<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]:
        
        ans = []
        def backtrack(curr, prev_str, prev_val, last_val):
            if curr == len(num):
                if prev_val == target:
                    ans.append(prev_str)
            else:
                for j in range(curr + 1, len(num) + 1):
                    curr_str = num[curr: j]
                    if len(curr_str) > 1 and curr_str[0] == '0':
                        continue
                    
                    curr_val = int(curr_str)
                    if prev_str == "":
                        backtrack(j, curr_str, curr_val, curr_val)
                    else:
                        backtrack(j, prev_str + "+" + curr_str, prev_val + curr_val, curr_val)
                        backtrack(j, prev_str + "-" + curr_str, prev_val - curr_val, -curr_val)
                        backtrack(j, prev_str + '*' + curr_str, prev_val - last_val + last_val * curr_val, last_val * curr_val)
        
        backtrack(0, "", 0, 0)
        return ans
17100