<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:
    def calculate(self, s: str) -> int:
        s = s.replace(" ", "")
        x = y = 0
        calc_expr = {
            '+': lambda x, y: x + y,
            '-': lambda x, y: x - y,
            '*': lambda x, y: x * y,
            '/': lambda x, y: x // y,
        }
        queue = deque()
        start = end = 0
        for end in range(len(s)):
            if s[end] in ('+', '-', '*', '/'):
                queue.append(s[start:end])
                queue.append(s[end])
                start = end + 1
        queue.append(s[start:end+1])
        
        next_queue = deque()
        while queue:
            ch = queue.popleft()
            if ch in ('*', '/'):
                x = int(next_queue.pop())
                y = int(queue.popleft())
                val = calc_expr[ch](x, y)
                next_queue.append(str(val))
            else:
                next_queue.append(ch)

        while len(next_queue) > 1:
            x = int(next_queue.popleft())
            op = next_queue.popleft()
            y = int(next_queue.popleft())
            val = calc_expr[op](x, y)
            next_queue.appendleft(str(val))
            
        return int(next_queue[0])


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