Evaluate Reverse Polish Notation

You are given an array of strings tokens that represents an arithmetic expression in a Reverse Polish Notation.

Evaluate the expression. Return an integer that represents the value of the expression.

Note that:

The valid operators are '+', '-', '*', and '/'.
Each operand may be an integer or another expression.
The division between two integers always truncates toward zero.
There will not be any division by zero.
The input represents a valid arithmetic expression in a reverse polish notation.
The answer and all the intermediate calculations can be represented in a 32-bit integer.

Example 1

Input: tokens = ["2","1","+","3","*"] Output: 9 Explanation: ((2 + 1) * 3) = 9

Example 2

Input: tokens = ["4","13","5","/","+"] Output: 6 Explanation: (4 + (13 / 5)) = 6

Example 3

Input: tokens = ["10","6","9","3","+","-11","*","/","*","17","+","5","+"] Output: 22 Explanation: ((10 * (6 / ((9 + 3) * -11))) + 17) + 5 = ((10 * (6 / (12 * -11))) + 17) + 5 = ((10 * (6 / -132)) + 17) + 5 = ((10 * 0) + 17) + 5 = (0 + 17) + 5 = 17 + 5 = 22

Constraints:

1 <= tokens.length <= 10⁴
tokens[i] is either an operator: "+", "-", "*", or "/", or an integer in the range [-200, 200].

Solution 1 - Using stack

Solution 1 - Using stack

First, let's understand this Reverse Polish Notation (RPN), in this notation we will have a list of operands and operators, when an operator is occurred, we ned to apply that operator on two left most operands. For example, consider this notation "4","13","5","/","+", here when first operator occurred '/' , we will apply this on two left side operands 13 and 5, so the result for this operation will be 13/5 = 2 (for this example, we are rounding down), now the notation becomes "4", "2", "+", we can now apply '+' operator on 4 and 2, so the result becomes 4+2 = 6.

In this approach, we are going to add elements into a Stack and when an operator symbol is occurred, we will remove top two elements from stack, and apply the operation and put back the result into stack.

Java

import java.util.Stack;

public class ReversePolishNotation {

    static int evalRPN(String[] tokens) {
        Stack<Integer> stack = new Stack<>();
        for(String token: tokens) {
            if("+".equals(token)) {
                int x1 = stack.pop();
                int x2 = stack.pop();
                stack.push(x2+x1);
            } else if("-".equals(token)) {
                int x1 = stack.pop();
                int x2 = stack.pop();
                stack.push(x2-x1);
            } else if("*".equals(token)) {
                int x1 = stack.pop();
                int x2 = stack.pop();
                stack.push(x2*x1);
            } else if("/".equals(token)) {
                int x1 = stack.pop();
                int x2 = stack.pop();
                stack.push(x2/x1);
            } else {
                stack.push(Integer.parseInt(token));
            }
        }
        return stack.pop();
    }

    public static void main(String[] args) {
        System.out.println(evalRPN(new String[]{"2","1","+","3","*"}));
        System.out.println(evalRPN(new String[]{"4","13","5","/","+"}));
        System.out.println(evalRPN(new String[]{"10","6","9","3","+","-11","*","/","*","17","+","5","+"}));
    }
}

Complexity Analysis:

Time complexity: Above code runs in O(n) time.
Space complexity: O(n).

Above implementations source code can be found at GitHub link for Java code