<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) {
        vector<int> st;
        stack<char> ops;
        int num = 0;
        s.push_back('+');
        bool in_num = false;
        for (int i = 0; i < s.size(); ++i) {
            if (s[i] >= '0' && s[i] <= '9') {
                in_num = true;
                num = num*10 + (s[i]-'0');
            } else if (in_num) {
                // number finish
                in_num = false;
                if (ops.empty()) {
                    st.push_back(num);
                    num = 0;
                } else {
                    char op = ops.top();
                    ops.pop();
                    if (op == '-') {
                        st.push_back(-num);
                    } else if (op == '*') {
                        int a = st.back(); st.pop_back();
                        st.push_back(a * num);
                    } else if (op == '/') {
                        int a = st.back(); st.pop_back();
                        st.push_back(a / num);
                    } else {
                        st.push_back(num);
                    }
                }
                num = 0;
            }
            
            if (s[i]=='+' || s[i] == '-' || s[i] == '*' || s[i] == '/') {
                ops.push(s[i]);
            }
        }

        int ans = 0;
        return accumulate(st.begin(), st.end(), 0);
    }
};
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