<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]:

        def evaluate(tokens):
            stack = []
            num = 0
            sign = '+'

            for i, token in enumerate(tokens):
                if token.isdigit():
                    num = int(token)
                if token in '+-*' or i == len(tokens) - 1:
                    if sign == '+':
                        stack.append(num)
                    elif sign == '-':
                        stack.append(-num)
                    elif sign == '*':
                        stack.append(stack.pop() * num)
                    sign = token
                    num = 0

            return sum(stack)

        @cache
        def findTarget(i):

            options = []
            for j in range(1, len(num) - i + 1):
                future_options = findTarget(i + j)
                if num[i] == '0' and j > 1:
                    break
                for option in future_options:
                    if option:
                        options.append([ num[i:i + j], "+"] + option)
                        options.append([ num[i:i + j], "-"] + option)
                        options.append([ num[i:i + j], "*"] + option)
                    else:
                        options.append([num[i:i + j]])

            if not options:
                return [[]]
            return options
        
        options = findTarget(0)
        return list(map(lambda x: ''.join(x), filter(lambda x:evaluate(x) == target, options)))
        
        
            

                        


            
      
        
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