<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]:
        candidates = set()
        n = len(num)
        def calculate(candidate):
            n = len(candidate)
            left = 0
            stack = []
            while left < n:
                if candidate[left] in "+-*":
                    stack.append(candidate[left])
                else:
                    current = int(candidate[left])
                    while left + 1 < n and candidate[left + 1] not in "+-*":
                        current = current*10 + int(candidate[left + 1])
                        left += 1

                    stack.append(current)

                left += 1
            
            n = len(stack)
            holder = []
            for i in range(n):
                if holder and holder[-1] == "*":
                   holder.pop()
                   holder[-1]*= stack[i]
                else:
                    holder.append(stack[i])

            n = len(holder)
            ans = []
            for i in range(n):
                if ans and ans[-1] == "+":
                   ans.pop()
                   ans[-1]+= holder[i]
                elif ans and ans[-1] == "-":
                    ans.pop()
                    ans[-1] -= holder[i]
                else:
                    ans.append(holder[i])

            if ans[0] == target:
                return candidate

            return None


        def possibleCandidate(i, current):
            if i == n:
                candidates.add(current)
                return

            a = ""
            for j in range(i, n):
                a += num[j]
                if a != "0" and a[0] == "0":
                    break

                if i == 0:
                    possibleCandidate(j + 1, a)
                else:
                    possibleCandidate(j + 1, current + "+" + a) 
                    possibleCandidate(j + 1, current + "-" + a)
                    possibleCandidate(j + 1, current + "*" + a)
        

        possibleCandidate(0, -1)
        ans = []
        for candidate in candidates:
            processedCandidate = calculate(candidate)
            if processedCandidate != None:
                ans.append(processedCandidate)

        return ans
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