<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>

import itertools
class Solution:
    def addOperators(self, num: str, target: int) -> List[str]:
        n = len(num)
        lst_signs = ["+", "-", "*", ""]
        lst_nums = [str(i) for i in range(10)]
        lst_combis = [p for p in itertools.product(lst_signs, repeat=n-1)]
        result = []
        for combi in lst_combis:
            expression = "".join([num[i]+combi[i] for i in range(n-1)] + [num[-1]])
            # Check leading zeros
            has_leading_zeros = False
            for i in range(len(expression)-1):
                if ((expression[i] == "0") and (expression[i+1] in lst_nums) and ((i==0) or (expression[i-1] not in lst_nums))):
                    has_leading_zeros = True
                    break
            if has_leading_zeros:
                continue
            # print(expression)
            if (eval(expression) == target):
                result.append(expression)
    
        return result





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