<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<string> t = toPostfix(s);
        stack<int> stk;

        for (const string x : t){
            if (x.empty()){
                break;
            }
            if (x[0] >= '0' && x[0] <= '9'){
                stk.emplace(toInt(x));
            }else{
                int a = stk.top();
                stk.pop();
                int b = stk.top();
                stk.pop();

                switch(x[0]){
                case '+':
                    stk.emplace(b + a);
                    break; 
                case '-':
                    stk.emplace(b - a);
                    break;
                case '*':
                    stk.emplace(b * a);
                    break; 
                case '/':
                    stk.emplace(b / a);
                    break; 
                }
            }
        }
        
        return stk.top();

    }
private:
    vector<string> toPostfix(string s){
        vector<string> t(s.size());
        int i = 0;
        stack<char> stk;
        map<char, int> priority = {{'+', 1}, {'-', 1},
                                   {'*', 2}, {'/', 2}};

        for (const char c : s){
            if (c >= '0' && c <= '9'){
                t[i] += c;
            }else if (c == '+' || c == '-' || c =='*' || c == '/'){
                i++;
                while(!stk.empty() && priority[stk.top()] >= priority[c]){
                    t[i++] = stk.top();
                    stk.pop();
                }
                stk.emplace(c);
            }
        }
        ++i;

        while(!stk.empty()){
            t[i++] = stk.top();
            stk.pop();
        }

        return t;
    }

    int toInt(string s){
        int x = 0;
        
        for (const char c : s){
            x = x * 10 - '0' + c;
        }

        return x;
    }
};
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