<p>Given a string <code>s</code> which represents an expression, <em>evaluate this expression and return its value</em>.&nbsp;</p>

<p>The integer division should truncate toward zero.</p>

<p>You may assume that the given expression is always valid. All intermediate results will be in the range of <code>[-2<sup>31</sup>, 2<sup>31</sup> - 1]</code>.</p>

<p><strong>Note:</strong> You are not allowed to use any built-in function which evaluates strings as mathematical expressions, such as <code>eval()</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> s = "3+2*2"
<strong>Output:</strong> 7
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> s = " 3/2 "
<strong>Output:</strong> 1
</pre><p><strong class="example">Example 3:</strong></p>
<pre><strong>Input:</strong> s = " 3+5 / 2 "
<strong>Output:</strong> 5
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 3 * 10<sup>5</sup></code></li>
	<li><code>s</code> consists of integers and operators <code>(&#39;+&#39;, &#39;-&#39;, &#39;*&#39;, &#39;/&#39;)</code> separated by some number of spaces.</li>
	<li><code>s</code> represents <strong>a valid expression</strong>.</li>
	<li>All the integers in the expression are non-negative integers in the range <code>[0, 2<sup>31</sup> - 1]</code>.</li>
	<li>The answer is <strong>guaranteed</strong> to fit in a <strong>32-bit integer</strong>.</li>
</ul>

class Solution {
public:
    int calculate(string s) {

        std::list<int> stack;

        /*
        construct stack of numbers where we can just add them together at the end
        */

        int num = 0;
        char operation = '+';
        for (int i = 0; i <= s.size(); i++) {
            if (i < s.size() && isdigit(s[i])) {
                num = num * 10 + (s[i] - '0');
            } else if (!iswspace(s[i]) || i == s.size()) {
                if (operation == '+') {
                    stack.push_back(num);
                } else if (operation == '-') {
                    stack.push_back(-1 * num);
                } else if (operation == '*') {
                    // we need to fetch right hand side of the operation 
                    auto popped = stack.back();
                    stack.pop_back();
                    stack.push_back(popped * num);
                } else if (operation == '/') {
                    auto popped = stack.back();
                    stack.pop_back();
                    stack.push_back(popped / num);                    
                }
                operation = s[i];
                num = 0;
            }

        }

        stack.push_back(num); // add last num if exists

        int result = 0;
        while (stack.size() != 0) {
            cout << stack.front() << endl;
            result += stack.front();
            stack.pop_front();
        }

        return result;
    }
};
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