<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>

struct Op {
    Op(int n, int o): num(n), op(o) {} 
    int num;
    int op;  // 0: num, 1: +, 2: -, 3: *, 4: /
};

class Solution {
public:
    int calculate(string s) {
        vector<Op> seq;
        
        for (char c : s) {
            if (c == '*') {
                seq.emplace_back(0, 3);
            } else if (c == '/') {
                seq.emplace_back(0, 4);
            } else if (c == '+') {
                seq.emplace_back(0, 1);
            } else if (c == '-') {
                seq.emplace_back(0, 2);
            } else if (c <= '9' && c >= '0') {
                if (seq.empty() || seq.back().op != 0) {
                    seq.emplace_back(c - '0', 0);
                } else {
                    seq.back().num = seq.back().num * 10 + (c - '0');
                }
            }
        }


        int lastop = 5;
        vector<Op> processed;
        for (const Op& op : seq) {
            if (op.op == 0) {
                if (lastop < 5) {
                   Op left = processed.back();
                   processed.pop_back();
                   if (lastop == 3) {
                      processed.emplace_back(left.num * op.num, 0);
                   } else {
                      processed.emplace_back(left.num / op.num, 0);
                   }
                   lastop = 5;
                } else {
                    processed.push_back(op);
                }
            } else if (op.op <= 2) {
                processed.push_back(op);
            } else {
                lastop = op.op;
            }
        }

        int num = 0;

        lastop = 1;
        for (int i = 0; i < processed.size(); ++i) {
            if (processed[i].op > 0) {
                lastop = processed[i].op;
            } else {
                if (lastop == 1) {
                    num += processed[i].num;
                } else {
                    num -= processed[i].num;
                }
            }
        }
        return num;
    }
};
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