:orphan:

Evaluate Reverse Polish Notation
================================

.. highlight:: none

Problem
-------
https://leetcode.com/problems/evaluate-reverse-polish-notation/

You are given an array of strings ``tokens`` that represents an
arithmetic expression in a `Reverse Polish
Notation <http://en.wikipedia.org/wiki/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 <= 10``\ :sup:```4```
- ``tokens[i]`` is either an operator: ``"+"``, ``"-"``, ``"*"``, or
  ``"/"``, or an integer in the range ``[-200, 200]``.

.. highlight:: python

Pattern
-------
Array, Math, Stack

Approaches
----------

.. tab-set::

    .. tab-item:: Stack

        **Code**

        .. literalinclude:: ../problems/medium/evaluate-reverse-polish-notation/evaluate_reverse_polish_notation__stack.py
            :language: python
            :lines: 11-

        **Test**

        >>> from evaluate_reverse_polish_notation__stack import evalRPN
        >>> evalRPN(["2", "1", "+", "3", "*"])
        9
        >>> evalRPN(["4", "13", "5", "/", "+"])
        6
        >>> evalRPN(["10", "6", "9", "3", "+", "-11", "*", "/", "*", "17", "+", "5", "+"])
        22

        .. autofunction:: evaluate_reverse_polish_notation__stack.exec_op

        .. autofunction:: evaluate_reverse_polish_notation__stack.evalRPN