Reverse Polish Notation (RPN) is a mathematical notation where every operator follows all of its operands. This eliminates the need for parentheses to indicate the order of operations. To evaluate an RPN expression, we can use a stack and a queue to process the expression and obtain the result.

What is Reverse Polish Notation?

In Reverse Polish Notation, operators are written after their operands. For example, instead of writing “2 + 3”, we write “2 3 +”. RPN expressions are evaluated from left to right without any need for parentheses.

The Stack and Queue Approach

To solve the RPN evaluation problem, we can use a stack to store operands and a queue to process the expression. Here’s a step-by-step breakdown of the approach:

1. Initialize an empty stack to store operands.
2. Convert the RPN expression into a queue, where each element represents an operand or an operator.
3. While the queue is not empty, do the following:
   • Dequeue the next element from the queue.
   • If the element is an operand, push it onto the stack.
   • If the element is an operator, pop the top two operands from the stack, perform the operation, and push the result back onto the stack.
4. The final result will be the value left on the stack after processing all elements.

Example Implementation in C++

#include <iostream>
#include <stack>
#include <queue>
#include <cstdlib>

using namespace std;

double evaluateRPN(const string& expression) {
    stack<double> operands;
    queue<string> tokens;

    // Convert expression into tokens
    size_t pos = 0;
    while ((pos = expression.find(' ')) != string::npos) {
        tokens.push(expression.substr(0, pos));
        expression.erase(0, pos + 1);
    }
    tokens.push(expression);

    while (!tokens.empty()) {
        string token = tokens.front();
        tokens.pop();

        if (isdigit(token[0])) {
            operands.push(stod(token));
        } else {
            double operand2 = operands.top();
            operands.pop();
            double operand1 = operands.top();
            operands.pop();

            if (token == "+") operands.push(operand1 + operand2);
            else if (token == "-") operands.push(operand1 - operand2);
            else if (token == "*") operands.push(operand1 * operand2);
            else if (token == "/") operands.push(operand1 / operand2);
        }
    }

    return operands.top();
}

int main() {
    string expression = "2 3 + 4 *";
    double result = evaluateRPN(expression);
    cout << "Result: " << result << endl;
    return 0;
}

In the above example, we have implemented a function evaluateRPN that takes an RPN expression as input and returns the result of evaluating it. The example expression “2 3 + 4 *” is evaluated, and the result is printed to the console.

Conclusion

By using a stack to store operands and a queue to process the RPN expression, we can easily evaluate RPN expressions without the need for parentheses or complex expression parsing. The example implementation in C++ demonstrates how this approach can be applied to solve the RPN evaluation problem efficiently.

#programming #C++