<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 {
    enum tokenType{
        num,
        op,
    };
    struct Token {
        long num;
        char op;
        tokenType t;
    };

public:
    int calculate(string str) {
        vector<Token> v;
        long currNum = 0;
        int fact = 1;

        for(auto x : str){
            if(x == ' ') continue;

            if(x >= '0' && x <= '9'){
                currNum = 10*currNum + x - '0';
                continue;
            }

            if( x == '+'){
                v.push_back(Token{ .num = fact * currNum, .t = tokenType::num });
                fact = 1;
                currNum = 0;
                continue;
            }
 
            if( x == '-'){
                v.push_back(Token{ .num = fact * currNum, .t = tokenType::num });
                fact = -1;
                currNum = 0;
                continue;
            }

            if( x == '*'){
                v.push_back(Token{ .num = fact * currNum, .t = tokenType::num });
                v.push_back(Token{ .op = '*', .t = tokenType::op });
                fact = 1;
                currNum = 0;
                continue;
            }
 
            if( x == '/'){
                v.push_back(Token{ .num = fact * currNum, .t = tokenType::num });
                v.push_back(Token{ .op = '/', .t = tokenType::op });
                fact = 1;
                currNum = 0;
                continue;
            }
        }
        v.push_back(Token{ .num = fact * currNum, .t = tokenType::num });
        

        stack<long> st;
        int i = 0;
        while(i < v.size()){
            auto & x = v[i];
            if(x.t == tokenType::num){
                st.push(x.num);
                ++i;
                continue;
            }

            if(x.op == '*'){
                auto val = st.top()*v[i+1].num;
                st.pop();
                st.push(val);
                i += 2;
                continue;
            }
  
            if(x.op == '/'){
                auto val = st.top()/v[i+1].num;
                st.pop();
                st.push(val);
                i += 2;
                continue;
            }
        }

        int ret = 0;
        while(!st.empty()){
            ret += st.top(); st.pop();
        }

        return ret;
    }
    
};
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