<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]:
        N = len(num)
        answers = []
        def recurse(index, prev_operand, current_operand, value, string):
            # Done processing all the digits in num
            if index == N:

                # If the final value == target expected AND
                # no operand is left unprocessed
                if value == target and current_operand == 0:
                    answers.append("".join(string[1:]))
                return
            
            # Extending the currrent operand by one digit
            current_operand = current_operand * 10 + int(num[index])
            str_op = str(current_operand)

            # NO OP
            if current_operand > 0:
                recurse(index + 1, prev_operand, current_operand, value, string)

            # ADDITION
            string.append('+'); string.append(str_op)
            recurse(index + 1, current_operand, 0, value + current_operand, string)
            string.pop(); string.pop()

            if string:
                # SUBTRACTION
                string.append('-'); string.append(str_op)
                recurse(index + 1, -current_operand, 0, value - current_operand, string)
                string.pop(); string.pop()

                # MULTIPLICATION
                string.append('*'); string.append(str_op)
                recurse(index + 1, current_operand * prev_operand, 0, value - prev_operand + (current_operand * prev_operand), string)
                string.pop(); string.pop()

        recurse(0, 0, 0, 0, [])
        return answers

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