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How to calculate expression in Reverse Polish Notation (RPN)?

C#  |  .NET  |  Algorithms

Reverse Polish Notation (also named postfix notation) is a mathematical notation. To explain it in a simple way, in this notation you first specify operands and then operator that should be applied, such as:

5 6 +

which is the same as:

5 + 6

from the notation that you know much better, so the expression is equal to 11.

Let's take a look at a bit more complex example:

5 6 + 2 4 - *

which is the same as:


so the result is equal to -22.

The code is presented below:

int rpn(string[] tokens)
    string[] operators = ["+", "-", "*", "/"];
    Stack stack = new();

    foreach (string token in tokens)
        if (!operators.Contains(token))

        int x = stack.Pop();
        int y = stack.Pop();
        int result = token switch
            "+" => y + x,
            "-" => y - x,
            "*" => y * x,
            _ => y / x

    return stack.Pop();

You can check this code by the following lines:

string[] tokens = ["5", "6", "+", "2", "4", "-", "*"];
Console.WriteLine($"Result is: {rpn(tokens)}");

The results are shown as follows:

Result is: -22

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