<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 comp(seq):
            q = []
            pop = None
            for x in seq:
                if type(x) is int:
                    if pop == '-':
                        q.append(-x)
                    elif pop == '*':
                        q.append(q.pop(-1) * x)
                    else:
                        q.append(x)
                else:
                    pop = x
            return sum(q)

        res = []
        n = len(num)
        def split(start, path):
            if num[start] == '0' and start < n - 1:
                path.append(0)
                for op in '-+*':
                    path.append(op)
                    split(start + 1, path)
                    path.pop(-1)
                path.pop(-1)
                return   
            for end in range(start + 1, n):
                path.append(int(num[start:end]))
                for op in '-+*':
                    path.append(op)
                    split(end, path)
                    path.pop(-1)
                path.pop(-1)
            path.append(int(num[start:n]))
            if comp(path) == target:
                res.append(path[:])
            path.pop(-1)

        split(0, [])
        return [''.join([str(x) for x in seq]) for seq in res]

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