<p>Given a string <code>num</code> that contains only digits and an integer <code>target</code>, return <em><strong>all possibilities</strong> to insert the binary operators </em><code>&#39;+&#39;</code><em>, </em><code>&#39;-&#39;</code><em>, and/or </em><code>&#39;*&#39;</code><em> between the digits of </em><code>num</code><em> so that the resultant expression evaluates to the </em><code>target</code><em> value</em>.</p>

<p>Note that operands in the returned expressions <strong>should not</strong> contain leading zeros.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;123&quot;, target = 6
<strong>Output:</strong> [&quot;1*2*3&quot;,&quot;1+2+3&quot;]
<strong>Explanation:</strong> Both &quot;1*2*3&quot; and &quot;1+2+3&quot; evaluate to 6.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;232&quot;, target = 8
<strong>Output:</strong> [&quot;2*3+2&quot;,&quot;2+3*2&quot;]
<strong>Explanation:</strong> Both &quot;2*3+2&quot; and &quot;2+3*2&quot; evaluate to 8.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;3456237490&quot;, target = 9191
<strong>Output:</strong> []
<strong>Explanation:</strong> There are no expressions that can be created from &quot;3456237490&quot; to evaluate to 9191.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= num.length &lt;= 10</code></li>
	<li><code>num</code> consists of only digits.</li>
	<li><code>-2<sup>31</sup> &lt;= target &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

class Solution:
    def addOperators(self, num: str, target: int) -> List[str]:
        if len(num) == 0: return None
        if len(num) == 1: return int(num) == target

        def compute_expression(s):
            stack = []
            curr_operator = "+"
            x = None

            for c in s:
                if c in "+-*":
                    if curr_operator == "+":
                        stack.append(x)
                    elif curr_operator == "*":
                        stack.append(x * stack.pop())
                    elif curr_operator == "-":
                        stack.append(-x)
                    x = None
                    curr_operator = c
                else:
                    if x == None: x = int(c)
                    elif x == 0: return None # not allow leading zeros
                    else: x = x * 10 + int(c)
            
            if curr_operator == "*": stack.append(x * stack.pop())
            elif curr_operator == "+": stack.append(x)
            elif curr_operator == "-": stack.append(-x)

            return sum(stack)

        results = []
        queue = deque()
        queue.append(num[0])
        for i in range(1, len(num)):
            len_queue = len(queue)
            for _ in range(len_queue):
                s = queue.popleft()
                queue.append( s+ "*" + num[i] )
                queue.append( s+ "+" + num[i] )
                queue.append( s+ "-" + num[i] )
                queue.append( s + num[i])
        
        while queue:
            s = queue.popleft()
            total = compute_expression(s)
            if total == target:
                print(s, total)
                results.append(s)
        
        return results
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