<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]:
        totalSols = []
        def checkOps(cbuild, remstr):
            if len(remstr) == 0:
                totalSols.append(cbuild)
                return
            a = remstr[1:]
            if cbuild == "":
                checkOps(cbuild + remstr[0], a)
                return
            if cbuild[-1] == "0" and (len(cbuild) == 1 or not cbuild[-2].isdigit()):
                checkOps(cbuild + "+" + remstr[0], a)
                checkOps(cbuild + "-" + remstr[0], a)
                checkOps(cbuild + "*" + remstr[0], a)
                return
            checkOps(cbuild + remstr[0], a)
            checkOps(cbuild + "+" + remstr[0], a)
            checkOps(cbuild + "-" + remstr[0], a)
            checkOps(cbuild + "*" + remstr[0], a)
        checkOps("", num)

        sol = []
        for x in totalSols:
            if eval(x) == target:
                sol.append(x)
        return sol
        
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