<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]:
        operator_sequences = [[]]
        for i in range(len(num) - 1):
            new_operator_sequences = []
            for sequence in operator_sequences:
                for operator in ["+", "-", "*", ""]:
                    new_operator_sequences.append([s for s in sequence] + [operator])
            operator_sequences = new_operator_sequences
        valid = []
        for sequence in operator_sequences:
            expression = [num[0]]
            cur_nums = [int(num[0])]
            last_operator = None
            skip = False
            for i, char in enumerate(num[1:]):
                expression.append(sequence[i])
                expression.append(char)
                if sequence[i] == "":
                    # print(cur_nums)
                    if cur_nums[-1] == 0:
                        skip = True
                        break
                        
                    cur_nums[-1] = cur_nums[-1] * 10 + int(char)
                else:
                    cur_nums.append(int(char))
            if skip:
                continue
            new_nums = [cur_nums[0]]
            j = 0
            for cur_num in cur_nums[1:]:
                while sequence[j] == "":
                    j += 1
                if sequence[j] == "*":
                    new_nums[-1] = new_nums[-1] * cur_num
                else:
                    new_nums.append(cur_num)
                j += 1

            # print(new_nums)
            cur_nums = new_nums
            # print(cur_nums)
            exp_value = cur_nums[0]
            j = 0
            for cur_num in cur_nums[1:]:
                while sequence[j] == "*" or sequence[j] == "":
                    j += 1
                if sequence[j] == "+":
                    exp_value += cur_num
                else:
                    exp_value -= cur_num
                j += 1
            # print(exp_value, "".join(expression))
            if exp_value == target:
                # print(cur_nums, j, exp_value, sequence)
                valid.append("".join(expression))
        
        return valid



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