<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:
    long long atoi(string num){
        if(num.length() == 0)return 0;
        long long val = 0, mul = 1;
        for(int i = num.length()-1; i >=0 ; i--){
            val += ((num[i]-'0')*mul);
            mul *= 10;
        }
        return val;
    }

    int calc(string s, int &pos){
        stack<long long> st;
        char sign = '?';
        while(pos < s.length() && s[pos] != ')'){

            string num = "";
            while(s[pos] == ' ')pos++;
            while(s[pos] <= '9' && s[pos] >= '0'){
                num += s[pos];
                pos++;
            }
            long long val = atoi(num);

            if(sign == '+' || sign == '?'){
                st.push(val);
            }else if(sign == '-'){
                st.push(-1*val);
            }
            else if(sign == '/'){
                long long tp = st.top();
                st.pop();
                st.push(tp/val); 
            }else if(sign == '*'){
                long long tp = st.top();
                st.pop();
                st.push(tp*val); 
            }else if(s[pos] == '('){
                pos++;
                st.push(calc(s,pos));
                pos++;
            }

            if(s[pos] > '9' || s[pos] < '0'){
                sign = s[pos];
            } 
            else{
                sign = '?';
            }
            pos++;
        }

        long long ans = 0;
        while(!st.empty()){
            ans += st.top();
            st.pop();
        }
        return ans;
    }

    int calculate(string s) {
        int ans = 0;
        for(int i = 0; i < s.length(); i++){
            ans += calc(s,i);
        }
        return ans;
    }
};
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