<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:
    struct Elem {
        enum Type {
            add = 0,
            sub = 1,
            mult = 2,
            div = 3,
            number = 5
        };
        Type type;
        int num =0;

        Elem(Type type) {
            this->type = type;
        }
        Elem(Type type, int num) {
            this->type = type;
            this->num = num;
        }
    };

    int calculate(string s) {
        int res = 0;
        stack<Elem> st;

        for (int ii =0; ii < s.size(); ++ii) {
            char ch = s.at(ii);

            if (ch == '+') {
                st.push(Elem(Elem::add));
            }
            if (ch == '-') {
                st.push(Elem(Elem::sub));
            }
            if (ch == '*') {
                st.push(Elem(Elem::mult));
            }
            if (ch == '/') {
                st.push(Elem(Elem::div));
            }

            int num = 0;
            if (ch >= '0' && ch <= '9') {
                while (ch >= '0' && ch <= '9') {
                    num = num*10 - '0' + ch;
                    ++ii;
                    if (ii == s.size()) break;
                    ch = s.at(ii);
                }
                --ii;
                res = ProcessStack(st, num);
                st.push(Elem(Elem::number, res));
            }
        }

        res = 0;
        while (!st.empty()) {
            Elem elem = st.top();
            st.pop();
            res += elem.num;
        }
        return res;
    }

    int ProcessStack(stack<Elem>& st, int start) {
        if (st.empty()) return start;

        Elem elem = st.top();
        if (elem.type == Elem::number) return start;

        if (elem.type == Elem::add) {
            st.pop();
        }
        if (elem.type == Elem::sub) {
            st.pop();
            start = -start;
        }
        if (elem.type == Elem::mult) {
            st.pop();

            Elem elem2 = st.top();
            st.pop();
            start = start * elem2.num;
            return ProcessStack(st, start);
        }
        if (elem.type == Elem::div) {
            st.pop();

            Elem elem2 = st.top();
            st.pop();
            start = elem2.num/start;
            return ProcessStack(st, start);
        }
        return start;
    }
};
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