<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:
    int64_t calculate(string s) {
        deque<char> operations_stack;
        deque<int64_t> numbers_stack;
        for (int64_t i = 0; i < s.size(); i++) {
            if (isdigit(s[i])) {
                int64_t n = 0;
                while(i < s.size() && isdigit(s[i])) {
                    n = n * 10 + s[i] - '0';
                    i++;
                }
                i--;
                numbers_stack.push_back(n);
                if (operations_stack.size()) {
                    // handle mul/div
                    char oper = operations_stack.back();
                    switch(oper) {
                        case '/': {
                            int64_t n2 = numbers_stack.back();
                            numbers_stack.pop_back();
                            int64_t n1 = numbers_stack.back();
                            numbers_stack.pop_back();
                            numbers_stack.push_back(n1 / n2);
                            operations_stack.pop_back();
                            break;
                        }
                        case '*': {
                            int64_t n2 = numbers_stack.back();
                            numbers_stack.pop_back();
                            int64_t n1 = numbers_stack.back();
                            numbers_stack.pop_back();
                            numbers_stack.push_back(n1 * n2);
                            operations_stack.pop_back();
                            break;
                        }
                    };
                }
            } else if (s[i] != ' ') {
                operations_stack.push_back(s[i]);
            }
        }
        
        while (numbers_stack.size() > 1) {
            char oper = operations_stack.front();
            switch(oper) {
                case '+': {
                    int64_t n1 = numbers_stack.front();
                    numbers_stack.pop_front();
                    int64_t n2 = numbers_stack.front();
                    numbers_stack.pop_front();
                    numbers_stack.push_front(n1 + n2);
                    operations_stack.pop_front();
                    break;
                }
                case '-': {
                    int64_t n1 = numbers_stack.front();
                    numbers_stack.pop_front();
                    int64_t n2 = numbers_stack.front();
                    numbers_stack.pop_front();
                    numbers_stack.push_front(n1 - n2);
                    operations_stack.pop_front();
                    break;
                }
            }
        }
        return numbers_stack.front();
    }
};
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