<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) {
        // build calc graph
        // 1st: tokenize: N / N
        // 2nd: evaluate: N
        //
        enum Op {
            plus,
            minus,
            mult,
            div
        };
        auto map = unordered_map<char, Op>({{'+', plus}, {'-', minus}, {'*', mult}, {'/', div}});
        auto vec = list<variant<int, Op>>();
        auto number = -1;
        for(auto c: s) {
            switch(c) {
                case ' ':
                    continue;
                case '+':
                case '-':
                case '*':
                case '/': {
                    if(number != -1) {
                        vec.push_back(number);
                        number = -1;
                    }

                    vec.push_back(map[c]);
                    break;
                }
                default:
                    if(number == -1) {
                        number = c - '0';
                    } else {
                        number *= 10;
                        number += c - '0';
                    }
                    break;
            }
        }

        if(number != -1) {
            vec.push_back(number);
            number = -1;
        }

        // 2 eval mul and div
        for(auto iter = vec.begin(); iter != vec.end(); ++iter) {
            if(holds_alternative<Op>(*iter)) {
                auto left = get<int>(*prev(iter, 1));
                auto right = get<int>(*next(iter, 1));
                if(get<Op>(*iter) == mult) {
                    auto pr = prev(iter, 1);
                    *prev(iter, 1) = left * right;
                    vec.erase(iter, next(iter, 2));
                    iter = pr;
                } else if(get<Op>(*iter) == div) {
                    auto pr = prev(iter, 1);
                    *prev(iter, 1) = left / right;
                    vec.erase(iter, next(iter, 2));
                    iter = pr;
                }
            } 
        }

        // 3 eval the rest
        for(auto iter = vec.begin(); iter != vec.end(); ++iter) {
            if(holds_alternative<Op>(*iter)) {
                auto left = get<int>(*prev(iter, 1));
                auto right = get<int>(*next(iter, 1));
                if(get<Op>(*iter) == plus) {
                    auto pr = prev(iter, 1);
                    *prev(iter, 1) = left + right;
                    vec.erase(iter, next(iter, 2));
                    iter = pr;
                } else if(get<Op>(*iter) == minus) {
                    auto pr = prev(iter, 1);
                    *prev(iter, 1) = left - right;
                    vec.erase(iter, next(iter, 2));
                    iter = pr;
                }
            } 
        }

        return get<int>(vec.front());
    }
};
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