<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:
    enum class token_type {
            NUM,
            OP
    };
    struct token {
        int num;
        char op;
        token_type type;

        token(int n) : num(n), op(0), type(token_type::NUM) {}
        token(char c) : num(0), op(c), type(token_type::OP) {}
    };

    int calculate(string s) {
        vector<token> tokens;
        string num;
        for(char c: s) {
            if (c == ' ') continue;
            if (isdigit(c)) num.push_back(c);
            else {
                if (!num.empty()) tokens.push_back(stoi(num));
                tokens.push_back(c);
                num.clear();
            }
        }
        if (!num.empty()) tokens.push_back(stoi(num));

        vector<int> nums;
        vector<char> ops;
        int i = 0;
        while(i < tokens.size()) {
            token t = tokens[i];
            if (t.type == token_type::NUM) nums.push_back(t.num);
            else if (t.op == '+' || t.op == '-') ops.push_back(t.op);
            else {
                int opnd1 = nums.back(); nums.pop_back();
                int opnd2 = tokens[i+1].num;
                if (t.op == '*') nums.push_back(opnd1 * opnd2);
                else nums.push_back(opnd1 / opnd2);
                i++;
            }
            i++;
        }
        int front = 0;
        for(char op: ops) {
            if (op == '+') nums[front+1] += nums[front];
            if (op == '-') nums[front+1] = nums[front] - nums[front+1];
            front++;
        }
        return nums[front];
    }
};
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