the stack.
There are no more tokens to read. The final result is -17, which is the last value remaining on the stack.
So the RPN notation 3 4 5 * + 6 - evaluates to -17.
Benefits of the Reverse Polish Notation Calculator
The Reverse Polish Notation (RPN) calculator has several benefits over traditional algebraic calculators, including:
Reduced Error
With RPN, there is less chance of making mistakes because the operator precedence is no longer a concern. RPN is also very easy to learn and use, making it less prone to errors.
Faster Calculations
RPN calculators use fewer keystrokes because operators come after the operands, which means calculations can be performed faster. This makes RPN ideal for complex mathematical operations.
No Need for Parentheses
In algebraic calculators, parentheses are used to group and order operations. In RPN, there is no need for parentheses because the order of operations is already taken care of by the stack.
Less Memory Usage
RPN calculators require less memory because they only need to store the operands and operators, rather than parentheses and other grouping symbols.
More Flexibility
RPN calculators are more flexible and can handle more complex expressions than traditional algebraic calculators. This is because RPN is not limited by the number of parentheses or the order of operations.
Better for Learning Programming
RPN calculators are a good way to learn about programming concepts such as stacks and data structures. They can also be used to teach the fundamentals of computer science and programming.
